Deep Foundations

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 ( $Q_u$ ) is the absolute sum of the resistance at its tip and the resistance along its sides:

Ultimate Pile Capacity

Total resistance of a pile, combining end bearing at the tip and skin friction distributed along the shaft.

Q_u = Q_p + Q_s

Variables

Symbol	Description	Unit
$Q_{u}$	Total ultimate capacity of the pile	-
$Q_{p}$	Point bearing (end bearing) resistance	-
$Q_{s}$	Skin friction (shaft) resistance	-

$Q_p = A_p \cdot q_p$ (Area of tip $\times$ unit point resistance)
$Q_s = \sum A_s \cdot f_s$ (Surface area $\times$ unit skin friction)

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, $Q_p \gg Q_s$ . 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, $Q_s \gg Q_p$ .

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

Pile Length, L (m): 10

Pile Diameter, D (m): 0.5

Friction Angle,

\\phi

(deg): 30

Total Capacity (

Q_u

)

0 kN

Skin Friction (

Q_s

)0 kN

Tip Resistance (

Q_p

)0 kN

Using Beta Method for skin friction and Nq method for tip resistance.

Blue arrows represent skin friction resistance ( $Q_s$ ) acting along the shaft. The red arrow represents point bearing resistance ( $Q_p$ ) 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 ( $q_p$ ):

Unit Point Bearing in Sand

Unit tip resistance of a pile in sand based on overburden effective stress and a bearing capacity factor; limited to a maximum value.

q_p = \sigma'_v N_q^* \le q_l

Variables

Symbol	Description	Unit
$q_{p}$	Unit point resistance	-
$\sigma'_v$	Effective vertical stress at the pile tip	-
$N_{q}^{*}$	Deep bearing capacity factor	-
$q_{l}$	Limiting point resistance (\approx 50 N_q^* \tan \phi)	-

Skin Friction ( $f_s$ ):

Unit Skin Friction in Sand

Unit shaft friction per unit area in sand based on the pile-soil interface friction and horizontal effective stress.

f_s = K \sigma'_v \tan \delta

Variables

Symbol	Description	Unit
$f_{s}$	Unit skin friction	-
$K$	Earth pressure coefficient	-
$\sigma'_v$	Effective vertical stress at depth z	-
$\delta$	Pile-soil interface friction angle	-

$K$ ranges from $1 - \sin \phi$ for bored piles to $> K_0$ for driven piles.
$\delta$ is usually $0.5\phi$ to $0.8\phi$ depending on pile material.

Piles in Clay (Cohesive Soils)

Clay relies on undrained shear strength (cohesion).

Point Bearing ( $q_p$ ):

Unit Point Bearing in Clay

Unit tip resistance of a pile in clay based on undrained cohesion and a bearing capacity factor; applicable to short-term undrained conditions.

q_p = c_u N_c^*

Variables

Symbol	Description	Unit
$q_{p}$	Unit point resistance	-
$c_{u}$	Undrained cohesion at the pile tip	-
$N_{c}^{*}$	Bearing capacity factor (typically 9.0 for L/D > 4)	-

Skin Friction ( $f_s$ ) - The $\alpha$ (Alpha) Method:

Alpha Method for Skin Friction

Unit skin friction along a pile shaft in cohesive soils; based on an empirical adhesion factor applied to the undrained cohesion.

f_s = \alpha c_u

Variables

Symbol	Description	Unit
$f_{s}$	Unit skin friction (adhesion)	-
$\alpha$	Empirical adhesion factor	-
$c_{u}$	Undrained cohesion along the shaft	-

For very soft clays, $\alpha \approx 1.0$ .
For stiff clays, $\alpha$ can be $\le 0.5$ due to remolding during driving.

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 ( $\eta$ )

The total capacity of a pile group ( $Q_{group}$ ) 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

Total load capacity of a pile group accounting for efficiency losses due to overlapping stress zones in the surrounding soil.

Q_{group} = \eta \cdot n \cdot Q_{single}

Variables

Symbol	Description	Unit
$Q_{group}$	Total capacity of the pile group	-
$\eta$	Group efficiency factor	-
$n$	Total number of piles in the group	-
$Q_{single}$	Capacity of a single pile	-

Friction Piles in Clay: $\eta < 1.0$ due to overlapping stress zones.
End-Bearing Piles in Sand: $\eta \ge 1.0$ due to densification during driving.

Converse-Labarre Formula (Empirical estimation for group efficiency):

Converse-Labarre Efficiency

Empirical formula to estimate the efficiency factor of a pile group based on pile spacing, diameter, and the number of rows and columns.

\eta = 1 - \frac{\theta}{90} \left[ \frac{(n-1)m + (m-1)n}{mn} \right]

Variables

Symbol	Description	Unit
$\eta$	Group efficiency	-
$\theta$	\arctan(D/s) in degrees	-
$m$	Number of rows in the group	-
$n$	Number of columns in the group	-
$D$	Pile diameter	-
$s$	Center-to-center spacing between piles	-

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 $2/3 L$ (where $L$ 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 ( $Q_{neg}$ ), stealing valuable capacity away from the structural load.
Design Adjustment: The allowable capacity must be adjusted: $Q_{all} = \frac{Q_u - Q_{neg}}{FS}$ .

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 ( $Q_{all}$ ).

ENR Dynamic Formula

Historical empirical formula for estimating pile capacity from driving data; based on the energy delivered by the hammer per blow.

Q_{all} = \frac{W_h H}{FS (S + C)}

Variables

Symbol	Description	Unit
$Q_{all}$	Allowable pile capacity	-
$W_{h}$	Weight of the hammer	-
$H$	Height of hammer drop	-
$S$	Set (penetration) of pile per blow	-
$C$	Empirical constant based on hammer type	-
$F S$	Factor of safety (traditionally 6.0)	-

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 ( $Q_u = Q_p + Q_s$ ), but empirical adjustments are made because the construction process disturbs the soil differently than driving a pile.

Drilled Shaft Point Bearing (Clay)

Tip resistance of a drilled shaft in cohesive soil based on undrained shear strength and a bearing capacity factor.

Q_{p} = A_p q_p = A_p (N_c^* c_u)

Variables

Symbol	Description	Unit
$Q_{p}$	Total point bearing capacity	-
$A_{p}$	Area of the shaft base	-
$q_{p}$	Unit point resistance	-
$N_{c}^{*}$	Bearing capacity factor	-
$c_{u}$	Undrained cohesion at the base	-

Drilled Shaft Skin Friction

Total shaft friction of a drilled shaft summed over all soil layers encountered along the shaft length.

Q_{s} = \sum_{i=1}^{n} p \Delta L_i f_{si}

Variables

Symbol	Description	Unit
$Q_{s}$	Total skin friction capacity	-
$p$	Perimeter of the shaft cross-section	-
$\Delta L_i$	Length of soil layer i	-
$f_{si}$	Unit skin friction in layer i	-

Drilled Shaft Capacity in Clay

Shaft Diameter (

D

)1.5 m

Shaft Length (

L

)15.0 m

Undrained Cohesion (

c_u

)100 kPa

Adhesion Factor (

\\alpha

)0.55

Tip Resistance

Q_p = A_p \cdot c_u \cdot N_c = 1590 \text{ kN}

Skin Friction

Q_s = p \cdot L \cdot \alpha \cdot c_u = 3888 \text{ kN}

Total Ultimate Capacity

Q_u = Q_p + Q_s = 5478 \text{ kN}

Key Takeaways

Deep foundations safely transmit immense structural loads via a combination of End Bearing ( $Q_p$ ) and Skin Friction ( $Q_s$ ).
Static Formulas (like the $\alpha$ -Method for clays) provide initial capacity estimates based on standard soil parameters.
Pile Groups in cohesive soils (clays) are physically less efficient ( $\eta < 1.0$ ) than the sum of individual piles due to severe stress overlap. Their settlement is calculated using the Equivalent Footing Method at a depth of $2/3 L$ .
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.

PreviousDesign of Shallow Foundations - Examples & Applications

NextDeep Foundations - Examples & Applications

Load Transfer Mechanism

Ultimate Capacity Components

Ultimate Pile Capacity

Pile Classifications by Load Transfer

Interactive Pile Capacity Lab

Single Pile Capacity Estimator

Static Capacity Formulas

Piles in Sand (Cohesionless Soils)

Unit Point Bearing in Sand

Unit Skin Friction in Sand

Piles in Clay (Cohesive Soils)

Unit Point Bearing in Clay

Alpha Method for Skin Friction

Pile Groups

Group Efficiency (η\etaη)

Pile Group Capacity

Converse-Labarre Efficiency

Settlement of Pile Groups (Equivalent Footing Method)

Negative Skin Friction (Downdrag)

Important

Downdrag Effects

Dynamic Pile Driving Formulas

Engineering News Record (ENR) Formula

ENR Dynamic Formula

Drilled Shafts and Caissons

Construction Methods

Bearing Capacity of Drilled Shafts

Drilled Shaft Point Bearing (Clay)

Drilled Shaft Skin Friction

Drilled Shaft Capacity in Clay

Tip Resistance

Skin Friction

Total Ultimate Capacity

Group Efficiency ( $\eta$ )