Terzaghis Bearing Capacity Theory
BEARING CAPACITYThe 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) 2) 3) 4) 5) 6) 7) 8) 9) The soil is semi-infinite, homogeneous and isotropic The problem is two-dimensional The base of the footing is rough The failure is by general shear The load is vertical and symmetrical The ground surface is horizontal The overburden pressure at foundation level is equivalent to a surcharge load The principle of superposition is valid Coulomb's law is strictly valid
Modes of shear Failure
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
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 (i) Strip footing resting on surface (ii)Load settlement curve lateral strains.
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 FailureThe zones of plastic equilibrium is divided into:
1 . Zone I of elastic
2. Zones II of radial shear state
3. Zones III of Rankinepassive state
Terzaghis general equation:qf = 0.5gBNg + cNc + gDNqSurcharge
Soil Self Weight
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 Soilqu =CNc + Df Nq + 0.5 B N This is Terzaghis Bearing capacity equation for determining ultimate bearing capacity of strip footing. Where Nc, Nq & Nr are Terzaghis bearing capacity factors & depends on angle of shearing resistance ().
Terzaghis Bearing Capacity FactorsN, 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 :Terzaghis Bearing Capacity equation is applicable for general shear failure. Terzaghi has suggested following empirical reduction to actual c & in case of local shear failure Mobilised cohesion Cm = 2/3 C
Based on the experimental results,Terzaghis suggested following equations for UBC Square footing qu = 1.2c Nc + Df Nq + 0.4 BNr Circular footing qu = 1.2cNc + Df Nq + 0.3 BNr