Soil Mechanics & Foundation Engineering : deep foundation

(i) Q_up = Q_eb + Q_sf

(ii) Q_up = q_bA_b + q_sA_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)

F₁ = 3 and F₂ = 2

(vii) For Pure Clays 

B. Dynamic Approach

Dynamic methods are suitable for dense cohesionless soil only.

(i) Engineering News Records 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

= 2.5 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, 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.

C. 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

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/cm²

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

 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, b_u = dia of bulb, Spacing = 1.5 b_u.

Negative Skin Friction

(i) For Cohesive sol

Q_nf = Perimeter. L₁αC for Cohesive soil.

where, Q_nf = Total negative skin frictions

 where, F_s = Factor of safety.

(ii) 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

(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_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_bA_b + q_sA_s

where q_b = 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

• Q_ug = η.Q_up
•  where, Q_ug = Allowable load on pile group.
• 

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 Uniform Clay

(iii) In case of Sand

 where, B = Size of pile group in meter.

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