# Ultimate Allowable Axial Compression Capacity of a Steel Pipe Pile in Stiff Clay ## Problem Restatement - **Pile**: Steel pipe, 12" diameter, 40 ft long - **Soil**: Stiff clay, \( c' = 150 \) psf (undrained shear strength) - **Unit weight of clay (\( \gamma \))**: 120 lb/ft³ - **Factor of safety**: 2.5 - **Required**: Ultimate allowable axial compression capacity in **kips** - **Assumptions**: - Cohesion is constant over pile length. - Pile is fully embedded; tip capacity is considered. - No groundwater table is considered. - Use the **α-method** (API, NAVFAC, or similar). --- ## Step 1: Compute Shaft (Skin) Resistance ### **α-Method for Clays** \[ Q_{s,\text{ult}} = \alpha \cdot c' \cdot P \cdot L \] Where: - \( \alpha \) = adhesion factor (typical for stiff clays: .7) - \( c' \) = undrained shear strength = 150 psf - \( P \) = perimeter of pile = \( \pi d \) - \( L \) = embedded length = 40 ft #### **Calculate Perimeter** \[ d = 12\,\text{in} = 1\,\text{ft} \] \[ P = \pi d = \pi \times 1\,\text{ft} = 3.14\,\text{ft} \] #### **Plug in Values** \[ Q_{s,\text{ult}} = .7 \times 150\,\text{psf} \times 3.14\,\text{ft} \times 40\,\text{ft} \] \[ Q_{s,\text{ult}} = .7 \times 150 \times 3.14 \times 40 \] \[ = .7 \times 150 = 105 \] \[ 105 \times 3.14 = 3297 \] \[ 3297 \times 40 = 131,880\,\text{lbs} \] --- ## Step 2: Compute End (Tip/Bearing) Resistance \[ Q_{b,\text{ult}} = N_c \cdot c' \cdot A \] Where: - \( N_c \) = bearing capacity factor for clay (typically 9) - \( c' \) = 150 psf - \( A \) = area of pile tip = \( \pi d^2 / 4 \) #### **Calculate Area** \[ A = \frac{\pi}{4} \times (1\,\text{ft})^2 = .785\,\text{ft}^2 \] #### **Plug in Values** \[ Q_{b,\text{ult}} = 9 \times 150\,\text{psf} \times .785\,\text{ft}^2 \] \[ = 13,500 \times .785 = 10,598\,\text{lbs} \] --- ## Step 3: Compute Total Ultimate Capacity \[ Q_{\text{ult}} = Q_{s,\text{ult}} + Q_{b,\text{ult}} \] \[ Q_{\text{ult}} = 131,880 + 10,598 = 142,478\,\text{lbs} \] --- ## Step 4: Apply Factor of Safety \[ Q_{\text{allowable}} = \frac{Q_{\text{ult}}}{\text{FS}} \] \[ Q_{\text{allowable}} = \frac{142,478}{2.5} = 56,991\,\text{lbs} \] Convert to **kips** (\( 1\,\text{kip} = 1,000\,\text{lbs} \)): \[ Q_{\text{allowable}} = \frac{56,991}{1,000} = \boxed{57\,\text{kips}} \] --- ## **Summary Table** | Capacity Type | Value (lbs) | Value (kips) | |---------------|-------------|--------------| | Shaft | 131,880 | 132 | | Tip | 10,598 | 10.6 | | **Ultimate** | 142,478 | 142 | | **Allowable** | 56,991 | 57 | --- ## **Assumptions and Procedure** - Used **α-method** for cohesive soils. - Adhesion factor \( \alpha = .7 \) for stiff clay. - \( N_c = 9 \) for tip resistance. - Cohesion and unit weight are constant over the pile length. - Neglected groundwater and negative skin friction. - Factor of safety applied to total capacity. --- ## **Final Allowable Axial Compression Capacity** \[ \boxed{57\ \text{kips}} \] for a 40 ft long, 12" diameter, steel pipe pile driven into stiff clay (\( c' = 150\,\text{psf} \)), using a factor of safety of 2.5.