Bearing Capacity and Theories

7/23/2019 Bearing Capacity and Theories

1/12

Bearing Capacity and Stability of Foundations

The ability of a soil to support a load from a structural foundation withoutfailing in shear is known as its bearing capacity.

The stability of foundation depends on:

1. The bearing capacity of the soil beneath the foundation.

2. The settlement of the soil beneath the foundation.

There are, therefore, two independent stability conditions to be fulfilled sincethe shearing resistance of the soil provides the bearing capacity and theconsolidation properties determine the settlement.

Bearing Capacity

The supporting power of soil is referred to as its bearing capacity. It may bedefined as the largest intensity of pressure which may be applied by astructure to the soil without causing failure of soil in shear or excessivesettlement. onsider a footing placed at depth ! below the ground surface,the overburden pressure at the base of the footing is qo=D.The total

pressure

at the base of the footing due to the self weight of the footing, weight of thesuperstructure and due to the weight of earth fill over the footing is known asthe gross pressure intensity. The difference in intensities of gross pressureafter the construction of the structure and of the original overburdenpressure is known as the net pressure .

The ultimate bearing capacity of soil may be determined by analyticalmethods "i.e., by bearing capacity theories# and field tests, or approximate

values may be adopted from $uilding odes which are based on experience.

Ultimate Bearing Capacity qu

The ultimate bearing capacity qu is defined as the least gross pressureintensity which would cause shear failure of the supporting soil immediatelybelow and ad%acent to a foundation.


2/12

Three distinct modes of failure have been identified and these are illustrated in &ig.1,they well be described with reference to a strip footing

In the case of general shear failure, continuous failure surfaces developed between theedges of the footing and the ground surface as shown in &ig.2. 's the pressure is

increased towards the value quthe state of plastic e(uilibrium is reached initially in thesoil around the edges of the footing then gradually spreads downwards and outwards.)ltimately the state of plastic e(uilibrium is fully developed throughout the soil above thefailure surfaces. *eaving of the ground surface occurs on both sides of the footingalthough the final slip movement would occur only on one side, accompanied by tiltingof the footing. This mode of failure is typical of soils of low compressibility "i.e. dense orstiff soils# and the pressure settlement curve is of the general form shown in &ig.2, theultimate bearing capacity being well defined.

In the mode of local shear failurethere is significant compression of the soilunder the footing and only partial development of the state of plastice(uilibrium. The failure surfaces, therefore, do not reach the ground surfaceand only slight heaving occurs. Tilting of the foundation would not beexpected. +ocal shear failure is associated with soils of high compressibilityand, as indicated in &ig.2, is characteried by the occurrence of relatively


3/12

large settlements "which would be unacceptable in practice# and the fact thatthe ultimate bearing capacity is not clearly defined.

-unching shear failure occurs when there is compression of the soil under thefooting, accompanied by shearing in the vertical direction around the edges of

the footing. There is no heaving of the ground surface away from the edgesand no tilting of the footing. elatively large settlements are also acharacteristic of this mode and again the ultimate bearing capacity is not welldefined. -unching shear failure will also occur in a soil of low compressibility ifthe foundation is located at considerable depth. In general the mode of failuredepends on the compressibility of the soil and the depth of foundation relativeto its breadth.

Net Ultimate Bearing Capacity qnu


4/12

The net ultimate bearing capacity is the minimum net pressure intensitycausing shear failure of soil.

qnu=qu - qo

qu=qnu+qo

Net Safe Bearing Capacity qns

The net safe bearing capacity is the net ultimate bearing capacity divided bythe desired factor of safety &.

Safe Bearing Capacity qs

The safe bearing capacity is the maximum pressure which the soil can carrysafely without risk of shear failure.

Allowable Bearing Capacity

The allowable bearing capacity is maximum pressure which is consideredsafe both with respect to shear failure and settlement.

/hen the term bearing capacity is used without any prefix it may beunderstood to refer to the ultimate bearing capacity.

BEARN! CA"AC#$ #%E&RES

$roadly, there are two approaches for the analysis of stability of foundations. The first ofthese is known as the conventional approach which generates from the work ofoulomb "10#. This is based on the assumption of a certain shape for the rapturesurface. The other approach which stems from the work of ankine "13# and 4otter"1056# is based on the assumption of simultaneous failure at every point in certain oneof the soil mass. This is referred here as plasticity theory approach. *owever, there isfound to be reasonably good agreement between the two approaches


5/12


6/12


7/12

The application of the load "&ig.# tends to push the wedge of soil abc intothe ground with a lateral displacement of ones II "radial shear ones# andones III "plane shear ones#. The downward movement of this soil wedge isresisted by the resultant of the passive pressure of the soil and the

cohesion , acting along the surface of the wedges ac, bcas it moves.onsidering the e(uilibrium of the wedge abc, Teraghi presented thefollowing bearing capacity expression for general shear failure:


8/12

where


9/12

< relates the passive pressure of the soil in ones II and III to the

sie of the footing, and angle of failure one I "&ig.#. The valuesare determined by means of the =circle or logarithmic

spiral.

It is proposed that ultimate bearing capacity for local shear failure conditionmay be computed based on the following soil parameters

Table 1 Bearing Capacity Factors for General Shear Conditions

and ocal Shear Conditions

Nc Nq N N)c N

)q N

)

* +., -.* *.* +., -.* *.*

+ ,. -./ *.+ /., -.0 *.1

-* 2./ 1., -.1 3.* -.2 *.+


10/12

-+ -1.2 0.0 1.+ 2., 1., *.2

1* -,., ,.0 +.* --.3 .2 -.,

1+ 1+.- -1., 2., -0.3 +./ .1

* ,.1 11.+ -2., -2.* 3. +.,

0 +1./ /.+ +.* 1., --., 2.*

+ +,.3 0-.0 01.0 1+.1 -1./ -*.-

0* 2+., 3-. -**.0 0.2 1*.+ -3.3

0+ -,1. -,. 12,.+ +-.1 +.- ,.,

03 1+3. 13,.2 ,3*.- //.3 +*.+ /*.0

+* 0,./ 0-+.- --+.1 3-. /+./ 3,.-


11/12

S(ape Factors

>(uation 1 is the bearing capacity e(uation for a long strip footing. It can alsobe used for rectangular footing of length + e(ual to or greater than 3 times thewidth $ i.e. . Teraghi has recommended that >( 1 could be used for circularand s(uare footings with the following modifications.

For circular footing


12/12

&or saturated clay may be assumed to be e(ual to ero, and hence:

For cohesion-less soils !c < 5.5"

4imitations5

"i# The shear strength of soil above the base level of footing isneglected.

"ii# This theory gives conservative values for footings whose depths aregreater than ero.

"iii# 9ubdivision of the bearing capacity problems in two types of shear isan arbitrary one, since two cases cannot cover the wide range ofconditions.

Documents

Bearing Capacity and Theories