Terzaghi’s Bearing Capacity Theory

BEARING CAPACITY

The load-carrying capacity of foundation soil

or rock which enables it to bear and transmit loads from

a structure.

Ultimate bearing capacity: Maximum pressure which a

foundation can withstand without the occurrence of shear

failure of the foundation.

Determination of bearing capacity

1. Terzaghi's bearing capacity theory

2. The general bearing capacity equation

3. Field tests

Terzaghi's bearing capacity theoryAssumptions:

1) The soil is semi-infinite, homogeneous and isotropic2) The problem is two-dimensional3) The base of the footing is rough4) The failure is by general shear5) The load is vertical and symmetrical6) The ground surface is horizontal7) The overburden pressure at foundation level is equivalent to a surcharge load8) The principle of superposition is valid9) Coulomb's law is strictly valid

Vesic (1973) classified shear failure of soil under a

foundation base into three categories depending

on the type of soil & location of foundation.

1) General shear failure.

2) Local shear failure.

3) Punching shear failure

Modes of shear Failure

1) General Shear failure

The load - Settlement curve in case of footing resting on surface of dense sand or stiff clays shows pronounced peak & failure occurs at very small stain.

The shearing strength is fully mobilized all along the slip surface & hence failure planes are well defined.

The failure occurs at very small vertical strains accompanied by large lateral strains.

(i) Strip footing resting on surface (ii)Load –settlement curve

2) Local Shear failure

The foundation movement is accompanied by sudden jerks.

The failure surface gradually extend out wards from the foundation.

The shear strength of soil is not fully mobilized along planes & hence Failure planes are not defined clearly.

The failure occurs at large vertical strain & very small lateral strains.

3) Punching Share failure

The loaded base sinks into soil like a punch.

The failure surface do not extend up to the ground surface.

Large vertical strains are involved with practically no lateral deformation.

Failure planes are difficult to locate.

Mechanism of Failure

The zones of plastic equilibrium is divided into:

1 . Zone I of elastic

equilibrium

2. Zones II of radial

shear state

3. Zones III of Rankine

passive state

Terzaghi’s general equation:

qf = 0.5gBN g + cNc + gDNq

Contribution of: Soil Self Weight Shear Strength Surcharge

The first term in the equation is related to cohesion of the soil .

The second term is related to the depth of the footing and overburden pressure.

The third term is related to the width of the footing and the length of shear stress area.

Ultimate Bearing Capacity of Soil

qu =C’Nc + γ Df Nq + 0.5 γ B N γ

This is Terzaghi’s Bearing capacity equation for determining

ultimate bearing capacity of strip footing. Where Nc, Nq & Nr

are Terzaghi’s bearing capacity factors & depends on angle of

shearing resistance (ø).

Terzaghi’s Bearing Capacity Factors

  Nγ, Nc and Nq are bearing capacity factors and are derived from various sources

Some observations on terzaghi's bearing capacity theory

Karl von Terzaghi was the first to present a comprehensive

theory for the evaluation of the ultimate bearing capacity

of rough shallow foundations.

This theory states that a foundation is shallow if its depth

is less than or equal to its width.

It is a method for determining bearing capacity for the

general shear failure .

The equations are given below:

Square footings:

Qu = 1.3c N +g D Nq +0.4 gB Ng

Circular footings:

Qu = 1.3 cNc + gDNq +0.3gB Ng

Strip footings:

Qu = c Nc + g D Nq + 0.5 g B Ng

where: C: Cohesion of soil

g : unit weight of soil

D: depth of footing

B: width of footing

 

Nc=cotf(Nq –1)

 

Nq=e2(3p/4-f/2)tanf / [2 cos2(45+f/2)]

 

Ng=(1/2) tanf( Kpr /cos2 f -1)

Kpr=passive pressure coefficient.

The differences in the bearing capacity values arising out of

differences in the size of the footing and in the shape of the footing

are termed ‘size effects’ and ‘shape-effects’, respectively.

 

Important points : 

Terzaghi’s Bearing Capacity equation is applicable

for general shear failure.

Terzaghi has suggested following empirical reduction to

actual c & ø in case of local shear failure

Mobilised cohesion Cm = 2/3 C

  Based on the experimental results,Terzaghi’s suggested following equations

for UBC –

Square footing qu = 1.2c’ Nc + γ Df Nq + 0.4 γ BNr

Circular footing qu = 1.2c’Nc + γ Df Nq + 0.3 γ BNr

Thank you