Deep Foundations
Deep foundations (piles, drilled shafts, caissons) transfer structural loads past weak, highly compressible surface soils to deeper, much stronger geological layers or intact bedrock. They are utilized when shallow foundations are either unsafe or uneconomical.
Load Transfer Mechanism
A deep foundation supports loads through two distinct mechanisms acting simultaneously.
Ultimate Capacity Components
The total ultimate capacity of a pile () is the absolute sum of the resistance at its tip and the resistance along its sides:
Ultimate Pile Capacity
$$
Q_u = Q_p + Q_s
$$Pile Classifications by Load Transfer
- End-Bearing Piles: These transfer the majority of the structural load to a hard, unyielding stratum (like solid rock or very dense gravel) located at the pile tip. In these cases, . They act structurally somewhat like columns.
- Friction Piles: These are used when bedrock is too deep to reach economically. The load is transferred primarily through skin friction/adhesion along the surface area of the pile into the surrounding soil matrix (typically deep, stiff clay deposits). Here, .
Interactive Pile Capacity Lab
Experiment with the simulator below to understand how varying pile dimensions (length, diameter) and soil properties dramatically affect the ratio of skin friction to end bearing.
Single Pile Capacity Estimator
Total Capacity ()
0 kN
Skin Friction ()0 kN
Tip Resistance ()0 kN
Using Beta Method for skin friction and Nq method for tip resistance.
Blue arrows represent skin friction resistance () acting along the shaft. The red arrow represents point bearing resistance () acting at the tip.
Static Capacity Formulas
Calculating the theoretical capacity of a pile before it is driven is known as static analysis. The methods differ fundamentally based on whether the soil is granular (sand) or cohesive (clay).
Piles in Sand (Cohesionless Soils)
Sand relies on friction. Capacity increases with depth but eventually hits a limit.
- Point Bearing ():
Unit Point Bearing in Sand
$$
q_p = \sigma'_v N_q^* \le q_l
$$- Skin Friction ():
Unit Skin Friction in Sand
$$
f_s = K \sigma'_v \tan \delta
$$Piles in Clay (Cohesive Soils)
Clay relies on undrained shear strength (cohesion).
- Point Bearing ():
Unit Point Bearing in Clay
$$
q_p = c_u N_c^*
$$- Skin Friction () - The (Alpha) Method:
Alpha Method for Skin Friction
$$
f_s = \alpha c_u
$$Pile Groups
In modern construction, piles are almost never used individually. They are driven in groups and capped with a massive concrete block (the pile cap) to support columns.
Group Efficiency ()
The total capacity of a pile group () is rarely equal to the capacity of a single pile multiplied by the number of piles. Stress zones in the soil overlap.
Pile Group Capacity
$$
Q_{group} = \eta \cdot n \cdot Q_{single}
$$Converse-Labarre Formula (Empirical estimation for group efficiency):
Converse-Labarre Efficiency
$$
\eta = 1 - \frac{\theta}{90} \left[ \frac{(n-1)m + (m-1)n}{mn} \right]
$$Settlement of Pile Groups (Equivalent Footing Method)
To estimate the consolidation settlement of a group of friction piles in clay, engineers assume the pile group acts as a giant, deep shallow foundation.
- An Equivalent Footing is assumed to exist at a depth of (where is the pile embedment length).
- The load from the pile cap is assumed to spread out from this depth at a 2:1 (vertical:horizontal) slope down to the compressible clay layers below.
- Standard 1D consolidation formulas are then used to calculate the settlement of the clay layers located below the equivalent footing.
Negative Skin Friction (Downdrag)
A critical failure mechanism that occurs when the soil surrounding the pile settles more than the pile itself.
Important
Instead of the soil supporting the pile, the settling soil literally hangs onto the pile shaft and drags it downward. This occurs commonly when placing heavy new fill over a soft clay layer, or when the groundwater table is severely lowered.
Downdrag Effects
- Effect: It acts as an additional massive dead load pushing downward on the pile (), stealing valuable capacity away from the structural load.
- Design Adjustment: The allowable capacity must be adjusted: .
Dynamic Pile Driving Formulas
Unlike static analysis, dynamic formulas estimate pile capacity strictly during the driving process based on empirical observations of hammer energy and pile set per blow.
Engineering News Record (ENR) Formula
A historical empirical formula used extensively in older designs to calculate safe working load ().
ENR Dynamic Formula
$$
Q_{all} = \frac{W_h H}{FS (S + C)}
$$Drilled Shafts and Caissons
Large diameter cast-in-place deep foundations constructed by excavating a cylindrical hole and filling it with concrete and reinforcement.
Construction Methods
- Dry Method: Used in soils above the water table that will not cave in when excavated.
- Casing Method: A steel pipe is driven or vibrated into the ground to prevent soil collapse, then the shaft is excavated inside.
- Wet (Slurry) Method: Drilling fluid (bentonite or polymer slurry) is used to maintain hole stability in caving soils below the water table.
Bearing Capacity of Drilled Shafts
The ultimate capacity of a drilled shaft is similar to a pile (), but empirical adjustments are made because the construction process disturbs the soil differently than driving a pile.
Drilled Shaft Point Bearing (Clay)
$$
Q_{p} = A_p q_p = A_p (N_c^* c_u)
$$Drilled Shaft Skin Friction
$$
Q_{s} = \sum_{i=1}^{n} p \Delta L_i f_{si}
$$Drilled Shaft Capacity in Clay
Tip Resistance
Skin Friction
Total Ultimate Capacity
Key Takeaways
- Deep foundations safely transmit immense structural loads via a combination of End Bearing () and Skin Friction ().
- Static Formulas (like the -Method for clays) provide initial capacity estimates based on standard soil parameters.
- Pile Groups in cohesive soils (clays) are physically less efficient () than the sum of individual piles due to severe stress overlap. Their settlement is calculated using the Equivalent Footing Method at a depth of .
- Negative Skin Friction is a dangerous condition that occurs when settling soil "grabs" the pile and drags it down, actively reducing the pile's safe carrying capacity.
- Dynamic Formulas (e.g., the Hiley formula) and Wave Equation Analysis are routinely used during actual pile driving operations in the field to verify capacities empirically based on blow counts.