### Ultimate vertical load capacity of pile or pier

Ultimate vertical load capacity of pile or pier

Qult = Qb+ Qs – Wp =9c_{u}A_{p}+α c_{u} 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
- α= adhesion factor
- p=perimeter
- L=Length

Load capacity at pile or pier base

Q_{b}= A_{b}(cNc + σ_{t}‘ Nq _ 0.5 Bγb’ N_{γ} )

- Where A
_{b}= Area of pile or pier base - c= Soil cohesion
- σ
_{t}‘=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= ∑ σ_{t}‘ K_{hc} tanδPL

- Where, σ
_{t}‘= Effective overburden pressure - K
_{hc}= 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 σ_{t}‘ Nq +∑ σ_{t}‘ K_{hc} tanδPL, Where, c=0, N_{γ} =0

Carrying Capacity of a Single Pile or Pier in Cohesive Soil

Qb-ult= A_{b}c N_{c} Where, c=.5q_{u}, N_{q} =0 and δ=0

Skin Friction factor for Driven Piles

Qs-ult =∑ α c_{u} 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

δ_{e}= PL /AE

- Where, δ
_{e}= 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= δ_{e} +(0.15+D/120) (where, Sf= Displacement at failure in inches, δ_{e}= Elastic compression, D= Pile diameter in inches)

### PILE CAPACITY FROM DRIVING DATA

Danish Formula

Q_{dy} = αW_{H}H/(S+0.5Se), Se=√(2αW_{H}HL/AE)

- Q
_{dy}= Ultimate dynamic bearing capacity of driven pile - α=Pile driving hammer efficiency (normally 1)
- WH= Weight of hammer
- H= Hammer drop (note that W
_{H}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