Soil Mechanics & Foundation Engineering : Deep Foundations

By Vishal Singh|Updated : February 28th, 2022

Deep Foundation

Bearing capacity of piles

The ultimate bearing capacity of a pile is the maximum load which it can carry without failure or excessive settlement of the ground. The bearing capacity also depends on the methods of installation


A. Analytical Method

(i) Qup = Qeb + Qsf

(ii) Qup = qbAb + qsAs


Qup = Ultimate load on pile

Qeb = End bearing capacity

Qsf = Skin friction

qb = End bearing resistance of unit area.

qs = Skin friction resistance of unit area.

Ab = Braking area

As = Surface area


(iii) qb ∼ 9C

where, C = Unit Cohesion at base of pile for clays

(iv) image002 

where, α = Adhesion factor

image003 Unit adhesion between pile and soil.

image004 Average Cohesion over depth of pile.



where, Fs = Factor of safety.



F1 = 3 and F2 = 2


(vii) For Pure Clays image008

B. Dynamic Approach

Dynamic methods are suitable for dense cohesionless soil only.

(i) Engineering News Records Formula

(a) image009 

(b) image010


Qup = Ultimate load on pile

Qap = Allowable load on pile

W = Weight of hammer in kg.

H = Height of fall of hammer in cm.

S = Final set (Average penetration of pile per blow of hammer for last five blows in cm)

C = Constant

= 2.5 cm → for drop hammer

= 0.25 cm → for steam hammer (single acting or double acting)

(c) for drop hammer 


(d) For single Acting Stream Hammer


(e) For Double Acting Stream Hammer


where P = Stream pressure

and a = Area of hammer on which pressure acts.

(ii) Hiley Formula (I.S. Formula)


where, Fs = Factor of safety = 3

ηh = Efficiency of hammer

ηb = Efficiency of blow.

ηh = 0.75 to 0.85 for single acting steam hammer

ηh = 0.75 to 0.80 for double acting steam hammer

ηh = 1 for drop hammer.


where, w = Weight of hammer in kg.

p = Weight of pile + pile cap

e = Coefficient of restitutions

= 0.25 for wooden pile and cast iron hammer

= 0.4 for concrete pile and cast iron hammer

= 0.55 for steel piles and cast iron hammer

S = Final set or penetrations per blow

C = Total elastic compression of pile, pile cap and soil

H = Height of fall of hammer.

C. Field Method

(i) Use of Standard Penetrations Data 


where, N = Corrected S.P.T Number

image017 Average corrected S.P.T number for entire pile length


Fs = Factor of safety

= 4 → For driven pile

= 2.5 → for bored pile.


(ii) Cone penetration test


where, qc = static cone resistance of the base of pile in kg/cm2

qc = average cone resistance over depth of pile in kg/cm2

image021 Area of bulb (m)2

Under-Reamed Pile

An 'under-reamed' pile is one with an enlarged base or a bulb; the bulb is called 'under-ream'.

Under-reamed piles are cast-in-situ piles, which may be installed both in sandy and in clayey soils. The ratio of bulb size to the pile shaft size may be 2 to 3; usually a value of 2.5 is used.



where, bu = dia of bulb, Spacing = 1.5 bu.


Negative Skin Friction


(i) For Cohesive sol

Qnf = Perimeter. L1αC for Cohesive soil.

where, Qnf = Total negative skin frictions

image026 where, Fs = Factor of safety.

(ii) For cohesionless soils

Qnf = P x force per unit surface length of pile 



(friction force = μH)

Where γ = unit weight of soil.

K = Earth pressure coefficient (Ka < K < Kp)

δ = Angle of wall friction. (φ/2<δ<φ)

Group Action of Pile

The ultimate load carrying capacity of the pile group is finally chosen as the smaller of the

(i) Ultimate load carrying capacity of n pile (n Qup)

and (ii) Ultimate load carrying capacity of the single large equivalent (block) pile (Qug).

To determine design load or allowable load, apply a suitable factor of safety.


(i) Group Efficiency (ηg)


Qug = Ultimate load capacity of pile group

Qup = Ultimate load on single pile

For sandy soil → ηg > 1

For clay soil → ηg < 1 and ηg > 1

Minimum number of pile for group = 3.

Qug = qbAb + qsAs

where qb = 9C for clays


  • For Square Group

Size of group, B = (n – 1) S + D

where, η = Total number of pile if size of group is x.x

They η = x2

  • Qug = η.Qup
  • image032 where, Qug = Allowable load on pile group.
  • image033

where, Sr = Group settlement ratio

Sg = Settlement of pile group

Si = Settlement of individual pile.


(ii) When Piles are Embended on a Uniform Clay



(iii) In case of Sand

image037 where, B = Size of pile group in meter.

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