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WORKBOOK
Shallow foundations ©drknmy2013
1 page
Define the following terms:
(a) Foundation;
(b) Base of the foundation;
(c) Embedment depth;
(d) Shallow foundation;
(e) Ultimate bearing
capacity;
(f) Allowable bearing
capacity;
(g) Factor of safety.
QUEST IONSOLUTIONS
2 page
SOLUTIONS
3 page
What are the ultimate net
bearing capacity and the
allowable bearing capacity
of shallow footings? and
How do I determine the
allowable bearing capacity
for shallow footings?
QUEST IONSOLUTIONS
4 page
SOLUTIONS
5 page
What are the assumptions
made in bearing capacity
analyses?
What soil parameters are
needed to calculate its
bearing capacity?
What effects do
groundwater and eccentric
loads have on bearing
capacity?
QUEST IONSOLUTIONS
6 page
SOLUTIONS
7 page
What are the assumptions
made in the derivation of
Terzhagi’s bearing
capacity theory?
Write the equation for the
ultimate bearing capacity
in local shear is
determined?
QUEST IONSOLUTIONS
8 page
SOLUTIONS
9 page
Differentiate between the
general shear failure and
the local shear failure. How
the ultimate bearing
capacity in local shear is
determined?
QUEST IONSOLUTIONS
10 page
SOLUTIONS
11 page
Discuss the effect of water
table on the bearing
capacity of the soil.
QUEST IONSOLUTIONS
12 page
SOLUTIONS
13 page
Discuss Meyerhof’s
bearing capacity theory.
How does it differ from
Terzhagi’s theory.
QUEST IONSOLUTIONS
14 page
SOLUTIONS
15 page
To obtain a higher bearing
capacity, either width of
the footing could be
increased or the depth of
foundation can be
increased. Discuss
critically the relative merits
and demerits.
QUEST IONSOLUTIONS
16 page
SOLUTIONS
17 page
Discuss the various factors
that affect the bearing
capacity of a shallow
footing. Write brief critical
notes on settlement of
foundations. How do you
ascertain whether a
foundation soil is likely to
fail in local shear or in
general shear?
QUEST IONSOLUTIONS
18 page
SOLUTIONS
19 page
Discuss the various types
of foundations and their
selection with respect to
different situations.
QUEST IONSOLUTIONS
20 page
SOLUTIONS
21 page
Discuss the effect of
shape on the bearing
capacity. Differentiate
between safe bearing
capacity and allowable soil
pressure.
QUEST IONSOLUTIONS
22 page
SOLUTIONS
23 page
Bring out clearly the effect
of ground water table on
the safe bearing capacity.
QUEST IONSOLUTIONS
24 page
SOLUTIONS
25 page
Describe the procedure of
determining the safe
bearing capacity based on
the standard penetration
test.
QUEST IONSOLUTIONS
26 page
SOLUTIONS
27 page
Explain the recommended
construction practices to
avoid detrimental
differential settlement in
large structures.
QUEST IONSOLUTIONS
28 page
SOLUTIONS
29 page
What is meant by bearing
capacity of soil? How will
you determine it in the
field? Describe the
procedure bringing out its
limitations.
QUEST IONSOLUTIONS
30 page
SOLUTIONS
31 page
Write brief critical notes
on:
(i) Standard Penetration
test
(ii) General shear failure
and local shear failure of
shallow foundations.
QUEST IONSOLUTIONS
32 page
SOLUTIONS
33 page
Give the algebraic
equations showing the
variation of safe bearing
capacity of soil (for clay
and sand to be given
separately) in shallow
foundation with:
(i) depth of foundation; (ii)
width of foundation; and
(iii) position of water table.
QUEST IONSOLUTIONS
34 page
SOLUTIONS
35 page
For the following cases,
determine the allowable
gross vertical load-bearing
capacity of the foundation.
Use Terzaghi’s equation
and assume general shear
failure in soil. Use FS =
4.00.
Part B(m)
Df(m) ’
(a) 1.22 0.91 25(b) 2 1 30(c) 3 2 30
Part c’(kN/m2)
(kN/m3)
(a) 28.75 17.29(b) 0 17(c) 0 16.5
Use continuous type for (a)
and (b), and square type
for (c).
(Answer: (a): 252.6 kN/m2;
(b) 176.8 kN/m2; (c) 280
kN/m2)
QUEST IONSOLUTIONS
36 page
SOLUTIONS
37 page
A square column
foundation has to carry a
gross allowable load of
1805 kN (FS = 3.0). Given:
Df = 1.5 m, = 15.9
kN/m3, ’ = 34, and c’ =
0. Use Terzaghi’s equation
to determine the size of
the foundation (B).
Assume general
shear failure.
(Answer: B = 2 m)
QUEST IONSOLUTIONS
38 page
SOLUTIONS
39 page
Use the general bearing
capacity equation to solve
C1 question.
(Answer: (a): 267.6 kN/m2;
(b) 184.7 kN/m2;
(c) 368.8 kN/m2)
QUEST IONSOLUTIONS
40 page
SOLUTIONS
41 page
The applied load on a
shallow square foundation
makes an angle of with the
vertical. Given: B = 1.83
m, Df = 0.9 m, = 18.08
kN/m3, ’ = 25, and c’ =
23.96 kN/m3. Use FS =
4.0 and determine the
gross allowable load. Use
Meyerhof’s method.
QUEST IONSOLUTIONS
42 page
SOLUTIONS
43 page
A column foundation,
showed below, is in plan.
Given: B = 3 m, L = 2 m,
Df = 1.5 m, D1 = 1 m, D2 =
0.5 m, ’ = 25, and c’ =
70 kN/m3. 1 = 17 kN/m3,
2 = 19.5 kN/m3. Use FS
= 3.0 and determine the
net allowable load the
foundation could carry.
Use Meyerhof’s method.
(Answer: 5760 kN)
QUEST IONSOLUTIONS
44 page
SOLUTIONS
45 page
For a square foundation
that is B x B in plan,
vertical gross allowable
load, Qall = 3330 kN, Df =
2 m, = 16.5 kN/m3, ’ =
30, and c’ = 0 kN/m3, FS
= 4.0. Determine the size
of the foundation. Use
Meyerhof’s method.
(Answer: B 3 m)
QUEST IONSOLUTIONS
46 page
SOLUTIONS
47 page
An eccentrically loaded
foundation is shown in
figure down below. Use FS
of 4 and determine the
maximum allowable load
that the foundation can
carry. Use Meyerhof’s
effective
area method.
(Answer: 377.8 kN)
QUEST IONSOLUTIONS
48 page
SOLUTIONS
49 page
Repeat C7 using Prakash
and Saran’s method.
(Answer: 287.37 kN)
QUEST IONSOLUTIONS
50 page
SOLUTIONS
51 page
A square footing is shown
in figure down below. Use
FS = 6 and determine the
size of the footing. Use
Prakash and Saran theory.
(Answer: qu (eccentric) =
936.47 kN/m2, Qu = 1066
kN/m)
QUEST IONSOLUTIONS
52 page
SOLUTIONS
53 page
Determine the ultimate
bearing capacity of a
square footing of size 1.2
m if the depth of
foundation is 1 m. Take c’
= 25 kN/m2, = 18 kN/m3
and c = 15 kN/m2.
QUEST IONSOLUTIONS
54 page
SOLUTIONS
55 page
A circular foundation is of
2.4 m diameter. If the
depth of foundation is 1 m,
determine the net
allowable load. Take =
19 kN/m3, c' = 30 kN/m2,
' = 15° and factor of
safety as 3.0. Use
Terzaghi's equation and
assume local shear failure.
QUEST IONSOLUTIONS
56 page
SOLUTIONS
57 page
A square column
foundation has to carry a
gross allowable load of
1805 kN (FS = 3.0). Given:
Df = 1.5 m, = 15.9
kN/m3, ’ = 34, and c’ =
0. Use Terzaghi’s equation
to determine the size of
the foundation (B).
Assume general
shear failure.
(Answer: B = 2 m)
QUEST IONSOLUTIONS
58 page
SOLUTIONS
59 page
A square footing with a
size of 8 ft by 8 ft is to
carry a total load of 40
kips. The depth of the
footing is 5 ft below the
ground surface, and
groundwater is located at
the ground surface. The
subsoil consists of a
uniform deposit of
soft clay, the cohesion of
which is 500 lb/ft2. The
soil’s unit weight is
110 lb/ft3. Compute the
factor of safety against
bearing capacity failure.
QUEST IONSOLUTIONS
60 page
SOLUTIONS
61 page
A square footing 0.3 m by
0.3 m is placed on the
surface of a dense
cohesionless sand (unit
weight 18.2 kN/m3) and
subjected to a load test. If
the footing fails at a load of
13.8 kN, what is the value
of for the sand?
QUEST IONSOLUTIONS
62 page
SOLUTIONS
63 page
A load test is performed
on a 0.3-m by 0.3-m
square footing on a dense
cohesionless sand (unit
weight 18.0 kN/m3). The
footing’s base is located
0.6 m below the ground
surface. If the footing fails
at a load of 82 kN, what is
the failure load per unit
area of the base of a
square footing 2.0 m by
2.0 m loaded with its base
at the same depth in the
same materials?
QUEST IONSOLUTIONS
64 page
SOLUTIONS
65 page
A square footing 2 m by 2
m is to be constructed
1.22 m below the ground
surface, as shown in
figure below. The
groundwater table is
located 1.82 m below the
ground surface. The
subsoil consists of a
uniform, medium dense,
cohesionless soil with the
following properties: Unit
weight of soil = 18.53
kN/m3; = 32; c = 0 kPa.
Determine the foundation
soil’s allowable bearing
capacity if a factor of
safety of 3 is used.
QUEST IONSOLUTIONS
66 page
SOLUTIONS
67 page
A square footing is to be
constructed on a uniform
thick deposit of clay with
an unconfined
compressive strength of 3
kips/ft2. The footing will be
located 5 ft below the
ground surface and is
designed to carry a total
load of 300 kips. The unit
weight of the supporting
soil is 128 lb/ft3. No
groundwater was
encountered during soil
exploration. Considering
general shear, determine
the square footing
dimension, using a factor
of safety of 3.
QUEST IONSOLUTIONS
68 page
SOLUTIONS
69 page
A proposed square footing
carrying a total load of 500
kips is to be constructed
on a uniform thick deposit
of dense cohesionless soil.
The soil’s unit weight is
135 lb/ft3, and its angle of
internal friction is 38. The
depth of the footing is to
be 5 ft. Determine the
dimension of this
proposed footing, using
a factor of safety of 3.
QUEST IONSOLUTIONS
70 page
SOLUTIONS
71 page
A wall footing is to be
constructed on a uniform
deposit of stiff clay, as
shown in figure. The
footing is to support a wall
that imposes 130 kN/m of
wall length. Determine the
required width of the
footing if a factor of safety
of 3 is used.
QUEST IONSOLUTIONS
72 page
SOLUTIONS
73 page
Compute and draw soil
pressure diagrams for the
footing shown in figure for
P = 70 kips and H = 20
kips.
QUEST IONSOLUTIONS
74 page
SOLUTIONS
75 page
Compute and draw soil
pressure diagrams for the
footing shown in figure for
P = 70 kips and H = 10
kips.
QUEST IONSOLUTIONS
76 page
SOLUTIONS
77 page
Considering general shear,
compute the safety factor
against a bearing capacity
failure for each of the two
loadings in Problem 9–14
if the bearing soil is
cohesionless, = 30; =
110 lb/ft3; and c = 0 kPa.
groundwater is 10 ft below
the base of the footing
QUEST IONSOLUTIONS
78 page
SOLUTIONS
79 page
Considering general shear,
compute the safety factor
against a bearing capacity
failure for each of the two
loadings in Problem 9–14
if the bearing soil is
cohesive, = 0; = 110
lb/ft3; and c = 3000 lb/ft2.
groundwater is 10 ft below
the base of the footing
QUEST IONSOLUTIONS
80 page
SOLUTIONS
81 page
Considering general shear,
compute the safety factor
against a bearing capacity
failure for each of the two
loadings in Problem 9–14
if the bearing soil is
cohesive, = 0; = 110
lb/ft3; and c = 3000 lb/ft2.
groundwater is located at
the ground surface.
QUEST IONSOLUTIONS
82 page
SOLUTIONS
83 page
Considering general shear,
compute the safety factor
against a bearing capacity
failure for each of the two
loadings in Problem 9–14
if the bearing soil is
cohesionless, = 30; =
110 lb/ft3; and c = 0 lb/ft2.
groundwater is located at
the ground surface.
QUEST IONSOLUTIONS
84 page
SOLUTIONS
85 page
For the footing shown in
figure, the vertical load,
including the column
load, surcharge weight,
and weight of the footing,
is 120 kips. The horizontal
load is 10 kips, and a
moment of 50 ft-kips
(clockwise) is also
imposed on the
foundation. 1. Compute
the soil contact pressure
and draw the soil contact
pressure diagram. 2.
Compute the shear on
section a–a (Figure 9–47).
3. Compute the moment
on section a–a (Figure 9–
47). 4. Compute the factor
of safety against
overturning. 5. Compute
the factor of safety against
sliding if the coefficient of
friction between the soil
and the base of the footing
is 0.60.
6. Compute the factor of
QUEST IONSOLUTIONS
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SOLUTIONS
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Das (2011)
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