--- | ----- | ------- | ---------- | ---------- | | 2x2 | 4 | 3D | 0.86 | 1.0 | | 3x3 | 9 | 3D | 0.77 | 1.0 | | 4x4 | 16 | 3D | 0.70 | 1.0 | | 2x2 | 4 | 4D | 0.90 | 1.0 |

Minimum spacing: 2.5D center-to-center Preferred spacing: 3D for friction piles, 2.5D for end-bearing

## Pile Capacity Formulas

The ultimate axial capacity of a single pile is the sum of skin friction resistance and end bearing resistance:

Qult = Qskin + Qtip - Wpile

Where Qskin is the total shaft resistance, Qtip is the base (toe) resistance, and Wpile is the effective weight of the pile. In practice, Wpile is often neglected when it is small relative to Qult, or it is accounted for by using buoyant unit weights below the water table.

### Skin Friction (Shaft Resistance)

For a pile segment of length delta-L in contact with soil, the skin friction contribution is:

dQskin = fs × As = fs × perimeter × delta-L

The total skin friction is the integral over the pile embedment length:

Qskin = integral from 0 to L of [ fs(z) × perimeter(z) ] dz

In **cohesionless soils (sand)**, the unit skin friction is computed using the Beta (effective stress) method:

fs = K × sigma'_v × tan(delta)

Where K is the lateral earth pressure coefficient (ranging from 0.5 to 1.5 depending on pile type and installation method), sigma'\_v is the effective vertical stress at depth z, and delta is the pile-soil interface friction angle (typically 0.5 to 0.8 times the soil friction angle phi).

In **cohesive soils (clay)**, the unit skin friction is computed using the Alpha (total stress) method:

fs = alpha × cu

Where alpha is an adhesion factor (0.3 to 1.0) that decreases with increasing undrained shear strength cu. The API RP 2A recommends:

alpha = 0.5 × (cu / sigma'_v)^(-0.5) for cu/sigma'_v <= 1.0 alpha = 0.5 × (cu / sigma'_v)^(-0.25) for cu/sigma'_v > 1.0 alpha <= 1.0

### End Bearing (Toe Resistance)

The unit end bearing resistance is computed as:

**For cohesionless soils (sand):**

qp = Nq × sigma'_v

Where Nq is a bearing capacity factor that depends on the soil friction angle phi. Meyerhof (1976) recommends limiting qp to a maximum of:

qp(max) = 50 × Nq (in ksf) for dense sand, 25 × Nq for loose sand

**For cohesive soils (clay):**

qp = Nc × cu

Where Nc is typically taken as 9.0 for deep foundations (depth-to-diameter ratio greater than 4). For bored piles in clay, Nc may be reduced to account for base disturbance.

The total end bearing is then:

Qtip = qp × Ab

Where Ab is the cross-sectional area of the pile toe. For open-ended pipe piles, Ab is the cross-sectional area of the steel plug (if fully plugged) or the steel annulus (if unplugged).

### Allowable Pile Capacity

Qallow = Qult / FS

The factor of safety FS is typically:

| Condition                                    | Factor of Safety |
| -------------------------------------------- | ---------------- |
| Static analysis only, no load test           | 2.5 - 3.0        |
| Static analysis with proof load test         | 2.0              |
| Static analysis with performance load test   | 1.5 - 2.0        |
| Wave equation analysis with driving criteria | 2.0 - 2.5        |

## Driven Pile Types Reference

The following table summarizes the most common driven pile types used in building and bridge foundations, along with their typical axial capacity ranges and common applications.

| Pile Type                        | Typical Size Range       | Typical Capacity Range (tons) | Common Application                                             |
| -------------------------------- | ------------------------ | ----------------------------- | -------------------------------------------------------------- |
| Steel H-Pile (HP)                | HP8x36 to HP14x117       | 40 - 200                      | Bridge piers, heavy building columns, penetrating dense layers |
| Steel Pipe Pile (open-end)       | 10 in. to 48 in. OD      | 50 - 300                      | Marine structures, deep foundations, high-capacity loads       |
| Steel Pipe Pile (closed-end)     | 10 in. to 24 in. OD      | 30 - 150                      | Building foundations, parking structures                       |
| Precast Concrete (square)        | 10 in. to 24 in.         | 30 - 150                      | Buildings, industrial facilities                               |
| Precast Concrete (cylinder)      | 36 in. to 54 in. dia.    | 100 - 400                     | Bridge foundations, marine structures                          |
| Prestressed Concrete             | 10 in. to 24 in. square  | 40 - 200                      | Bridges, heavy industrial buildings                            |
| Timber Pile                      | 8 in. to 18 in. tip dia. | 15 - 40                       | Light structures, marine fenders, temporary works              |
| Composite (concrete-filled pipe) | 10 in. to 24 in. OD      | 50 - 200                      | Combined structural capacity, marine environments              |

Steel H-piles are preferred when hard driving is anticipated or when the pile must penetrate through dense soil layers to reach bearing strata. Their low displacement minimizes heave in clay soils. Pipe piles can be driven open-ended to reduce displacement and then inspected internally. Concrete piles offer high durability in corrosive environments but are heavier to handle and more susceptible to damage during driving.

## Worked Example: HP12x53 Driven Pile

**Problem:** Determine the ultimate axial capacity of an HP12x53 steel H-pile driven 40 ft into a mixed soil profile.

**Soil Profile:**

| Layer | Depth (ft) | Soil Type   | Properties                     |
| ----- | ---------- | ----------- | ------------------------------ |
| 1     | 0 - 15     | Medium clay | cu = 1200 psf, gamma = 115 pcf |
| 2     | 15 - 35    | Dense sand  | phi = 36 deg, gamma = 125 pcf  |
| 3     | 35 - 40    | Dense sand  | phi = 38 deg, gamma = 130 pcf  |

Water table is at 10 ft below grade.

**Step 1: Pile geometry**

HP12x53 cross-section:

- Area = 15.5 in^2
- Flange width = 12.0 in.
- Perimeter (for skin friction) = 4.09 ft (sum of all exposed surfaces)

**Step 2: Skin friction in Layer 1 (clay, 0-15 ft)**

Using the Alpha method:

Effective stress at mid-layer (z = 7.5 ft):

sigma'_v = 115 × 7.5 = 863 psf

Adhesion factor alpha (API method):

cu/sigma'_v = 1200/863 = 1.39 > 1.0 alpha = 0.5 × (1.39)^(-0.25) = 0.5 × 0.908 = 0.454

Unit skin friction:

fs = 0.454 × 1200 = 545 psf

Skin friction in Layer 1:

Qs1 = fs × perimeter × L1 = 545 × 4.09 × 15 = 33,437 lb = 33.4 kip

**Step 3: Skin friction in Layer 2 (sand, 15-35 ft)**

Using the Beta method with K = 1.0 and delta = 0.7 × 36 = 25.2 deg:

Effective stress at mid-layer (z = 25 ft):

sigma'_v = 115 × 10 + (115 - 62.4) × 5 + (125 - 62.4) × 10 = 1150 + 263 + 626 = 2039 psf

Unit skin friction:

fs = K × sigma'_v × tan(delta) = 1.0 × 2039 × tan(25.2) = 1.0 × 2039 × 0.471 = 960 psf

Skin friction in Layer 2:

Qs2 = 960 × 4.09 × 20 = 78,528 lb = 78.5 kip

**Step 4: Skin friction in Layer 3 (sand, 35-40 ft)**

Effective stress at mid-layer (z = 37.5 ft):

sigma'_v = 1150 + 263 + 626 × 2.0 + (130 - 62.4) × 2.5 = 1150 + 263 + 1252 + 169 = 2834 psf

Unit skin friction (K = 1.0, delta = 0.7 × 38 = 26.6 deg):

fs = 1.0 × 2834 × tan(26.6) = 2834 × 0.501 = 1420 psf

Skin friction in Layer 3:

Qs3 = 1420 × 4.09 × 5 = 29,039 lb = 29.0 kip

**Step 5: End bearing at pile toe (z = 40 ft)**

Effective stress at the toe:

sigma'_v(toe) = 1150 + 263 + 1252 + 169 × 2 = 1150 + 263 + 1252 + 338 = 3003 psf

Bearing capacity factor for phi = 38 deg: Nq = 60 (Meyerhof)

Unit end bearing:

qp = Nq × sigma'_v = 60 × 3003 = 180,180 psf = 180.2 ksf

Limiting qp to 50 × Nq = 50 × 60 = 3000 ksf — not exceeded.

End bearing:

Qtip = qp × Ab = 180.2 × (15.5/144) = 180.2 × 0.1076 = 19.4 kip

**Step 6: Total ultimate capacity**

Qult = Qs1 + Qs2 + Qs3 + Qtip = 33.4 + 78.5 + 29.0 + 19.4 = 160.3 kip (80.2 tons)

Allowable capacity with FS = 2.5:

Qallow = 160.3 / 2.5 = 64.1 kip (32.1 tons)

In this example, skin friction accounts for 87.9% of the total capacity (141 kip of 160 kip), which is typical for piles with significant embedment in granular soils.

## Pile Capacity by Type

The following table provides typical allowable axial capacity ranges for common pile types driven in competent soil conditions. Actual capacity depends on soil profile, pile dimensions, installation method, and local building code requirements.

| Pile Type         | Diameter/Size | Embedment (ft) | Allowable Capacity (tons) | Governing Soil Type               |
| ----------------- | ------------- | -------------- | ------------------------- | --------------------------------- |
| Steel H-Pile      | HP10x42       | 30 - 60        | 40 - 80                   | End bearing on rock or dense sand |
| Steel H-Pile      | HP12x53       | 40 - 80        | 60 - 150                  | Skin friction + end bearing       |
| Steel H-Pile      | HP14x117      | 50 - 100       | 100 - 200                 | Heavy loads, deep bearing         |
| Steel Pipe (open) | 12 in. OD     | 40 - 80        | 50 - 120                  | Sand and mixed profiles           |
| Steel Pipe (open) | 24 in. OD     | 50 - 100       | 100 - 300                 | High-capacity marine and bridge   |
| Precast Concrete  | 12 in. square | 30 - 60        | 30 - 80                   | Clay and sand profiles            |
| Precast Concrete  | 18 in. square | 40 - 80        | 60 - 150                  | Heavy building foundations        |
| Timber            | 10 in. tip    | 20 - 40        | 10 - 20                   | Soft clay, loose sand             |
| Timber            | 14 in. tip    | 25 - 50        | 15 - 40                   | Medium-dense sand                 |

Note: These ranges are for preliminary sizing only. Final design must be based on project-specific geotechnical investigation, static analysis, and preferably confirmed by pile load testing.

## Pile Driving Formulas

Pile driving formulas relate the hammer energy and pile set (penetration per blow) to the static capacity of the pile. They are empirical and should be used in conjunction with static analysis, not as a standalone method.

### Gates Formula (Modified)

The Gates formula (modified by FHWA) estimates the nominal pile capacity from driving data:

Rn = 1.7 × E × (1 - log10(S)) × 10^(-6)

Where:

- Rn = nominal pile resistance (kips)
- E = rated hammer energy (ft-lb)
- S = average permanent set per blow (inches)

This formula is applicable for piles driven with drop hammers, single-acting hammers, and double-acting hammers. It tends to be conservative and is best used for piles with capacities below 300 kips.

### Engineering News Record (ENR) Formula

The original ENR formula is:

Rn = (E × efficiency) / (S + C)

Where:

- E = rated hammer energy (ft-lb)
- efficiency = hammer efficiency (0.7-0.85 for single-acting, 0.5-0.7 for diesel)
- S = permanent set per blow (inches)
- C = empirical constant (0.1 in. for drop hammers, 0.0 for air/steam hammers)

The ENR formula is simple but tends to overestimate capacity for high-capacity piles and is generally considered less reliable than wave equation analysis. Many building codes have abandoned it in favor of the Gates formula or wave equation.

### Wave Equation Analysis

Wave equation analysis (using software such as GRLWEAP) models the pile as a one-dimensional wave propagation problem:

d^2u/dt^2 = (E_p / rho) × d^2u/dx^2

The analysis simulates the hammer impact and tracks the stress wave as it travels down the pile, accounting for:

- **Hammer characteristics**: rated energy, efficiency, ram weight, stroke, helmet mass
- **Driving system**: cushion stiffness, helmet weight, pile cap properties
- **Pile properties**: cross-section, length, material density and modulus
- **Soil resistance**: distribution of skin friction and end bearing along the pile, soil damping and quake values

Wave equation analysis produces a bearing graph relating the number of blows per inch (or foot) to the nominal pile capacity. It is the most rigorous dynamic analysis method and is widely specified in transportation projects. It also predicts driving stresses, which helps prevent pile damage during installation.

For critical projects, wave equation analysis is supplemented or replaced by dynamic pile monitoring using Pile Driving Analyzer (PDA) equipment, which measures strain and acceleration at the pile head during driving and back-calculates the static capacity using Case method or CAPWAP signal matching.

## Pile Group Efficiency

When piles are installed in a group, the individual pile capacities may not be simply additive due to overlapping stress zones in the soil. The group efficiency accounts for this interaction.

### Converse-Labarre Formula

The Converse-Labarre formula computes group efficiency for a rectangular pile group:

eta = 1 - theta × [(n - 1) × m + (m - 1) × n] / (90 × m × n)

Where:

- eta = group efficiency (0 to 1)
- theta = arctan(D/S) in degrees, where D = pile diameter, S = pile spacing
- m = number of rows
- n = number of piles per row

**Example:** A 3 × 4 pile group with 12-in. diameter piles at 3D spacing (S = 36 in.):

theta = arctan(12/36) = 18.4 deg eta = 1 - 18.4 × [(4-1)×3 + (3-1)×4] / (90 × 3 × 4) = 1 - 18.4 × [9 + 8] / 1080 = 1 - 312.8 / 1080 = 1 - 0.290 = 0.71

Group capacity = 0.71 × 12 × single pile capacity.

### Spacing Requirements

Minimum pile spacing is governed by constructability and group efficiency considerations:

| Soil Type           | Minimum Center-to-Center Spacing | Recommended Spacing  |
| ------------------- | -------------------------------- | -------------------- |
| Cohesionless (sand) | 2.5 × diameter or 30 in.         | 3.0 - 3.5 × diameter |
| Cohesive (clay)     | 3.0 × diameter                   | 3.0 - 4.0 × diameter |
| End-bearing on rock | 2.0 × diameter or 24 in.         | 2.5 - 3.0 × diameter |

For cohesionless soils, the group efficiency can equal or exceed 1.0 because pile driving densifies the soil between piles. The group capacity in sand is often taken as the lesser of: (a) the sum of individual pile capacities, or (b) the capacity of an equivalent block foundation (the soil block enclosed by the pile group plus the perimeter skin friction and end bearing of the block).

For cohesive soils, group efficiency is always less than 1.0 at typical spacings, and the designer must also check the block failure mode, where the entire soil block fails as a unit. Block capacity is calculated using the perimeter shear of the block plus end bearing over the full block area.

## Worked Example: Single Pile Axial Capacity

**Problem:** Calculate the allowable axial compressive capacity of a 12-inch diameter driven steel pipe pile (closed-end) in the following soil profile. Target factor of safety FS = 2.5.

**Given:**

- Pile: 12 in. dia. (1 ft), closed-end steel pipe, length = 40 ft
- Soil profile: 0-15 ft: Medium sand (gamma = 115 pcf, phi = 33 deg)
  15-40 ft: Dense sand (gamma = 125 pcf, phi = 38 deg)
- Water table at 10 ft depth
- Use Beta method for sand (cohesionless)

**Solution:**

Step 1 -- End bearing at pile tip (40 ft depth):

Effective stress at 40 ft: sigma_v' = 10115 + 5(115-62.4) + 25*(125-62.4) = 1150 + 263 + 1565 = 2,978 psf

Nq (phi = 38 deg) ≈ 60 (Berezantsev)

qp = Nq _ sigma_v' = 60 _ 2,978 / 1000 = 178.7 ksf Qp = qp _ Ap = 178.7 _ (pi _ 0.5^2) = 178.7 _ 0.785 = 140.3 kips

Step 2 -- Skin friction in upper layer (0-15 ft, medium sand):

Average effective stress: sigma_v'_avg = (0 + 10115 + 553.6) / 2 = (0 + 1150 + 268) / 2 = 709 psf

Beta = 0.35 (medium sand, driven pile per FHWA)

fslayer1 = Beta * sigmav'_avg = 0.35 * 709 = 248 psf Qs*layer1 = fs * As = 0.248 _ (pi _ 1.0 _ 15) = 0.248 * 47.1 = 11.7 kips

Step 3 -- Skin friction in lower layer (15-40 ft, dense sand):

sigma_v'_top = 10115 + 553.6 = 1418 psf sigma_v'_bot = 1418 + 25*62.6 = 1418 + 1565 = 2983 psf sigma_v'_avg = (1418 + 2983) / 2 = 2201 psf

Beta = 0.45 (dense sand, driven pile)

fslayer2 = 0.45 * 2201 = 990 psf Qslayer2 = 0.990 * (pi _ 1.0 _ 25) = 0.990 * 78.5 = 77.7 kips

Step 4 -- Total capacity:

Qult = Qp + Qs_layer1 + Qs_layer2 = 140.3 + 11.7 + 77.7 = 229.7 kips

Qallow = Qult / FS = 229.7 / 2.5 = 91.9 kips

**Result:** Allowable compressive capacity = 92 kips per pile (FS = 2.5). A pile load test would typically allow a reduced FS = 1.5-2.0, increasing allowable capacity to 115-153 kips.

## Frequently Asked Questions

**What is the difference between the Alpha and Beta methods?**
The Alpha method is used for cohesive (clay) soils and relates skin friction directly to the undrained shear strength cu through an adhesion factor alpha. The Beta method is used for cohesionless (sand) soils and relates skin friction to the effective overburden stress through a coefficient beta that depends on the soil friction angle and the pile-soil interface friction. In mixed profiles, different layers use different methods.

**Why does pile capacity require a factor of safety?**
Pile capacity calculations are based on empirical correlations with significant uncertainty. The actual soil conditions may vary from the assumed profile, installation effects (driving, drilling) alter the in-situ soil state, and the long-term capacity may differ from the short-term capacity due to setup or relaxation. Typical factors of safety are 2.0-3.0 for static analysis, which may be reduced to 1.5-2.0 if pile load tests are performed.

**What is group efficiency and when does it matter?**
When piles are closely spaced in a group, the stress zones of adjacent piles overlap, reducing the capacity per pile compared to an isolated pile. The group efficiency factor eta (typically 0.65-1.0) multiplies the sum of individual pile capacities to give the group capacity. For cohesionless soils, group efficiency may exceed 1.0 due to densification between piles. For cohesive soils, it is usually less than 1.0 and decreases as spacing decreases.

## Code References

- **IBC Section 1810** -- Deep foundation requirements including minimum pile spacing, group effects, and load testing provisions
- **ASCE 7-22 Section 18.3** -- Geotechnical investigation requirements for seismic design categories
- **AASHTO LRFD Section 10.7** -- Resistance factors for driven piles (0.45-0.70 depending on load test method) and static analysis methods per FHWA-NHI-16-009
- **ASTM D1143 / D1143M** -- Standard test methods for deep foundations under static axial compressive load (pile load test procedure)
- **ASTM D4945** -- Standard test method for high-strain dynamic testing of deep foundations (PDA testing)

## Related pages

- [Concrete footing calculator](/tools/concrete-footing/)
- [Retaining wall calculator](/tools/retaining-wall/)
- [Anchor bolts calculator](/tools/anchor-bolts/)
- [Baseplate anchors calculator](/tools/baseplate-anchors/)
- [Tools directory](/tools/)
- [How to verify calculator results](/guides/)
- [Disclaimer (educational use only)](/disclaimer/)
- [Concrete footing design](/reference/concrete-footing-design/)
- [Load combinations calculator](/tools/load-combinations/)
- [Unit converter](/tools/unit-converter/)

## Disclaimer (educational use only)

This page is provided for **general technical information and educational use only**. It does **not** constitute professional engineering advice, a design service, or a substitute for an independent review by a qualified structural engineer. Any calculations, outputs, examples, and workflows discussed here are simplified descriptions intended to support understanding and preliminary estimation.

All real-world structural design depends on project-specific factors (loads, combinations, stability, detailing, fabrication, erection, tolerances, site conditions, and the governing standard and project specification). **You are responsible** for verifying inputs, validating results with an independent method, checking constructability and code compliance, and obtaining professional sign-off where required.

The site operator provides the content **"as is" and "as available"** without warranties of any kind. To the maximum extent permitted by law, the operator disclaims liability for any loss or damage arising from the use of, or reliance on, this page or any linked tools.