1. GEOTECHNICAL ENGINEERING - II
Engr. Nauman Ijaz
Bearing Capacity of the Soil
Chapter # 05
UNIVERSITY OF SOUTH ASIA

2. FOUNDATION
It is the bottom most structural element of
the sub structure which transmits the
structural load including its own weight on
to and / into the soil
underneath/surrounding with out casing
shear failure or bearing capacity failure
(sudden collapse) and excessive
settlement.

3. CONTACT PRESSURE
The pressure generated by the
structural loading and self weight of
the member on to or into the soil
immediately underneath is called
Contact pressure (σo).
σo = Q / A
The contact pressure is independent of
soil parameters; it depends only on the
load and the x-sectional area of the
element carrying the load.

4. Q = 1000KN
σo = Q / A
= 1000/(0.5 × 0.5)
= 4000 Kpa
A
A
0.5m
Fig # 01
0.5m
Sec A-A

5. Super-Structure and
Sub- Structure
The part of the structure which is above
the GSL and can be seen with naked eye
is known as Super-Structure.
That part of structure which is below the
GSL and can not be seen with naked eyes
is known as Sub-Structure.

6. Q = 1000KN
Super- Structure
GSL
Sub- Structure
Df
B×L (2×2.5 m²)
σo = Q / A
Fig # 02
= 1000/(2 × 2.5)
= 200 Kpa

7. Foundation Depth (Df)
It is the depth below the lowest
adjacent ground to the bottom of the
foundation.
Need or Purpose of a Foundation
Foundation is needed to transfer the
load to the underlying soil assuming
safety against bearing capacity failure
and excessive settlement.

8. This can be done by reducing the contact
pressure such that it is either equal to or less
than allowable bearing capacity (ABC) of soil.
i.e σo < qa.
In Fig- 1, the contact pressure under the concrete
column is 4000Kpa which is much less than 21MPa
(crushing strength of concrete) but much
greater than 200KPa (ABC) of soil and
needed to be reduced prior to transfer it to
the soil underneath the column.
The reduction can be achieved by;

9. Lateral spreading of load using a large
pad underneath the column (Fig # 02)
σo = 1000 /5 = 200Kpa = ABCof soil
The larger pad is known as Spread footing.
FLOATING FOUNDATION
Balance Partly or completely the load
added to the load removed due to
excavation is known as Floating
foundation.i.e Provide basements.

10. Types of Foundation
Foundation may be characterized as
being either “ Shallow” or “Deep”.
Shallow Foundation
Are those located just below the lowest
part of the super structure which they
support ( and get support from the soil
just beneath the footing) and a least
width generally greater than their
depth beneath the ground surface, i.e
Df / B < 1
Df = 3 m (generally)

11. Deep Foundations
Are those which extend considerably
deeper into the earth ( and get supported
from the side friction (skin friction) and / or
bottom (end bearing) and generally with a
foundation depth to width ratio (D/B)
exceeding five.

12. TYPES OF FOUNDATION
Shallow foundations may be classified
in several ways as below;
SPREAD FOOTING OR
INDIVIDUAL FOOTING
This type of foundation supports one column
only as shown below. This footing is also
known as Pad footing or isolated footing. It
can be square or rectangular in shape. This
type of footing is the easiest to design and
construct and most economical therefore.

13. For this type of footing, length to
breadth ratio (L/B) < 5.
PLAN
GSL
ELEVATION

14. ISOLATED FOOTING

15. CONTINUOUS FOOTING
If a footing is extended in one direction
to support a long structure such as
wall, it is called a continuous footing or
a wall footing or a strip footing as
shown below.
Loads are usually expressed in force
per unit length of the footing.
For this type of footing , Length to
Breadth ratio (L/B) > 5.

16. A strip footing is also provided for a row
of columns which are closely spaced that
their spread footings overlap or nearly
touch each other.
In such a case it is more economical to
provide a strip footing than a number of
spread footing in one line.

18. COMBINED FOOTING
A combined footing is a larger footing
supporting two or more columns in one row.
This results in a more even load distribution
in the underlying soil or rock, and
consequently there is less chances of
differential settlement to occur.
While these footings are usually rectangular
in shape, these can be trapezoidal ( to
accommodate unequal column loading or
close property lines)

20. STRAP FOOTING
Two or more footings joined by a beam (called Strap)
is called Strap Footing.
This type is also known as a cantilever footing or
pump-handle foundation.
This form accommodates wide column spacing's or
close property lines.
Strap is designed as a rigid beam to with stand
bending moments, shear stresses.
The strap simply acts as a connecting beam and does
not take any soil reaction.
To make this sure, soil below is dug and made loose.

22. MAT OR RAFT FOOTING
A large slab supporting a number of
columns not all of which are in a straight
line is known as Mat or Raft or Mass
foundation.
These are usually considered where the
base soil has a low bearing capacity and /
or column loads are so large that the sum
of areas of all individual or combined
footings exceeds one half the total building
area ( to economize on frame costs).

23. Furthermore, mat foundations are useful in
reducing the differential settlements on
individual columns.
A particular advantage of mat for basement
at or below ground water table is to provide
a water barrier.

25. SELECTION OF FOUNDATION TYPE
The selection of the type of foundation for a
given structure-subsoil system is largely a
matter of judgment/elimination based on
both an analysis of scientific data and
experience.
It is not possible to establish rigorous
regulations and detailed recommendations
for the solution of all soil problems, as the
planning and designing of foundations for
structures is more of an art than a science.

26. 1.
The type of foundation most appropriate for a
given structure depends on several factors
but commonly the principal factors are three
which are as follow:
The function of the structure and the
loads it must carry.
– Purpose of the structure i.e residential, office,
industrial, bridge etc
– Service life
– Loading number of stories, basement.
– Type i.e framed RCC, masonry, column
spacing etc.
– Construction method and schedule.

27. 2.
Sub-surface Condition.
– Thickness and sequence of soil strata
with subsoil parameters.
– GWT position and function limits.
– Presence of any underground
anomalies.
3.
The cost of foundation in
comparison with the cost of the
super structure i.e funds available
for the construction and foundation.

28. COMPARISON OF SHALLOW
AND DEEP FOUNDATIONS
Sr/No
DESCRIPTION
SHALLOW FOUNDATION
DEEP FOUNDATION
1
Depth
Df / B < 1
Df / B > 4+
2
Load Distribution
Lateral Spread
Lateral and/or Vertical
spread.
•For end bearing lateral
spread.
•For frictional vertical
spread.
•Generally both.
3
Construction
•Open pit construction.
•Easy control and the best
QA/QC.
•Less skill labour is required.
•Min. Disturbance.
•During construction
dewatering is required for
shallow GWT.
•In hole or driven
•Difficult QA/QC.
•Very skilled labour is
required.
•Max.disturbance.
•Dewatering may or may
not be required.

29. Sr/No
DESCRIPTION
SHALLOW
FOUNDATION
DEEP
FOUNDATION
4
Cost
Less as compared
with deep
foundations.
Usually 3 times or
more costly than
shallow.
5
Structural Design
Consideration
Flexural bending
Axial Compression
6
Settlement
More than that of
deep foundation.
Usually 50% of the
shallow foundation
for similar loading.
7
Environmental Suitability
Does not suit to all
environments
specially for off
shores sites.
Suitable for all
environment
including off shore.

30. CRITERIA FOR FOUNDATION
DESIGN
1.
2.
When designing foundation; there are two
criteria which must be considered and
satisfied separately.
There must be accurate factor of safety
against a bearing capacity failure in the
soil i.e soil shouldn’t fail in shear.
The settlement and particularly the
differential settlement must be kept within
reasonable limits.

31. Causes of Deformation
Deformation of an element of soil is a function
of a change in effective stress (change in
volume) not change in total stress. Various
causes of deformation of a structure are listed
as follow;
1.
2.
3.
4.
5.
Application of structural loads.
Lowering of the ground water table.
Collapse of soil structure on wetting.
Heave of swelling soils.
Deterioration of the foundation ( Sulphate attack
on concrete, corrosion of steel piles, decay of
timber piles).

32. 6. Vibration of sandy soil.
7. Seasonal moisture movement.
8. The effect of frost action.

33. DEFINITIONS OF
BEARING PRESSURE
Gross Bearing Pressure (q gross):
The intensity of vertical loading at the base
of foundation due to all loads above that
level.
2. Net Bearing Pressure: (q net):
The difference between q gross and the total
overburden pressure Po at foundation level
(i.e q net = q gross – Po). Usually q net is the
increase in pressure on the soil at
foundation level.
1.

34. 3. Gross Effective Burden Pressure (q’gross):
The difference between the qgross and the
pore water pressure (u) at foundation level.
(i.e q’gross = qgross – u).
4. Net Effective Bearing Pressure (q’net):
The difference between q’gross and the
effective over burden pressure Po at
foundation level. (i.e q’net = q’gross – Po).
5. Ultimate Bearing Pressure (qf):
The value of bearing pressure at which the
ground fails in shear. It may be expressed as
gross or net or total effective pressure.

35. 6. Maximum Safe Bearing Pressure (qs):
The value of bearing pressure at which the risk
of shear failure is acceptably low; may be
expressed as gross or net or effective pressure.
7. Allowable Bearing Pressure (qa):
Takes account the tolerance of the structure to
settlement and may be much less than qs.
8. Working Bearing Pressure (qw):
Bearing Pressure under working load. May be
expressed as gross or net or total or effective
pressure.

36. FAILURE MODES
A soil underneath any foundation may fail in
one or a combination of the following three
modes;
1. General Shear Failure.
2. Punching Shear Failure.
3. Local Shear Failure. (an intermediate mode of
failure between conditions a and b)

37. GENERAL SHEAR FAILURE
Results in sudden catastrophic associated
with plastic flow and lateral expulsion of
soil.

38. Failure usually accompanied by tilting and
failure signs are imminent around the
footing.
The soil adjacent to the footing bulges
Failure load is well defined on the load
settlement graph.
Shallow foundations on dense/hard soil
and footing on saturated NCC under undrained loading.
Relative density RD > 70%
Void Ratio < 0.55 dense.

39. PUNCHING SHEAR FAILURE
Failure Mechanism, relatively slow ,no
lateral expulsion, failure is caused by
compression of soil underneath the
footing.

40. Failure is confined underneath the footing and no
signs of failure are visible around the foundation.
No tilting the footing settle almost uniformly.
Failure load is difficult to be defined from the shape
of load-settlement graph. There is continuous
increase in load with settlement.
Foundation in and/or on loose/soft soils placed at
relatively shallow depth undergoes such type of
failure.
Footing on saturated NCC under drained loading.
RD < 20%, Void Ratio > 0.75 loose.

41. LOCAL SHEAR FAILURE
Failure is between the
General shear and
Punching shear.
Footing on saturated
NCC under drained
loading undergoes
such type of failure.
RD < 20%, Void ratio
> 0.75, loose.

42. SOURCES OF OBTAINING
BEARING CAPACITY
VALUES
1.
2.
3.
4.
5.
Building codes, official regulations and civil
engineering handbooks (Prescriptive
method).
Soil Load Test.
Laboratory Testing.
Method based on observations ( used for
embankment design).
Analytical Method (Bearing Capacity
theories)

43. BUILDING CODES
In building codes bearing capacity values
are tabulated for various type of soil. These
values are based on many years of
observation in practice as shown in table
represents presumptive (Presumed) bearing
capacity values of National Building Code
(NBC).
These values may be used for preliminary of
feasibility design.

44. MERITS AND DEMERITS OF
CODE VALUES
MERITS:
1. These values are used for preliminary
design because of their readily
availability and economy.
2. For small jobs in the areas for which the
code values have been listed, final
designs may be based on these values.

45. DEMERITS:
1. The tabulated values neglect to report the
effects of moisture, density and other soil
properties which are known to have influence
on bearing capacity.
2. The Building Codes do not indicate how and
what methods are used to arrive at these
values.
3. Effect of shape, size and depth of foundation
is ignored.
4. Values of building Codes are not usually
updated.
5. Type of structure is not taken into account.

46. PRESUMPTIVE BEARING CAPACITY VALUES
OF NATIONAL BUILDING CODE
SOIL TYPE
MAX. BEARING CAPACITY (TSF)
CLAY:
SOFT
MEDIUM STIFF
1 TO 1.5
2.5
COMPACT (FIRM)
2
HARD
5
SAND:
FINE, LOOSE
2
COARSE, LOOSE
3
COMPACT,COARSE
4 TO 6
GRAVEL:
LOOSE
4 TO 6
SAND – GRAVEL MIXTURE COMPACT
6
VERY COMPACT
10

47. SOIL TYPE
MAX. BEARING CAPACITY (TSF)
SAND-CLAY MIX., COMPACT
3
SAND-CLAY MIX, LOOSE,SATURATED
1
HARD PAN, COMPACTED OR
CEMENTED
10 to 12
ROCK:
SOFT
8
MEDIUM HARD
40
HARD
60
SEDIMENTARY ROCK:
SHALE
8 to 10
HARD SHALE
8 to 10
LIME STONE
10 to 20
SAND STONE
10 to 20
Chalk
8
IGNEOUS ROCKS:
GRANITE,LAVA,BASALT,DIORITE etc
20 to 40 to 100

48. TERZAGHI’S THEORY
Terzaghi modified the Prandtl’s theory and
presented a classic bearing capacity equation
(1943) which is still in use in its original form and in
many modified forms proposed by various
research workers.
ASSUMPTIONS:
1. Footing base is rough.
2. Footing is shallow; i.e Df / B < 1 and shear along CD is
neglected.
3. Footing is a strip footing i.e L/B > 10 and the stress
distribution is assumed to be plain.

49. FOOTING MODEL USED BY TERZAGHI TO DETERMINE qult

50. In fig zone I forms wedge under the footing and moves
downward with footing. The soil in zone II and III are in state of
general shear failure and move up and away from the footing as
it moves down into the soil.
Terzaghi considered the equilibrium of the wedge ABC and
summing up the vertical forces ΣFv = 0 produced the following
equation for (c-ϕ) soil.
qult
=
c Nc
cohesion
+
q Nq
+ 0.5 γ B Nγ
overburden
Friction
Where;
qult = Gross ultimate bearing capacity including the effect of Terzaghi
overburden pressure, q = γDf
Ni = Bearing capacity factors, the values of which depends on angle of
internal friction ϕ.

51. The first term is the cohesion term and accounts
for cohesive resistance along failure surface.
The 2nd term is the surcharge term and accounts
for the resistance supplied by the mass of soil
above the base of footing.
The third term is the self weight term and accounts
for frictional resistance generated along failure
surface. The self weight is a function of the footing
width B because increasing the footing width
increases volume of soil in zone II and III, thereby
increasing the normal forces acting on the failure
surface in turn increases the resistance along the
failure surface.

52. The safe bearing capacity values are
computed by dividing the ultimate values of
gross or net bearing capacity by an appropriate
factor of safety usually 3 or more.
qs net = Safe bearing capacity = qult net / FOS
qs
= Safe gross bearing capacity
= qult net / FOS + γDf

53. BEARING CAPACITY FACTORS OF
TERZAGHI

54. Later on Terzaghi proposed shape
factors Sc and Sγ for the first and last
terms of equation to account for the
different shapes of the footings such
as circular, square, rectangular etc.
SHAPE
FACTOR
STRIP
CIRCULAR
Square
Rectangular
Sc
1
1.3
1.3
1 + 0.2 (B/L)
Sγ
1
0.6
0.8
1- 0.2 (B/L)

55. Terzaghi's bearing capacity Eq. has been modified for other types
of foundations by introducing the shape factors. The equations
are:
– Square Foundations:
– Circular Foundations:
– Rectangular Foundations:

56. MAYERHOFF GENERAL BEARING CAPACITY EQUATION

57. M A Y E R H O F ’ S B E A R I N G CAPACITY
FACTORS
ϕ
Nc
Nq
Nγ
0
5.1
1
0
5
6.5
1.6
0.1
10
8.3
2.5
0.4
15
11
3.9
1.2
20
14.9
6.4
2.9
25
20.7
10.7
6.8
30
30.1
18.4
15.1
35
46.4
33.5
34.4
40
75.3
64.1
79.4

58. EFFECT OF GROUND WATER TABLE
If there is enough water in the soil to
develop a ground water table, and this
ground water table is within the potential
shear zone, then pore water pressure will be
present, the effective stress and shear
strength along the failure surface will be
smaller and the ultimate bearing capacity
will be reduced.
When exploring the sub-surface conditions,
we determine the current location of the
ground water table and worst case (highest)
location that might reasonably be expected
during the life of the proposed structure.

59. We have three cases that describes the
worst-case field conditions.
Case – I :
Ground water table is at or above base of footing
(Dw < D). We simply compute γ’ = γb = γ - γw
Case – II :
Ground water table is below the base of
the footing, but still within the potential
Shear zone, below the footing (D < Dw <
D+B), we interpolate γ’ between buoyant unit
weight and unit weight using,
γ’ = γ – γw [1 – (Dw – D)/ B]

60. Case # I
Ground water table
above base of
footing
Case # II
Ground water table
In this zone
Case # III
Ground water table
Deeper than D+B

61. Case – III :
Ground water table is below the
potential shear zone below the footing
(D + B < Dw ), no ground water
correction is necessary.
γ’ = γ

62. NUMMERICAL PROBLEM :
Compute the FOS against a bearing
capacity failure for the square spread
footing as shown in the figure with ground
water table at position A.

63. SOLUTION :
D = 2ft
Dw = 7ft
D + B = 6ft
D+B < Dw, so ground water Case#III applies γ’ = γ.
From the table ;
Nc = 40.40, Nq = 25.30, Nγ = 23.70 when ϕ’ = 31o
Terzaghi’s equation for square footing;
qu = 1.3×0×40.4 + 121×2×25.3 + 0.4×121×4×23.70
qu = 10,710 lb/ft2

64. q = P/A + γc D - u
q = 76000/(4×4) + (150×2) – 0
q = 5050 lb/ft2
Factor of safety = FOS = F = qult / q
F = 10,710/5050
F = 2.1

65. NUMMERICAL PROBLEM :
Compute the FOS against a bearing
capacity failure for the square spread
footing as shown in the figure with ground
water table at position B.

66. SOLUTION :
D = 2ft
Dw = 3ft
D + B = 6ft
D < Dw < D+B, so ground water Case#II applies.
γ’ = γ – γw [1 – (Dw – D)/ B]
γ’ = 121 – 62.4 [1 – (3 – 2)/ 4] = 74.2 lb/ft3
From the table ;
Nc = 40.40, Nq = 25.30, Nγ = 23.70 when ϕ’ = 31o
Terzaghi’s equation for square footing;
qu = 1.3×0×40.4 + 121×2×25.3 + 0.4×74.2×4×23.70
qu = 8936 lb/ft2

67. q = P/A + γc D - u
q = 76000/(4×4) + (150×2) – 0
q = 5050 lb/ft2
Factor of safety = FOS = F = qult / q
F = 8936/5050
F = 1.8

68. NUMMERICAL PROBLEM :
A1350KN column load is to be supported on a square
spread footing founded in a clay with Su = 150Kpa. The
depth of embedment, D will be 500mm, and the soil has a
unit weight of 18.5KN/m3.The ground water table is at a
considerable depth below the bottom of the footing.
Using FOS of 3, determine the required footing width.
Case # III applies. As ground water table is at
considerable depth below the bottom of footing.
γ’ = γ
From the table ;
Nc = 5.7, Nq = 1.0, Nγ = 0.0 when ϕ’ = 0o
Terzaghi’s equation for square footing;
qu = 1.3×150×5.7 + 18.5×0.5×1.0 + 0.4×18.5×B×0
qu = 1121 KPa

69. Factor of safety = FOS = F = qult / qa
qa = qult / F = 1121 / 3 = 374 Kpa
qa = P/A + γc D - u
374 = 1350/(B2) + (23.6×0.5) – 0
B = 1.93 m
Round up = 2m

70. STANDARD PENETRATION TEST
One of the oldest and most common in-situ test is
the Standard Penetration test.
It was developed in the late 1920’s and has been
extensively used in North and South America, UK
and Japan.
ASTM Standard D 1586.
It consists of Penetrometer having diameter 51mm
and 600mm long tube.
The penetrometer is connected to the surface with
standard rods and is hammered into the ground
with a tip hammer.

71. TEST PRODEDURE
1.
2.
3.
4.
The test procedure according to ASTM D1586 are as follow;
Drill a 60-200mm (2.5 – 8inch) diameter exploratory boring to
the depth of the first test.
Insert the SPT sampler (also known as SPLIT-SPOON
Sampler) into the boring. Shape and dimensions are shown in
the figure. It is connected via steel rods to a 63.5Kg (140lb)
hammer.
Use either rope or an automatic tripping mechanism.
Raise the hammer to a height 760mm (30inch) and allow it to
fall. This energy derives the sampler into the bottom of the
boring. Repeat the process until the sampler has penetrated a
distance of 460mm (18inch), recording the number of hammer
blows required for each 150mm (6inch) interval. Stop the test if
more than 50 blows are required for any of the intervals or if
more than 100 total blows are required.

72. 5. Either of these events is known as Refusal and is noted on
the boring logs.
6. Compute the N-value by summing the blow counts for the
last 300mm (12inch) of penetration. The blow count for the
first 150mm (6inch) is retained for reference purpose, but
not used to compute N because the bottom of the boring is
likely to be disturbed by the drilling process and may be
covered with loose soil left in the boring.
7. Extract the SPT sampler, then remove and save the soil
sample.
8. Drill the boring to the next test and repeat the same
procedure.

75. IMPORTANT POINTS
Soft or very loose soil typically have NValues less than 5.
Soil of average stiffness generally
have 20< N <40.
Very dense and hard soils have N of
50 or more.
Very high N-values > 75 typically
indicate very hard soil or rock.

76. What is SPT – N value??
Number of blows required to penetrate
split spoon sampler for 12inch
penetration when a standard weight of
140lbs is dropped from a standard
height of 30inches.

77. ADVANTAGES
1.
2.
3.
SPT does have at least three important
advantages over other in-situ methods.
First, it obtains a sample of the soil being tested.
This permit direct soil classification. Most of the
other methods do not include sample recovery.
It is very fast and inexpensive test.
Nearly all drill rigs used of soil exploration are
equipped to perform this test. Whereas other insitu test requires specialize equipment that may
not readily available.

78. ASSIGNMENT
A foundation 3.0m square is placed at 1.5m
below the GSL on a uniform deposit of
sandy gravel having following properties.
1.
2.
3.
4.
c’ = 0, ϕ’ = 32o γ = 19.5 KN/m³ γ’ = 10.5 KN/m³
Calculate the gross ultimate bearing capacity for
the following position of water table:
GWT well below the zone of influence.
GWT at the base of the footing.
GWT rises to the GSL.
GWT at 2m below the footing base.