Soil Mechanics & Foundation Engg.: Foundation

Shallow Foundation & Bearing Capacity

Bearing Capacity

 It is the load carrying capacity of the soil.

• Ultimate bearing capacity or Gross bearing capacity (q_u)

It is the least gross pressure which will cause shear failure of the supporting soil immediately below the footing.

• Net ultimate bearing capacity (q_un ):

It is the net pressure that can be applied to the footing by external loads that will just initiate failure in the underlying soil. It is equal to ultimate bearing capacity minus the stress due to the weight of the footing and any soil or surcharge directly above it. Assuming the density of the footing (concrete) and soil ( γ) are close enough to be considered equal, then

Where, D_f is the depth of footing 

• Safe bearing capacity:

It is the bearing capacity after applying the factor of safety (FS). These are of two types,

Safe net bearing capacity (q_ns):

It is the net soil pressure which can be safety applied to the soil considering only shear failure. It is given by,

Safe gross bearing capacity (q_s ):

It is the maximum gross pressure which the soil can carry safely without shear failure. It is given by,

Allowable Bearing Pressure:

It is the maximum soil pressure without any shear failure or settlement failure

where, q_s = Safe bearing capacity.

Method to determine bearing capacity

(i) Rankines Method (∅ - soil)

 or 

(ii) Bells Theory (C - ∅)

where, N_c and N_q are bearing capacity factors.

For pure clays → C = 4, q = 1

(iii) Fellinious Method: (C-soil)

• The failure is assumed to take place by slip and the consequent heaving of a mass of soil is on one side.

• Location of Critical circle

(iv) Prandtl Method: (C - ∅)

 For strip footing

For C-soil 

(v) Terzaghi Method (C - ∅)

Assumptions

S – Strip footing, S – Shallow foundation, G – General shear failure, H – Horizontal ground, R – Rough base

For strip footing

For square footing

For rectangular footing

For circular footing

where,

D = Dia of circular footing

CN_c → Contribution due to constant component of shear strength of soil.

 → Contribution due to surcharge above the footing

 → Contribution due to bearing capacity due to self weight of soil.

Bearing capacity factors

where,  = influence factor

For C-soil:

N_C = 5.7,  N_q = 1, N_γ = 0

(vi) Skemptons Method (c-soil)

This method gives net ultimate value of bearing capacity.

Applicable for purely cohesive soils only.

For strip footing. 

For circular and square footing.

Values of N_C

•  at the surface.
  Then N_C = 5 For strip footing
  N_C = 6.0 For square and circular footing.
  where D_f = Depth of foundation.
• If 
  
  for strip footing
   For square and circular footing.
  B =D in case of circular footing.
   for rectangular footing
• if  N_C =7.5
  for strip footing
  N_C = 9.0 for circular, square and rectangular footing.

(vii) Meyorhoff's Method → (C - ∅ soil)

(viii) IS code:

Effect of Water Table on Bearing Capacity of Soil 

where  and  are water table correction factor.

when 

If  they    

If  they 

If water table rise to G.L

 and 

Plate Load Test

1. Significant only for cohesionless.

2. Short duration test hence only results in immediate settlement.

(i)        (ii) 

..for ∅=soil            … for C-soil

If plate load test carried at foundation level then

(iii)

(iv) 

… for dense sand.                      … for clays

(v) 

… for silts.

where,

q_uf =Ultimate bearing capacity of foundation

q_up = Ultimate bearing capacity of plate

S_f = Settlement of foundations

S_p = Settlement of plate

B_f = Width of foundation in m

B_p = Width of plate in m

Housels Approach

where, Q_p = Allowable load on plate m and n are constant

P = Perimeter A_p = Area of plate

A_f = Area of foundation

Standard Penetration Test

Significant for Granular Soils

(i)  and 

where, N₁ = Overburden pressure correction

N₀ = Observed value of S.P.T. number.

 = Effective overburden pressure at the level of test in kM/m².

(ii) For Saturated  fine sand and silt, when N₁ > 15

where, N₂ = Dilatancy correction or water table correction.

 related to N value using peck Henson curve or (code method)

• Teng's formula relate N value with reading capacity of granular soil.

Pecks Equation

D_w = depth of water table below G.L

D_f = Depth of foundation

B = Width of foundation

N = Avg. corrected S.P.T. no.

S = Permissible settlement of foundation

C_w = Water table correction factor

q_{a net} = Net allowable bearing pressure.

Teng's Equations

C_w =Water table correction factor

D_w = Depth of water table below foundation level

B = Width of foundation

C_d =Depth correction factor

S = Permissible settlement in 'mm'.

I.S Code Method

q_ns =Net safe bearing pressure in kN/m²

B = Width in meter.

S = Settlement in 'mm'.

I.S. Code Formula for Raft:

C_w : Same as of peck Henson.

Meyer-Hoffs Equation

where, q_ns = Net safe bearing capacity in kN/m².

B < 1.2 m

B ≥ 1.2 m (where q_ns is in kN/m².

Cone Penetrations Test

(i) 

where, = Static cone resistance in kg/cm²

c = Compressibility coefficient

 = Initial effective over burden pressure in kg/cm².

(ii) 

where, 'S' = Settlement.

(iii)  B > 1.2 m.

where, q_ns = Net safe bearing pressure in kN/m².

(iv)  B < 1.2 m.

where, R_w = Water table correction factor.

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) 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.