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**Chapter 14 ****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)

(ii)

where,

Q_{up} = Ultimate load on pile

Q_{eb}= End bearing capacity

Q_{sf} = Skin friction

q_{b} = End bearing resistance of unit area.

q_{s} = Skin friction resistance of unit area

A_{b} = Bearing area

A_{s} = Surface area

(iii) q_{b} ~ 9C where, C = Unit Cohesion at the base of pile

(iv) where, a = Adhesion factor

a = Unit adhesion between pile and soil.

= Average Cohesion over depth of pile.

where, F_{s} = Factor of safety

(vi)

F_{1 }= 3 and F_{2} = 2

F_{1} = F_{2} = 2.5

(vii) For pure clays

**B. Dynamic Approach:**Dynamic methods are suitable for dense cohesionless soil only.**(i) Engineering News Formula**

(a)

(b)

where,

Q_{up} = Ultimate load on pile

Q_{ap} = 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

= 2.5cm for drop hammer

= 0.25 cm for steam hammer (single acting or double acting)**(c) For drop hammer**

-For single Acting Steam Hammer

Q_{ap=} WH/6(S+0.25)

-For Double Acting Steam Hammer

where P = Steam pressure and a = Area of hammer on which pressure acts.

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

where,

F_{s} = Factor of safety = 3

η_{h} = Efficiency of hammer

η_{b} = Efficiency of blow

η_{h} = 0.75 to 0.85 for single acting steam hammer

η_{h}= 0.75 to 0.80 for double acting steam hammer

η_{h}=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 penetration 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 penetration Data

where,N = Corrected S.P.T. Number

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

F_{s} = Factor of safety

=4 for driven pile

= 2.5 for for bored pile

-For non Displacement pile (H-piles)

qb = 200N q_{s} =

**UNDER-REAMED PILE**

An ‘under-reamed’ pile is one with an enlarged based 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,b_{u} = dia of bulb, Spacing = 1.5 b_{u}.

** Cone Penetration Test:**

where,

q_{c} = Static cone resistance of the base of pile in kg/cm^{2}.

= Average cone resistance over depth of pile in kg/cm^{2}.

A_{b}= π/4 .(b_{u})^{2}=Area of bulb (m^{2}).**NEGATIVE SKIN FRICTION:**

Negative skin friction is usually a downward shear drag acting on a pile or pile group because of downward movement of surrounding soil relative to the piles. This shear drag movements are anticipated to occur when a pile penetrates into compressible soil layer that can consolidate.

It is reported that, A small relative movement between the soil and the pile of around 10 mm may be adequate for the full negative skin friction to materialize.

(i) Negative skin friction of piles in cohesive soil

where,

F_{n}=negative skin friction

P= Perimeter of the pile

L_{c}=pile length in compressible soil

c_{a}=unit adhesion

Unit adhesion=

where,

α= adhesion factor

c_{u}=Undrain Cohesion of the compressible layer

(ii) For cohesion less soils

where,

k= lateral earth pressure coefficient

γ= Unit weight of soil

δ= Angle of friction between pile and soil

**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 Q_{up}) and (ii) Ultimate load carrying capacity of the single large equivalent (block) pile (Q_{ug}).

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

**(i) Group Efficiency (η _{g})**

Q

Q

For sandy soil - η

For clay soil - η

Minimum number of pile for group action = 3

Q_{ug} =q_{b}A_{b} +q_{s}A_{s}

where q_{b} =9C for clays

A_{b} =B^{2}

q_{s} =

A_{s} =4B.L

-**For square Group:**

Size of group,B = (n -1)S+D

where, n = Total number of pile If size of group is x.x

n =X^{2}

where, S_{r} = Group Settlement Ratio

S_{g} = Settlement of pile group

S_{i} = Settlement of individual pile.**(ii) When Piles are Embended on a Unifrom Clay**

(iii) In case of Sand

where, B = Size of pile group in meter.

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