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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

86 page

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SOLUTIONS

88 page

Das (2011)

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Das (2011)

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Das (2011)

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