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Chapter 5
Ultimate Bearing Capacity
of Shallow Foundations:Special Cases
Omitted parts:
Sections 5.6, 5.7 , 5.10 , 5.12
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The ultimate bearing capacity problems described in Chapter 4 assume that :
•The soil supporting the foundation is homogeneous and extends to a great
depth below the bottom of the foundation.
•The ground surface is horizontal.
However, that is not true in all cases:
• It is possible to encounter a rigid layer at a shallow depth.
•The soil may be layered and have different shear strength parameters.
• It may be necessary to construct foundations on or near a slope.
• It may be required to design a foundation subjected to uplifting load.
This chapter discusses bearing capacity problems related to these special
cases.
Ultimate Bearing Capacity of Shallow Foundations
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Foundation Supported by a Soil with a RigidBase at Shallow Depth
If a rigid, rough base is located at a
depth of H < D below the bottom of the
foundation, full development of the
failure surface in soil will be restricted.
In such a case, the soil failure zone and
the development of slip lines at
ultimate load will be as shown in the
Figure below.
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Foundation Supported by a Soil with a RigidBase at Shallow Depth
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Foundation Supported by a Soil with a RigidBase at Shallow Depth
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Rectangular Foundation on Granular Soil
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Square and Circular Foundations on Granular Soil
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Foundations on Saturated Clay
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EXAMPLE 5.1
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EXAMPLE 5.2
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Foundations on Layered Clay (f = 0)
For undrained loading (f = 0 condition) :
let cu(1) = shear strength of the upper clay layer
cu(2) = shear strength of the lower clay layer
The variation of Nc is given in the Figure
The relationships for Fcs and Fcd given in Table 4.3
If the lower layer of clay is softer than the top
one (cu(2) /cu(1) < 1), the value of (Nc) is lower
than when the soil is not layered (cu(2) /cu(1) = 1).
This means that the ultimate bearing capacity
is reduced by the presence of a softer clay
layer below the top layer.
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Weaker Layer underlain by Stronger Layer (f = 0)
Ultimate bearing capacity of a foundation supported by a weaker clay
layer [cu(1)] underlain by a stronger clay layer [cu(2)] i.e (cu(1) /cu(2) < 1) :
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EXAMPLE 5.3
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Stronger Layer underlain by Weaker Layer (c’- f’ soil )
If the depth H is relatively small compared
with the foundation width B, a punching
shear failure will occur in the top soil layer,
followed by a general shear failure
In the bottom soil layer (Figure a).
If the depth H 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 (Figure b).
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Stronger Layer underlain by Weaker Layer (c’- f’ soil )
The variation of Ks with q2/q1 and f1 is shown in Figure.
The variation of ca/c1 with q2/q1 is shown in Figure .
If the height H is relatively large, then the failure surface in soil
will be completely located in the stronger upper-soil layer.
For this case,
Combining Eqs. (a) and (b) yields
(a)
(b)
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Stronger Layer underlain by Weaker Layer (c’- f’ soil )
For rectangular foundations
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Stronger Layer underlain by Weaker Layer (c’- f’ soil )
Top layer is strong sand and bottom layer is saturated soft clay f2 = 0
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Stronger Layer underlain by Weaker Layer (c’- f’ soil )
Top layer is stronger sand and bottom layer is weaker sand
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Stronger Layer underlain by Weaker Layer (c’- f’ soil )
Top layer is stronger saturated clay and bottom layer is weaker saturated
clay (f1 = f2 = 0)
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EXAMPLE 5.4
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EXAMPLE 5.5
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Weaker Layer underlain by Stronger Layer (c’- f’ soil )
When a foundation is supported by a
weaker soil layer underlain by a stronger
layer, the ratio of q2/q1 will be greater than
one.
If H/B is relatively small, the failure surface
in soil at ultimate load will pass through
both soil layers.
However, for larger H/B ratios, the failure
surface will be fully located in the top,
weaker soil layer.
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Weaker Layer underlain by Stronger Layer (c’- f’ soil )
The ultimate bearing capacity:
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EXAMPLE 5.6
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Bearing Capacity of Foundations on Top of a Slope
The ultimate bearing capacity for continuous foundations:
Ngq
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Weaker Layer underlain by Stronger Layer (c’- f’ soil )
The following points need to be kept in mind in
determining Ncq :
1. The term
is defined as the stability number.
2. If B<H, use the curves for Ns = 0.
3. If B>=H, use the curves for the calculated stability
number Ns .
Ncq
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EXAMPLE 5.8
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EXAMPLE 5.9
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EXAMPLE 5.10
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Bearing Capacity of Foundations on a Slope
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Foundations on Rock
qu=c’Nc+qNq+0.5gBNg
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EXAMPLE 5.13