Deep Foundations (Piles)

The ultimate load capacity ($Q_u$) of a single pile is derived from two distinct components of resistance mobilized as the pile settles under load.

End bearing requires significant downward movement (typically 10% of the pile diameter) to fully mobilize, whereas skin friction mobilizes very quickly, often with only 5-10 mm of settlement.

Typically, soil provides upward skin friction to support the pile. However, if the soil surrounding the pile settles more than the pile itself (e.g., due to a recent fill placed over compressible clay, or lowering of the groundwater table causing consolidation), the soil grips the pile and drags it downward. This creates a massive additional downward load on the pile, severely reducing its effective carrying capacity and potentially inducing structural failure or excessive settlement.

Engineers estimate the static capacity before driving the pile using soil properties from borings.

• For sands (the $\beta$ method): $f_s = K \cdot \sigma_v' \cdot \tan \delta$, where $K$ is the lateral earth pressure coefficient, $\sigma_v'$ is vertical effective stress, and $\delta$ is the soil-pile friction angle.
• For clays (the $\alpha$ method): $f_s = \alpha \cdot s_u$, where $\alpha$ is an empirical adhesion factor and $s_u$ is the undrained shear strength.

Piles subjected to uplift (tension) forces, such as those under transmission towers or tall chimneys resisting wind loads, rely entirely on skin friction ($Q_s$) and their own self-weight. End bearing provides zero resistance. The allowable uplift capacity is typically calculated using the static skin friction equations but often with a higher factor of safety, as skin friction in tension is generally slightly less than in compression due to Poisson's effect (the pile diameter slightly decreases under tension, reducing lateral stress).

The total elastic settlement of a single pile under a working load $Q_w$ is the sum of three components: $S_t = S_1 + S_2 + S_3$.

• $S_1$ (Elastic Compression of Pile): The physical shortening of the pile material itself. Calculated as $S_1 = \frac{(Q_{wp} + \xi Q_{ws}) L}{A_p E_p}$, where $Q_{wp}$ is load carried at the point, $Q_{ws}$ is load carried by friction, $A_p$ is cross-sectional area, $E_p$ is modulus of the pile, and $\xi$ is a distribution factor (often 0.5 to 0.67).
• $S_2$ (Settlement of Pile Point): Due to load transmitted at the pile tip. Calculated using Boussinesq or similar elastic solutions.
• $S_3$ (Settlement from Shaft Friction): Due to load transmitted along the pile shaft, pulling the surrounding soil down elastically.

Piles must often resist lateral loads (wind, earthquakes, waves). The analysis is complex due to soil-structure interaction.

• Broms' Method: A simplified, widely used method assuming rigid-plastic soil behavior. It distinguishes between "short" piles (which fail by rigid rotation) and "long" piles (which fail by forming a plastic hinge in the pile material). Solutions are provided in chart form for both cohesive and cohesionless soils.
• p-y Curve Method: A more advanced, non-linear analysis. The pile is modeled as a beam on elastic foundations, where the soil is represented by a series of non-linear springs. The "p-y" curves define the relationship between soil resistance ($p$) and pile deflection ($y$) at various depths. This requires specialized software (like LPILE) and is standard for major structures.

Empirical formulas estimate the ultimate capacity of driven piles based on the energy delivered by the pile hammer and the measured penetration per blow ("set") during driving. While widely used for quality control, they are less reliable than static analysis or load testing.

Modern dynamic capacity evaluation relies on Pile Driving Analysis (PDA). Strain gauges and accelerometers are bolted near the pile head to measure strain and acceleration during hammer impacts. By applying the wave equation (CAPWAP analysis - Case Pile Wave Analysis Program) to this data, engineers can accurately separate and quantify skin friction, end bearing, driving stresses, and pile integrity in real-time. This is far more reliable than empirical formulas like the ENR equation.

Piles are almost always driven in clusters or groups, tied together at the top by a rigid reinforced concrete pile cap. The capacity of a pile group ($Q_{group}$) is not necessarily the sum of the individual capacities of its constituent piles ($n \cdot Q_{single}$). The overlapping stress zones from adjacent piles can reduce the overall capacity, particularly in friction piles in clay.

The design structural capacity of the pile must be adequate to safely carry both the applied structural loads and the down-drag load. Furthermore, the total geotechnical resistance (positive skin friction below the neutral plane + end bearing) must exceed the structural load plus $Q_n$.

Estimating the settlement of a friction pile group in clay involves replacing the entire pile group with an imaginary "equivalent shallow footing." This equivalent footing has dimensions ($B_g \times L_g$) equal to the overall plan dimensions of the pile group.

• The equivalent footing is assumed to be located at a depth of $2/3$ the pile length ($2L/3$) measured from the top of the piles.
• The total load of the pile group is assumed to be applied uniformly over this equivalent area.
• The stress increase ($\Delta \sigma_z$) in the underlying clay layers is calculated using the 2:1 method starting from this $2L/3$ depth.
• Standard primary consolidation settlement calculations are then performed for the compressible clay strata below this imaginary footing.