CE 360
FOUNDATION
ENGINEERING
BEARING CAPACITY AND
FOUNDATION DESIGN
Learning Outcomes
• Understand the function of a foundation
• Know the different types of foundations
• Know the different types of foundation failures
• Understand the different factors that affect the bearing
capacity of soils
• Estimate the bearing capacity of soils from laboratory
and field tests
• Design shallow foundations
2
What is a Foundation?
• “Foundation” can generally be defined as “that which
supports something”
• A foundation is a member of an engineering structure
whose function is to support the structure and transmit the
superstructural load to the soil.
• The depth in the soil at which a foundation may be placed
gives rise to two categories of foundations, namely,
a) Shallow Foundations
b) Deep Foundations
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Building
Foundation
4
Bridge
Foundation
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Pylon
Showing
Foundation
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Shallow Foundations
• Definition and Types of Shallow Foundations
• Types of Foundation Failures
• Bearing Capacity Theory
• Effect of Water Table on Bearing Capacity
7
Shallow Foundations
• Shallow foundations are usually placed in the soil at a depth
from the ground surface less than the width (Df < B)
• However, any type of foundation that is placed in the soil at
a depth that does not exceed four times the width of the
foundation may be considered as a shallow foundation??.
i.e.,
D f  4B
where,
Df = depth in the soil at which the foundation is placed
B = width of the foundation
• Shallow foundations are practical for a depth of up to 5m
8
Sketch of Shallow Foundation
Note that the depth is measured from the ground surface to the
underside of the foundation slab.
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Types of Shallow Foundations
Shallow foundations come in several types. They are:
a) Isolated footing (also Spread footing or Pad footing)
A relatively small reinforced concrete slab which offers
support to a single column of a structure
Side View
Plan View
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Pad Foundation
• (Top left) reinforcement cage and starter bars
• (Top right) cast pad foundation
Construction of a
Pad Foundation
12
Types of Shallow Foundations
b) Strip footing (also Continuous footing or Wall footing )
This is the type of foundation that supports load-bearing
walls.
13
Types of Shallow Foundations
b) Strip footing (also Continuous footing or Wall footing )
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Types of Shallow Foundations
c) Combined footing
• A single reinforced concrete slab which supports two
or more columns of a structure.
• This type of foundation is used when two or more
columns are so close to each other such that their
individual footings would overlap
Side View
Plan View
15
Types of Shallow Foundations
c) Combined footing
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Types of Shallow Foundations
d) Raft or Mat foundation
This is a large reinforced concrete slab which supports
several columns or the structure as a whole and may cover
the entire area of the building.
This type of foundation is used when;
i. The allowable soil pressure is low.
ii. There are several pockets of weak soil layers over the
foundation area.
iii. The foundation columns are so close to each other
such that the individual footings would overlap or
nearly touch each other.
17
Types of Shallow Foundations
d) Raft or Mat foundation
Side View
Plan View
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Raft (Mat) Foundation
Construction
Types of Shallow Foundations
When shallow foundations are characterised by their sizes
(i.e. length and width) then they are distinguished as follows:
B
 0 , for strip footings
L
and
B
 0 , for all other footings
L
where,
B = width (breadth) of foundation
L = length of foundation
20
Foundation loads impose stress on the
soil at the foundation depth in addition to
what existed before the load application.
Effects of
Foundation
Loads on
Soils
The additional stress imposed may lead
to instability in an otherwise stable soil or
cause deformations in the soil large
enough to be detrimental to the
structure applying the stress.
The soil will mobilise strength to contain
the additional stress imposed on it to the
maximum that it can before failure
occurs.
21
Some Causes of
Foundation Failure
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23
24
25
26
27
28
29
Bearing Capacity
• The strength mobilised by soils to support the additional
stress imposed on them by foundation loads is referred to
as bearing capacity.
• The ultimate bearing capacity (qult) is the maximum
foundation stress that the soil can sustain before
undergoing a sudden catastrophic failure in shear.
• The allowable bearing capacity (qall) is the maximum safe
stress that can be sustained by a foundation soil without
failure by shear or excessive settlement.
• The allowable bearing capacity (qall) is therefore the “design”
bearing capacity
30
Bearing Capacity
The allowable bearing capacity is obtained by dividing the
ultimate bearing capacity by an appropriate factor of safety
(FS). The factor of safety is usually between 2.5 to 3.
i.e.,
qu
qall =
FS
where,
qall = allowable bearing capacity
qult = ultimate bearing capacity
FS = factor of safety
31
Bearing Capacity Theory
• In 1943, Terzaghi presented foundation failure conditions for a strip
footing.
• The failure zones under the foundation were separated into three
distinct zones as follows:
• The triangular zone ACD immediately under the foundation;
• The radial shear zones ADF and CDE with curves DE and DF being
log spirals;
• Two triangular passive Rankine zones AFH and CEG
32
Bearing Capacity Theory
The soil above the foundation level was replaced by an
equivalent surcharge ( q = D f ).
Analysis of the forces acting on the failure plane resulted in
the following expression:
𝒒𝒖𝒍𝒕 = 𝒄𝑵𝒄 + 𝟎. 𝟓𝜸𝑩𝑵𝜸 + 𝒒𝑵𝒒
where,
Df = foundation depth
qult = ultimate bearing capacity
c = cohesion of the foundation soil
B = foundation width
γ = unit weight of the soil
Nc , Nq , Nγ are bearing capacity factors dependent on
friction angle .
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Terzaghi’s Bearing Capacity
Factors
exp([3 / 2 −  ] tan  )
Nq =

2
2 cos  45 + 
2


1  Kp
N  = 
− 1 tan 
2
2  cos  
N c = cot  (N q − 1)
Kp = passive earth pressure coefficient
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Terzaghi’s
Bearing
Capacity
Factors
Terzaghi’s Bearing Capacity Factors
φ
0
1
2
3
4
5
6
7
8
9
10
11
12
Nc
5.70
6.00
6.30
6.62
6.97
7.34
7.73
8.15
8.60
9.09
9.61
10.16
10.76
Nq
1.00
1.10
1.22
1.35
1.49
1.64
1.81
2.00
2.21
2.44
2.69
2.98
3.29
Nγ
0.00
0.01
0.04
0.06
0.10
0.14
0.20
0.27
0.35
0.44
0.56
0.69
0.85
φ
13
14
15
16
17
18
19
20
21
22
23
24
25
Nc
11.41
12.11
12.86
13.68
14.60
15.12
16.56
17.69
18.92
20.27
21.75
23.36
25.13
Nq
3.63
4.02
4.45
4.92
5.45
6.04
6.70
7.44
8.26
9.19
10.23
11.40
12.72
Nγ
1.04
1.26
1.52
1.82
2.18
2.59
3.07
3.64
4.31
5.09
6.00
7.08
8.34
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Terzaghi’s Bearing Capacity Factors
φ
Nc
Nq
Nγ
φ
Nc
Nq
Nγ
26
27
28
29
30
31
32
33
34
35
36
37
38
27.09
29.24
31.61
34.24
37.16
40.41
44.04
48.09
52.64
57.75
63.53
70.01
77.50
14.21
15.90
17.81
19.98
22.46
25.28
28.52
32.23
36.50
41.44
47.16
53.80
61.55
9.84
11.60
13.70
16.18
19.13
22.65
26.87
31.94
38.04
45.41
54.36
65.27
78.61
39
40
41
42
43
44
45
46
47
48
49
50
85.97
95.66
106.81
119.67
134.58
151.95
172.28
196.22
224.55
258.28
298.71
347.50
70.61
81.27
93.85
108.75
126.50
147.74
173.28
204.19
241.80
287.85
344.63
415.14
95.03
115.31
140.51
171.99
211.56
261.60
325.34
407.11
512.84
650.67
831.99
1072.80
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Bearing Capacity
It is to be noted that the ultimate bearing capacity of a soil is
not a fundamental property of the soil as its value depends
on the following:
• the strength properties of the soil (i.e., c and ) ;
• the pressure applied on the soil by the overburden;
• the type and size of the foundation applying the
superstructure load;
• the depth below the surface of the soil at which the
foundation is placed
• the influence of the water table.
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Square and Circular Foundations
To deal with the bearing capacity of square and circular
foundations, Terzaghi proposed the following equations:
qu = 1.3cN c + 0.4BN  + qN q
(square)
qu = 1.3cN c + 0.3BN  + qN q
(circular)
For circular foundations, B=diameter of the footing.
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Example Problem 1.1
A square foundation that carries a load of 400kN is to be
placed at a depth of 1.2m in soil with the following strength
parameters:
Φ = 27° and c = 16kN/m2
If the unit weight of the soil is 18.5kN/m3 and assuming a
footing width of 1.1m, estimate the allowable bearing
capacity of the soil using a factor of safety of 3
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Solution
For a square foundation
qu = 1.3cN c + 0.4BN  + qN q
For Φ = 27 ; Nc=29.24, Nq=15.9, Nγ=11.6
Hence,
𝑞𝑢𝑙𝑡 = 1055.596𝑘𝑁/𝑚2
𝑞𝑎𝑙𝑙 =
𝑞𝑢𝑙𝑡
𝐹𝑆
𝑞𝑎𝑙𝑙 = 351.86kN/m2
41
Example Problem 1.2
For a continuous wall footing placed at a depth of 0.6m with
a width of 1.1m, determine the allowable bearing capacity of
the soil with the following strength parameters:
Φ = 0° , c = 67kN/m2 and γ =20.4kN/m3
Assume a factor of safety of 3 against bearing capacity failure
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Effect of Water Table on Bearing
Capacity
43
Effect of Water Table
on Bearing Capacity
• When the water table is close
to the base of the foundation
or even above it, adjustments
to the bearing capacity
equation are required to
account for the effect of the
water.
44
Effect of Water Table –
Case 1 (Water table
above foundation level)
• When the water table is located
above the foundation such that
0≤D1≤Df
• Adjustments
• The parameter  in the second term
of the ultimate bearing capacity
equation should be replaced by the
buoyant unit weight 𝜸′ = 𝜸𝒔𝒂𝒕 − 𝜸𝒘
• The overburden pressure parameter q
in the bearing capacity equation
should be expressed in terms of
effective stress as 𝒒 = 𝜸𝑫𝟏 + 𝜸′𝑫𝟐
𝒒𝒖𝒍𝒕 = 𝒄𝑵𝒄 + 𝟎. 𝟓𝜸′ 𝑩𝑵𝜸 + (𝜸𝑫𝟏 + 𝜸′𝑫𝟐 )𝑵𝒒
45
Effect of Water Table –
Case 2 (Water table at
foundation level)
• When the water table is located at
the foundation level such that Dw=Df
• Adjustments
• The parameter  in the second term
of the ultimate bearing capacity
equation should be replaced by the
buoyant unit weight 𝜸′ = 𝜸𝒔𝒂𝒕 − 𝜸𝒘
𝒒𝒖𝒍𝒕 = 𝒄𝑵𝒄 + 𝟎. 𝟓𝜸′𝑩𝑵𝜸 + 𝒒𝑵𝒒
46
Effect of Water Table –
Case 3 (Water table
below foundation level)
• When D≥B, no effect on bearing
capacity (no adjustments).
• When D<B
Use γav for the 0.5𝛾𝐵𝑁𝛾 term
Df
𝟏
𝑩
Where γav = [𝜸𝑫 + 𝜸′ 𝑩 − 𝑫 ]
B
D
𝒒𝒖𝒍𝒕 = 𝒄𝑵𝒄 + 𝟎. 𝟓𝜸𝒂𝒗 𝑩𝑵𝜸 + 𝒒𝑵𝒒
47
Example Problem 1.3
A 2m by 2m square footing is placed at a depth of 1.8m below
the ground surface. The groundwater table is located at the
ground surface. The subsoil properties are as follows:
Φ = 20° , c = 14kN/m2 and γsat =16.5kN/m3
Assuming a factor of safety of 3 against bearing capacity
failure, determine the allowable bearing capacity of the soil.
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