Soil Mechanics & Foundation Engineering : Shallow foundation

By Sajal Gupta|Updated : July 7th, 2021

Shallow Foundation & Bearing Capacity

Bearing Capacity

 It is the load carrying capacity of the soil.

  • Ultimate bearing capacity or Gross bearing capacity (qu)

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

Shallow Foundation & Bearing Capacity

Bearing Capacity

 It is the load carrying capacity of the soil.

  • Ultimate bearing capacity or Gross bearing capacity (qu)

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

  • Net ultimate bearing capacity (qun ):

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, Dis 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 (qns):

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 (qs ):

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

 

image011

where, qs = Safe bearing capacity.

Method to determine bearing capacity

(i) Rankines Method ( - soil)

image013

image014 or 

image015

(ii) Bells Theory (C - )

image016 

where, Nc and Nq 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.

image017image018

  • Location of Critical circle

image019

(iv) Prandtl Method: (C - )

 For strip footing

image020

For C-soil 

image021image022image023

(v) Terzaghi Method (C - )

Assumptions

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

image024

For strip footing

image025

For square footing

image026

For rectangular footing

image027

image028

For circular footing

image029

where,

D = Dia of circular footing

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

image030 → Contribution due to surcharge above the footing

image031 → Contribution due to bearing capacity due to self weight of soil.

Bearing capacity factors

image032 

where, image033 = influence factor

image034

image035

image036

For C-soil:

NC = 5.7,  Nq = 1, Nγ = 0

(vi) Skemptons Method (c-soil)

This method gives net ultimate value of bearing capacity.

Applicable for purely cohesive soils only.

image038

For strip footing. 

image039

For circular and square footing.

 image040

Values of NC

  • image041 at the surface.
    Then NC = 5 For strip footing
    NC = 6.0 For square and circular footing.
    where Df = Depth of foundation.
  • If image042

    image043for strip footing
    image044 For square and circular footing.
    B =D in case of circular footing.
    image045 for rectangular footing
  • if image046 NC =7.5
    for strip footing
    NC = 9.0 for circular, square and rectangular footing.

image047

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

image048

(viii) IS code:

image049

Effect of Water Table on Bearing Capacity of Soil 

image050

image051

where image052 and image053 are water table correction factor.

image054image055

when image056

If image057 they image058   

If image059 they image060

If water table rise to G.L

image061 and image060

Plate Load Test

1. Significant only for cohesionless.

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

(i) image062       (ii) image063

..for ∅=soil            … for C-soil

If plate load test carried at foundation level then

image064

image065

(iii)

 image064 

(iv) image066

… for dense sand.                      … for clays

(v) image067

… for silts.

where,

quf =Ultimate bearing capacity of foundation

qup = Ultimate bearing capacity of plate

Sf = Settlement of foundations

Sp = Settlement of plate

Bf = Width of foundation in m

Bp = Width of plate in m

Housels Approach

image068

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

P = Perimeter Ap = Area of plate

Af = Area of foundation

Standard Penetration Test

Significant for Granular Soils

(i) image070 and image071

where, N1 = Overburden pressure correction

N0 = Observed value of S.P.T. number.

image004 = Effective overburden pressure at the level of test in kM/m2.

(ii) For Saturated image004  fine sand and silt, when N1 > 15

image072

where, N2 = Dilatancy correction or water table correction.

image073 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

image074

Dw = depth of water table below G.L

Df = Depth of foundation

B = Width of foundation

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

S = Permissible settlement of foundation

Cw = Water table correction factor

qa net = Net allowable bearing pressure.

Teng's Equations

image075

Cw =Water table correction factor

Dw = Depth of water table below foundation level

B = Width of foundation

Cd =Depth correction factor

S = Permissible settlement in 'mm'.

I.S Code Method

image076

qns =Net safe bearing pressure in kN/m2

B = Width in meter.

S = Settlement in 'mm'.

I.S. Code Formula for Raft:

image077

Cw : Same as of peck Henson.

Meyer-Hoffs Equation

image079 

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

B < 1.2 m

image080image081

image082

B ≥ 1.2 m (where qns is in kN/m2.

Cone Penetrations Test

(i) image083

where, = Static cone resistance in kg/cm2

c = Compressibility coefficient

image085 = Initial effective over burden pressure in kg/cm2.

(ii) image086

where, 'S' = Settlement.

(iii) image087 B > 1.2 m.

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

(iv) image088 B < 1.2 m.

where, Rw = Water table correction factor.

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Sajal GuptaSajal GuptaMember since Mar 2020
B.E- Civil, Thapar University, Patiala Cracked Gate-2017, 2018, 2020 1 yr work exp at Wapcos, MoWR
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