Deep Foundation (Pile) Axial Capacity

Stratigraphic Pile Analysis (α/β Methods)

1. Pile Geometry & Installation
Installation Method	Bored / Drilled Shaft Driven (Displacement)
Cross-Section Shape	Circular Square
Diameter / Width (D)		mm
Total Pile Length (L)		m
Stick-up above ground		m

2. Environmental Factors
Depth to Water Table (Dw)		m
Factor of Safety (FS)		-

3. Soil Stratigraphy Top to Bottom

Depth Bottom (m)	Soil Type	γ (kN/m³)	cu (kPa)	φ' (°)

Ultimate Shaft Resistance

Total Skin Friction (Q_s) 0.0 kN

Ultimate Base Resistance

End Bearing (Q_b) 0.0 kN

Ultimate Capacity (Q_u) 0.0 kN $Q_u = Q_s + Q_b$

Allowable Capacity (Q_all) 0.0 kN $Q_{all} = Q_u / FS$

Soil Stratigraphy & Pile Profile To-scale representation

Cumulative Capacity Profile

Skin Friction (Q_s)

Total Capacity (Q_u)

Discretized Shaft Resistance Analysis

Layer	Depth Range (m)	Thickness (m)	Soil Type	Avg $\sigma'_v$ (kPa)	Method	Unit Friction $f_s$ (kPa)	Shaft $Q_s$ (kN)

Geotechnical Theory & Methodology

1. Discretized Integration Approach

The pile is broken down into small increments ($dz = 0.1m$). Effective vertical stress ($\sigma'_v$) is calculated continuously down the profile, accounting for soil unit weight and groundwater buoyancy. The ultimate capacity is the integral of skin friction plus end bearing: $Q_u = \int (f_s \cdot Perimeter) dz + q_b \cdot Area$.

2. Cohesive Soils (Clay) - $\alpha$ Method

Skin friction is based on the undrained shear strength ($c_u$). The adhesion factor ($\alpha$) dictates how much of $c_u$ transfers to the pile.

$$f_s = \alpha \cdot c_u$$

Standard API interpolation is used: $\alpha = 1.0$ for $c_u \le 25$ kPa, dropping linearly to $\alpha = 0.5$ for $c_u \ge 75$ kPa. End bearing: $q_b = 9 c_u$.

3. Cohesionless Soils (Sand) - $\beta$ Method

Skin friction is proportional to the effective overburden pressure via the coefficient $\beta = K \tan(\delta)$.

$$f_s = \beta \cdot \sigma'_v \quad ; \quad q_b = \sigma'_{v,tip} \cdot N_q$$

For driven piles, lateral earth pressure $K=1.0$. For bored piles, $K=0.7$. Interface friction $\delta = 0.8\phi'$. Bearing capacity factor $N_q$ is calculated via standard Meyerhof limits. Sand $f_s$ is capped at 100 kPa.

4. Mixed Soils (c-$\phi$)

Uses a combined approach summing both the cohesive ($\alpha$ method) and frictional ($\beta$ method) components for both skin friction and end bearing.

Typical Pile Dimensions (Reference)

Typical Diameter / Width (D) (mm)

Timber Piles	150 - 350
Precast Concrete (Driven)	250 - 600
Steel Pipe / H-Piles	200 - 1000
Bored / Drilled Shafts	600 - 3000+
Micropiles	100 - 300

Typical Length (L) (m)

Timber Piles	10 - 20
Precast Concrete (Driven)	10 - 30
Steel Pipe / H-Piles	15 - 40+
Bored / Drilled Shafts	10 - 60+
Micropiles	10 - 30

Typical Soil Parameters (Reference)

Unit Weight, γ (kN/m³)

Soft Clay	14 - 17
Stiff Clay	17 - 21
Loose Sand	15 - 18
Dense Sand	18 - 22

Clay Strength, c_u (kPa)

Very Soft	< 12
Soft	12 - 25
Medium	25 - 50
Stiff	50 - 100
Very Stiff	100 - 200
Hard	> 200

Sand Friction, φ' (°)

Very Loose	< 28°
Loose	28° - 30°
Medium	30° - 36°
Dense	36° - 41°
Very Dense	> 41°

References

• American Petroleum Institute (API). (2014). Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms—Working Stress Design (API RP 2A-WSD) (22nd ed.).
• Tomlinson, M. J., & Woodward, J. (2014). Pile Design and Construction Practice (6th ed.). CRC Press. Google Scholar
• Das, B. M. (2010). Principles of Foundation Engineering (7th ed.). Cengage Learning. Google Scholar

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CivilSheets by Sothearith Seak