### Ultimate vertical load capacity of pile or pier

Ultimate vertical load capacity of pile or pier

Qult = Qb+ Qs – Wp =9cuAp+α cu p L

• Qult= Ultimate vertical load capacity of pile or pier
• Qb= Component of load capacity due to bearing capacity at pile or pier base
• Qs= Component of load capacity due to side friction
• p=perimeter
• L=Length

Load capacity at pile or pier base

Qb= Ab(cNc + σt‘ Nq _ 0.5 Bγb’ Nγ )

• Where Ab= Area of pile or pier base
• c= Soil cohesion
• σt‘=Effective vertical stress at pile or pier base
• B=Base diameter
• γb’=Effective unit weight of soil in the failure zone beneath base
• Nc, Nq, Nγ = Bearing capacity factors.

The load capacity due to skin friction on the shaft of the pile

Qs= ∑ σt‘ Khc tanδPL

• Where, σt‘= Effective overburden pressure
• Khc = Ratio of horizontal to vertical pressure–pile in compression
• δ = friction angle between pile and soil
• P= Perimeter or circumference of pile, For circular pile, P=∏D
• L= length of the pile.

Carrying Capacity of a Single Pile or Pier in Granular Soil

Qult= Ab σt‘ Nq +∑ σt‘ Khc tanδPL, Where, c=0, Nγ =0

Carrying Capacity of a Single Pile or Pier in Cohesive Soil

Qb-ult= Abc Nc Where, c=.5qu, Nq =0 and δ=0

Skin Friction factor for Driven Piles

Qs-ult =∑ α cu PL

### Settlement of Pile Groups

Granular Soil

Sg= Si√(B / D )

• where Sg= Settlement of pile group
• Si =Settlement of a single pile estimated or determined from load tests
• B= Smallest dimension of pile group
• D= Diameter of individual pile.

Displacement

δe= PL /AE

• Where, δe = Elastic compression
• P= Axial load on pile
• L = Pile length (for end-bearing pile)
• A= Cross-sectional area of pile material
• E = Modulus of elasticity of pile material

Displacement

Sf= δe +(0.15+D/120) (where, Sf= Displacement at failure in inches, δe= Elastic compression, D= Pile diameter in inches)

### PILE CAPACITY FROM DRIVING DATA

Danish Formula

Qdy = αWHH/(S+0.5Se), Se=√(2αWHHL/AE)

• Qdy= Ultimate dynamic bearing capacity of driven pile
• α=Pile driving hammer efficiency (normally 1)
• WH= Weight of hammer
• H= Hammer drop (note that WH H= Hammer energy)
• S= Inelastic set of pile, in distance per hammer blow
• Se= Elastic set of pile, in distance per hammer blow
• L = Pile length
• A= Pile end area
• E= Modulus of elasticity of pile material