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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

1. Analytical Method
   (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
   ≈ F₁ = F₂ = 2.5
   (vii) For Pure Clays 
2. 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.
3. 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/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.

A_s1 = πbL₁q_s1 = αC α < 1.
A_s2 = πbuL₂q_s2 = αC α < 1.
where, b_u = dia of bulb, Spacing = 1.5 b_u.
Q_up = q_bA_b + q_s1A_s1 + Q_s2A_s2

Negative Skin Friction

1. For Cohesive sol
   Q_nf = Perimeter. L₁ α C for Cohesive soil.
   where, Q_nf = Total negative skin frictions
   
   where, F_s = Factor of safety.
2. 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

1. Ultimate load carrying capacity of n pile (n Q_up)
   and
2. 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.

1. 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_bA_b + q_sA_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 = x²
   (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.
2. When Piles are Embended on a Uniform Clay
   
3. In case of Sand
   
   where, B = Size of pile group in meter.