Bearing Capacity Theories

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

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    Course instructor

    Dr. Trudeep N. Dave Institute of Infrastructure Technology Research and Management

    E-mail: [email protected]

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

    Bearing Capacity Theory Bearing Capacity

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    To perform satisfactorily, shallow foundations must have two main characteristics:

    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 settlement allowed 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 Most common type of shear failure; occurs in strong soils and rocks

    • b) Local Shear Failure Intermediate between general and punching shear failure

    • c) Punching Shear Failure Occurs in 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 Displacement Curves (after Vesicʼ (1973))

    a) General Shear Failure b) Local Shear Failure

    c) Punching Shear Failure

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    Comments on Shear Failure

    • Usually only necessary to analyze general shear failure.

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

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

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    Development of Bearing Capacity Theory

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

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

    • Vesicʼ and others improved on Terzaghi's original theory and added 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 semi infinite 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 shear strength; is only a surcharge load against the overturning load

    • Applied load is compressive and applied vertically to the 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, conservative valuesof c (cohesion) should be used.

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

    • Terzaghi's method is simple and familiar to many geotechnical engineers; however, it does not take into account many factors, nor does it consider cases such as rectangular 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 are not saturated; may necessitate reducing the cohesion measuredin the laboratory

    • Pore water pressure increases; reduces both effective stress and shear strength in the soil (same problem as is experienced 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 the vertical 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 as shown in Figures a and b. For this case, the components of the moment M about the x and y axisare Mx and My respectively. This condition is equivalent toa load Q placed eccentrically on the footing with x = e B and y = e L as shown in 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 shape factors 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 of Equations.

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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 and the cohesion are not constant throughout the depth. The ultimate surface failure 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 then the failure surface will be completely located in the top soil layer, which is the upper limit for the ultimate bearing capacity.

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

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

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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 and Hannas punching

    shear coefficient Ks

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    The Bearing Capacity of Layered Soils

    • Variation of c’ a/c’ 1

    with q2/q1 based on the

    theory of Meyerhof and Hanna (1978)

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    Example on layered soils

    Example on layered soils

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    Example on layered soil

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