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**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

**Analytical Method****(i)**Q_{up}= Q_{eb}+ Q_{sf}**(ii)**Q_{up}= q_{b}A_{b}+ q_{s}A_{s}

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}= Braking area

A_{s}= Surface area**(iii)**q_{b}∼ 9C

where, C = Unit Cohesion at base of pile for clays**(iv)**

where, α = Adhesion factor

Unit adhesion between pile and soil.

Average Cohesion over depth of pile.**(v)**

where, F_{s}= Factor of safety.**(vi)**

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

≈ F_{1 }= F_{2}= 2.5**(vii) For Pure Clays****Dynamic Approach**

Dynamic methods are suitable for dense cohesionless soil only.**(i) Engineering News Records Formula****(a)**Q_{up}= WH/S + C**(b)**Q_{ap }=_{ }Q_{up}/6 = WH/(S + C)

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

= 2.5 cm → for drop hammer

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

Q_{ap }= WH/6(S + 2.5)**(d)**For single Acting Stream Hammer

Q_{ap }= WH/6(S + 02.5)**(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, 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 penetrations per blow

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

H = Height of fall of hammer.**Field Method****(i)**Use of Standard Penetrations Data

where, N = Corrected S.P.T Number

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

Q_{ap}= Q_{up}/F_{s}

F_{s }= Factor of safety

= 4 → For driven pile

= 2.5 → for bored pile.**(ii)**Cone penetration test

where, q_{c}= static cone resistance of the base of pile in kg/cm^{2}

q_{c}= average cone resistance over depth of pile in kg/cm^{2}

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.

A_{s1 }= πbL_{1}q_{s}_{1} = αC α < 1.

A_{s2 }= πbuL_{2}q_{s2} = αC α < 1.

where, b_{u} = dia of bulb, Spacing = 1.5 b_{u}.

Q_{up} = q_{b}A_{b} + q_{s1}A_{s1 }+ Q_{s2}A_{s2}

**Negative Skin Friction**

**For Cohesive sol**

Q_{nf}= Perimeter. L_{1 }α C for Cohesive soil.

where, Q_{nf}= Total negative skin frictions

where, F_{s}= Factor of safety.**For cohesionless soils**

Q_{nf}= P x force per unit surface length of pile

(friction force = μH)

Where γ = unit weight of soil.

K = Earth pressure coefficient (K_{a}< K < K_{p})

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

- Ultimate load carrying capacity of n pile (n Q
_{up})

and - 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.**

**Group Efficiency (η**_{g})

n_{g}= Q_{ug}/n.Q_{up}

Q_{ug }= Ultimate load capacity of pile group

Q_{up }= Ultimate load on single pile

For sandy soil → η_{g}> 1

For clay soil → η_{g}< 1 and η_{g}> 1

Minimum number of pile for group = 3.

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

where q_{b}= 9C for clays**(i) 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 = x^{2}**(ii)**Q_{ug}= η.Q_{up}**(iii)**Q_{ug}= Q_{ug}/FOS where, Q_{ug}= Allowable load on pile group.**(iv)**S_{r}= S_{g}/S_{i}

where, S_{r}= Group settlement ratio

S_{g}= Settlement of pile group

S_{i}= Settlement of individual pile.**When Piles are Embended on a Uniform Clay****In case of Sand**

where, B = Size of pile group in meter.

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