Lecture 8.0 Bearing Capacity of Shallow Foundation

8/12/2019 Lecture 8.0 Bearing Capacity of Shallow Foundation

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LECTURE

8

Bearing Capacity of

Shallow Foundation

Dr. J. Berlin P. Juanzon CE, MBA, MSCM


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a) General Shear FailureMost common type of shearfailure; occurs in strong soils

and rocks

b) Local Shear FailureIntermediate betweengeneral and punching shear

failure

c) Punching Shear FailureOccurs in very loose sands

weak clays 2


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3

General shear failure

Local shear failure

Punching shear failure


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Application of limit equilibrium methods first done byPrandtl on the punching of thick masses

of metal.

Prandtl's methods adapted by Terzaghi to bearingcapacity failure of shallow foundations.

Vesicand others improved on Terzaghi's originaltheory and added other factors for a more complete

analysis

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Depth of foundation is less than or equal to itswidth

No sliding occurs between foundation and soil(rough foundation)

Soil beneath foundation is homogeneous semiinfinite mass

Mohr-Coulomb model for soil General shear failure mode is the governing

mode (but not the only mode)

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No soil consolidation occurs

Foundation is very rigid relative to the soil

Soil above bottom of foundation has no shear

strength; is only a surcharge load against the

overturning load

Applied load is compressive and appliedvertically to the centroid of the foundation

No applied moments present

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Since soil cohesion can be difficult to quantify,conservative values of c (cohesion) should be used.

Frictional strength is more reliable and does not need

to be as conservative as cohesion.

Terzaghi's method is simple and familiar to manygeotechnical engineers; however, it does not take into

account many factors, nor does it consider cases suchas rectangular foundations.

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General Shear Failures

1. Strip Footing:

= + +1

2

2. Square Footing:

= 1.3+ + 0.43. Rectangular Footing:

= 1.3[1 +.

] + +

[1

.

]

4. Circular Footing:

= 1.3+ + 0.3

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Local Shear Failures

1. Strip Footing:

= + +1

2

2. Square Footing:

= 1.3 + + 0.43. Rectangular Footing:

= 1.3[ 1+.

] + +

[1

.

]

4. Circular Footing:

= 1.3 + + 0.3

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1. Gross Allowable Load:

=

; = 2

2. Net Allowable Load:

() =

; = 2

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A footing 6m square carries a total load, including

its own weight of 10,000kN. The base of the footingis at a depth of 3.0m below the ground surface. Thesoil strata at the site consists of a layer of stiff fullysaturated clay 27.5m thick overlaying dense sand.

The average bulk density of the clay is 1,920kg/m3

and its average shear strength determined fromun-drained triaxial test is 130kN/m2. 1. Determine the gross foundation pressure.

2. Determine the net foundation pressure.

3. Calculate the factor of safety of the foundation againstcomplete shear failure under the un-drained condition(both gross and net)

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Modifications of Bearing Capacity

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Groundwater Effects


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Shallow groundwater affects shear strength in twoways:

Reduces apparent cohesion that takes place when

soils are not saturated; may necessitate reducing thecohesion measured in the laboratory

Pore water pressure increases; reduces botheffective stress and shear strength in the soil (sameproblem as is experienced with unsupportedslopes)

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If water table is located so that D1< Df. The factor

q in the bearing capacity equations will be:

= 1 + 2( )

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Df

D1

D2

Water table

B

Where:

q= efective surcharge

= unit weight of soil

sat= saturated unit weight

of soilw= unit weight of water

Also the value ofin the last term of the equations has to

be replaced by = )


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If water table is located so that 0< d < B. The factor

q in the bearing capacity equations will be:

=

20

Df

dWater table B

Where:

q= efective surcharge

= unit weight of soild= depth of water table from bottom

of foundation

The factor in the last term of theequations has to be replaced by factor

= + d/ )


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If water table is located so that d B, the waterwill have no effect on the ultimate bearingcapacity.

21

Df

d

Water table

B

= . + + . Use: =


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If water table is located at the bottom of the

foundation.

22

DfWater table

B

= . + + . Use: =

Change the value of in the last term of the equations by

= )


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A square footing carries an allowable load of60,000kg including its own weight. The bottom of thefooting and the ground water table is 1.2m below theground surface. Using the formula:

1. Compute the effective surcharge at the bottom of thefooting.

2. Compute the value of B using a gross factor of safety of 3.Assume general shear failure.

3. Compute the net factor of safety.Use s= 1,850kg/m

3; sat= 1,960kg/m3 C=1600kg/m3; =30o

From table Nc= 35 Nq= 22 N=19

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= 1.3 + + 0.4


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A square footing has a dimension of 1.2m x1.2m and has its bottom 1.0m below theground surface. 1. If the ground water table is located at depth of 1.2m from

the ground surface, compute the allowable load that thefooting could carry if it has a factor of safety of 3.

2. Find the ultimate bearing capacity of the soil if thegroundwater table is at the bottom of the footing

3. Find the ultimate bearing capacity of the soil if theground water table is 0.50m above the bottom of thefooting.

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In layered soil profiles, the unit weight of the soil, the angle offriction and the cohesion are not constant throughout the depth.The ultimate surface failure may extend through two or more ofthe soil layers.

Consider the case when the stronger soil is underlain by a weakersoil. If H, the thickness of the layer of soil below the footing, isrelatively large then the failure surface will be completely locatedin the top soil layer, which is the upper limit for the ultimatebearing capacity.

If the thickness His small compared to the foundation width B, apunching shear failure will occur at the top soil stratum, followedby a general shear failure in the bottom soil layer.

If His relatively deep, then the shear failure will occur only on thetop soil layer.

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The Bearing Capacity ofMulti-Layered Soils

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Meyerhof and Hanna (1978) andMeyerhof(1974)

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Meyerhof andHannas

punching shearcoefficient Ks

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Variationof ca/c1

with q2/q1based on thetheory of

Meyerhof andHanna (1978)

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Lecture 8.0 Bearing Capacity of Shallow Foundation