Bearing Capacity Theories

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      010Foundation Engineering(3-1-0-4)

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    Course instructor

    Dr. Trudeep N. DaveInstitute of Infrastructure Technology Research and Management

    E-mail: [email protected]

    Class timings:Monday: 11:00 to 12:00Tuesday: 10.00 to 11.00Thursday: 11.00 to 12.00

    Bearing Capacity TheoryBearing Capacity

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    To perform satisfactorily, shallow foundations must have two maincharacteristics:

    1. They have to be safe against overall shear failure in the soil that

    supports them.

    2. They cannot undergo excessive displacement, or settlement.(The term excessive is relative, because the degree of settlementallowed for a structure depends on several considerations.)

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    General Shear Failure

    Local Shear Failure

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    Punching Shear Failure

    Bearing Capacity Failure

    • a) General Shear Failure Mostcommon type of shear failure;occurs in strong soils and rocks

    • b) Local Shear FailureIntermediate between generaland punching shear failure

    • c) Punching Shear Failure Occursin very loose sands weak clays

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    Bearing Capacity Failure

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    General shear failure 

    Local shear failure 

    Punching shear failure 

    Soil Conditions and earing

    Capacity Failure

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    Load DisplacementCurves (after Vesicʼ (1973))

    a) General Shear Failureb) Local Shear Failure

    c) Punching Shear Failure

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    Comments on Shear Failure

    • Usually only necessary to analyze general shearfailure.

    • Local and punching shear failure can usually beanticipated by settlement analysis.

    • Failure in shallow foundations is generally settlementfailure; bearing capacity failure must be analyzed,but in practical terms is usually secondary tosettlement analysis.

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    Development of Bearing CapacityTheory

    • Application of limit equilibrium methods first done by Prandtlon thepunching of thick masses of metal.

    • Prandtl's methods adapted by Terzaghi to bearing capacityfailure of shallow foundations.

    • Vesicʼ and others improved on Terzaghi's original theory andadded other factors fora more completeanalysis

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    Assumptions for Terzaghi's Method

    • Depth of foundation is less than or equal to its width

    • No sliding occurs between foundation and soil(rough foundation)

    • Soil beneath foundation is homogeneous semiinfinite mass

    • Mohr-Coulombmodel for soil

    • General shear failure mode is the governing mode(but not the only mode)

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    Assumptions for Terzaghi's Method

    • No soil consolidationoccurs

    • Foundation is very rigid relative to the soil

    • Soil above bottom of foundation has no shearstrength; is only a surcharge load against theoverturning load

    • Applied load is compressive and applied vertically tothe centroid of the foundation

    • No appliedmoments present

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    Failure Geometry for Terzaghi's Method

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    Notes on Terzaghi's Method

    • Since soil cohesion can be difficult to quantify, conservativevaluesof c (cohesion) should be used.

    • Frictional strength is more reliable and doesnot need to beas conservative as cohesion.

    • Terzaghi's method is simple and familiar to manygeotechnical engineers; however, it does not take intoaccount many factors, nor does it consider cases such asrectangular foundations.

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    The General Bearing Capacity Equation.

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    The General Bearing Capacity Equation.

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    Other Factors

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    Other Factors

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    • For continuous footing,s = 1

    • For perpendicular load,i = 1• For level foundation,b =1

    • For level ground,g =1

    • Need to compute factors- Bearing Capacity Factor N,- Depth Factor d

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    Groundwater Effects

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    Groundwater Effects

    Shallow groundwater affects shearstrengthin two ways:

    • Reduces apparent cohesion that takes place when soils arenot saturated; may necessitate reducing the cohesionmeasuredin the laboratory

    • Pore water pressure increases; reduces both effective stressand shear strength in the soil (same problem as isexperienced with unsupportedslopes)

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    Groundwater Effects

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    FOOTINGS WITH ECCENTRIC OR INCLINED LOADINGS

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    Eccentricity

    Inclination

    FOOTINGS WITH One Way Eccentricity

    In most instances, foundations are subjectedto moments in additionto thevertical load as shown below. In such cases the distribution of pressure by

    the foundation upon thesoil is notuniform.

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    FOOTINGS WITH One Way Eccentricity

    • Note that in these equations, when the eccentricity e becomes B/6,qmin is zero.• For e > B/6, qmin will be negative, which means that tension will

    develop.• Because soils can sustain very little tension, there will be a

    separation between the footing and the soil under it.• Also note that the eccentricity tends to decrease the load bearing

    capacity of a foundation.• In such cases, placing foundation column off-center, as shown in

    Figure is probably advantageous.• Doing so in effect, produces a centrally loaded foundation with a

    uniformly distributed pressure.

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    FOOTINGS WITH One Way Eccentricity

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    Footing with Two-way Eccentricities

    • Consider a footing subject to a vertical ultimate load Q ult anda moment M asshown in Figures a and b. For this case, the components of the moment Mabout the x and y axisare Mx and My respectively. This condition is equivalenttoa load Q placed eccentrically on the footing with x = e B and y = e L as shownin Figured.

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    Footing with Two-way Eccentricities

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    Example 1

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    Example 1

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    Example 2

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    Example 2

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    Footings with Inclined Loads

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    Footings with Inclined Loads

    1. Compute the inclination factors using the equations given below:

    β inclination of load with respect to vertical

    2. Use the inclination factors just computed to compute Hansen shapefactors as

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    Footings with Inclined Loads

    3. These are used in the following modifications of the "edited“

    Hansen bearing capacity equation:

    Use the smaller value of qu\t  computed by either ofEquations.

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    The Bearing Capacity of Multi-

    Layered Soils

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    The Bearing Capacity of Layered Soils

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    The Bearing Capacity of Layered Soils

    • In layered soil profiles, the unit weight of the soil, the angle of friction andthe cohesion are not constant throughout the depth. The ultimate surfacefailure may extend through two or more of the soil layers.

    • Consider the case when the stronger soil is underlain by a weaker soil. If H,the thickness of the layer of soil below the footing, is relatively large thenthe failure surface will be completely located in the top soil layer, which isthe upper limit for the ultimate bearing capacity.

    • If the thickness H is small compared to the foundation width B, a punchingshear failure will occur at the top soil stratum, followed by a general shearfailure in the bottom soil layer.

    • If H is relatively deep, then the shear failure will occur only on the top soillayer.

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    The Bearing Capacity of Layered Soils

    • Meyerhof and Hanna (1978) and Meyerhof(1974)

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    The Bearing Capacity of Layered Soils

    • Meyerhof andHannas punching

    shear coefficient Ks

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    The Bearing Capacity of Layered Soils

    • Variationof c’ a/c’ 1

    with q2/q1based on the

    theory of Meyerhofand Hanna (1978)

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    Example on layered soils

    Example on layered soils

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    Example on layered soils

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    Ground Factors

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    Base Factor

    • For footings with angled foundation bases

    • When footing is level, b = 159

    RigidityFactors

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    Bearing Capacity from Field Tests

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    Bearing Capacity from SPT

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    Bearing Capacity from SPT

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    Bearing Capacity from SPT

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    Bearing Capacity using CPT

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    Bearing Capacity for FieldLoad Tests PLT

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    Bearing Capacity for Field Load Tests PLT

    • For Granular Soils:

    • For Cohesive Soils:

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    Correction of Standard penetration number

    • It has been suggested that the SPT be standardized to some energyratio E r which should be computed as

    • Note that larger values of E r decrease the blow count N nearly linearly,that is, E r45 gives N = 20 and E r90 gives N = 10;

    • Example of N for E r45 = 20 we obtain for the arbitrarily chosen E r = 70,(E r70):

    68N for E r70 = 13