Shallow Foundations - 1 - Notes | Study Foundation Engineering - Civil Engineering (CE)

Shallow Foundation & Bearing Capacity

Bearing Capacity

It is the load carrying capacity of the soil.

1. 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.
2. 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
   q_nu = q_u - γD_y
   Where, D_f is the depth of footing
3. Safe bearing capacity
   It is the bearing capacity after applying the factor of safety (F_S). These are of two types,

Safe net bearing capacity (qns)
It is the net soil pressure which can be safety applied to the soil considering only shear failure. It is given by,
q_NS = q_n2/FS

Safe gross bearing capacity (qs)
It is the maximum gross pressure which the soil can carry safely without shear failure. It is given by,
q_s = q_ns + γD_f

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

1. Rankines Method (∅ - soil)    or 
   
2. Bells Theory (C - ∅)
   q_u = CN_c + γD_fN_q
   where, N_c and N_q are bearing capacity factors.
   For pure clays → C = 4, q = 1
3. Fellinious Method: (C-soil)
   (i) The failure is assumed to take place by slip and the consequent heaving of a mass of soil is on one side.
   
   (ii) Location of Critical circle
4. Prandtl Method: (C - ∅)
   (i) For strip footing 
   q_u = CN_c + γD_fN_q + 1/2γBN_γ →
   (ii) For C-soil 
   N_c = 5.14, N_q = 1, N_γ = 0
5. Terzaghi Method (C - ∅)
   (i) Assumptions
   S – Strip footing, S – Shallow foundation, G – General shear failure, H – Horizontal ground, R – Rough base(a) For strip footing
   q_u = CN_c + γD_fN_q + (1/2) γBN_γ
   (b) For square footing
   qu = 1.3CNc + γD_fN_{q + 0.4 γBNγ}
   (c) For rectangular footing
   
   
   (d) For circular footing
   
   where,
   D = Dia of circular footing
   CN_c → Contribution due to constant component of shear strength of soil.
   γD_fN_q → Contribution due to surcharge above the footing
   _1/2(γBNγ) → Contribution due to bearing capacity due to self weight of soil.
   (ii) Bearing capacity factors
   Nq = N∅.θ^πtan∅
   where, N_∅ = influence factor
   
   N_γ = 1.8tan∅(N_q - 1)
   N_C = cot∅(N_q - 1)
   For C-soil:
   N_C = 5.7, N_q = 1, N_γ = 0
6. Skemptons Method (c-soil)
   This method gives net ultimate value of bearing capacity.
   Applicable for purely cohesive soils only.
   q_nu = CN_c
   For strip footing.
   N_C = 5 to 7.5
   For circular and square footing.
   N_C = 6 to 9.0
   (i) Values of N_C
   (a) D_f/B = 0 i.e.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.
   (b) If 0 ≤ D_f/B ≤ 2.5
    for strip footing
     For square and circular footing.
   B = D in case of circular footing.
      for rectangular footing
   (c) if D_f/B ≤ 2.5 N_C =7.5
   for strip footing
   N_C = 9.0 for circular, square and rectangular footing.
   
7. Meyorhoff's Method → (C - ∅ soil)
    
8. IS code