# Bearing Capacity Theory

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Bearing Capacity Theory

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

Bearing Capacity Failure
General shear failure Local shear failure Punching shear failure

Soil Conditions and Bearing Capacity Failure

Load Displacement Curves (after Vesicʼ (1973))
a) General Shear Failure b) Local Shear Failure c) Punching 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.

Development of Bearing Capacity Theory
Application of limit equilibrium methods first done by Prandtl on the punching 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 for a more complete analysis

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-Coulomb model for soil General shear failure mode is the governing mode (but not the only mode)

Assumptions for Terzaghi's Method
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 applied vertically to the centroid of the foundation No applied moments present

Failure Geometry for Terzaghi's Method

Notes on Terzaghi's Method
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 many geotechnical engineers; however, it does not take into account many factors, nor does it consider cases such as rectangular foundations.

The General Bearing Capacity Equation.

The General Bearing Capacity Equation.

The General Bearing Capacity Equation.

Other Factors

Other Factors For continuous footing, s = 1 For perpendicular load,
For level foundation, b =1 For level ground, g =1 Need to compute factors - Bearing Capacity Factor N, - Depth Factor d

Groundwater Effects

Groundwater Effects Shallow groundwater affects shear strength in two ways: Reduces apparent cohesion that takes place when soils are not saturated; may necessitate reducing the cohesion measured in the laboratory Pore water pressure increases; reduces both effective stress and shear strength in the soil (same problem as is experienced with unsupported slopes)

Groundwater Effects

Eccentricity Inclination

FOOTINGS WITH One Way Eccentricity
In most instances, foundations are subjected to moments in addition to the vertical load as shown below. In such cases the distribution of pressure by the foundation upon the soil is not uniform.

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.

FOOTINGS WITH One Way Eccentricity

Footing with Two-way Eccentricities
Consider a footing subject to a vertical ultimate load Qult and a moment M as shown in Figures a and b. For this case, the components of the moment M about the x and y axis are Mx and My respectively. This condition is equivalent to a load Q placed eccentrically on the footing with x = eB and y = eL as shown in Figure d.

Footing with Two-way Eccentricities

Example 1

Example 1

Example 2

Example 2

Compute the inclination factors using the equations given below: βͦ inclination of load with respect to vertical Use the inclination factors just computed to compute Hansen shape factors as

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.

The Bearing Capacity of Multi-Layered Soils

The Bearing Capacity of Layered Soils

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.

The Bearing Capacity of Layered Soils
Meyerhof and Hanna (1978) and Meyerhof(1974)

The Bearing Capacity of Layered Soils
Meyerhof and Hannas punching shear coefficient Ks

The Bearing Capacity of Layered Soils
Variation of c’a/c’1 with q2/q1 based on the theory of Meyerhof and Hanna (1978)

Example on layered soils

Example on layered soils

Example on layered soils

Ground Factors

Base Factor For footings with angled foundation bases
When footing is level, b = 1

Rigidity Factors

Bearing Capacity from Field Tests

Bearing Capacity from SPT

Bearing Capacity from SPT

Bearing Capacity from SPT

Bearing Capacity using CPT

Bearing Capacity for Field Load Tests PLT

Bearing Capacity for Field Load Tests PLT
For Granular Soils: For Cohesive Soils:

Correction of Standard penetration number
It has been suggested that the SPT be standardized to some energy ratio Er which should be computed as Note that larger values of Er decrease the blow count N nearly linearly, that is, Er45 gives N = 20 and Er90 gives N = 10; Example of N for Er45 = 20 we obtain for the arbitrarily chosen Er = 70, (Er70): N for Er70 = 13