Bearing Capacity of Pile Foundations: Universal Equations

In its most general form, a single pile’s load-carrying capacity (usually referred to as bearing capacity) can be divided in two sections according to the following formula:

Q_u = Q_p + Q_s  (1)

where:

Q_u is the ultimate load-carrying capacity

Q_p is the load-carrying capacity of the pile’s end point

Q_s is the skin-frictional resistance

 

Universal equation for Q_p and Q_s

 

Some first universal equations can be derived for the end point and skin frictional bearing capacities, while later on we are going to discuss some specific methods that can be used for their calculation.

Namely, the load-carrying capacity of the pile’s end point is defined as:

Q_p = A_p · q_p  (2)

where:

A_p is the area of the pile’s tip

q_p is the unit point resistance

 

The full equation for the unit point resistance q_p is very similar to Terzagi’s generalized equation for the bearing capacity of shallow foundations, and can be expressed as:

q_p = c’·N_c + q’·N_q + γ·D·N_γ  (3)

where:

c’ is the soil’s cohesion at the pile tip

q’ is the vertical effective stress at the tip of the pile

γ is the unit weight of the soil

N_c, N_q, N_γ are bearing capacity factors

D is the pile’s width

 

Since a pile’s width is relatively small, and especially when compared to that of shallow foundations, the last term of equation (3) can be ignored.

So, if we substitute equation (3) back to equation (2), we get that:

Q_p = A_p · q_p = A_p · (c’· N_c +q’·N_q)  (4)

 

As for the skin-frictional resistance, it can be defined as:

Q_s = Σ (p · ΔL · f)  (5)

where:

p is the perimeter of the pile’s section

f is the unit frictional resistance at any depth

ΔL is the incremental length of the pile where p and f are taken as constant

 

In addition to the aforementioned, after a pile’s ultimate bearing capacity has been calculated, it is possible to also determine its allowable load-bearing capacity, using a reasonable factor of safety by means of the following relationship:

Q_all = Q_u / FS  (6)

where:

Q_all is the single pile’s allowable load-carrying capacity

FS is the factor of safety

References:

Das, B.M. (2007). Principles of Foundation Engineering (7th Edition). Global Engineering

https://skyciv.com/docs/skyciv-foundation/piles/various-equations-for-estimating-pile-capacity/