Shallow Foundations Complete Study Notes

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.

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