CN215 Soil Mechanics
s
School of Environment and Technology
Semester 2 Examinations 2007-2008
CN215
SOIL MECHANICS
Instructions to candidates:
Time allowed: TWO hours
Attempt ALL questions in section A
and ONE question from section B
Formulae sheet and Design charts provided
Graph paper provided
9:30-12:30hours, Friday 6 June 2008
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CN215 Soil Mechanics
SECTION A: Attempt ALL questions in this section
Question 1
The cross section of a concrete dam founded on a permeable soil which
overlies an impermeable rock stratum is shown in Figure 1 below.
a)
Draw a flow net for the indicated water levels, assuming the soil to be
isotropic.
(12 marks)
b)
Determine:
i)
The seepage rate under the dam if the permeability of the soil is
0.0175 mm / s. Assume permeability of the soil is the same in all
directions.
(5 marks)
ii)
The uplift pressure on the base of the dam
(8 marks)
+13.5 m
+1.5 m
0.0 m
0.0 m
-3.0 m
18 m
Permeable layer
-18 m
Impermeable layer
Figure 1
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CN215 Soil Mechanics
Question 2
a)
A cylindrical sample of a hard soil with a cohesion c' (due to
cementation) and a friction angle of ' is loaded in unconfined
compression.
i)
Derive an expression for the unconfined compressive stress
(UCS) in terms of c' and '.
(10 marks)
ii)
If the above sample has a UCS value of 1100 kPa and ' = 38
degrees, what is its cohesive strength (c')?
(5 marks)
b)
The plan of a building’s foundation is shown in Figure 2 below. Using
Newmark’s Chart, determine the vertical stress increase at a depth of
3.5 m below the corner at point X if the applied vertical stress is 240
kPa.
(10 marks)
5.0m
0.5m
1.5m
X
1.0m
Figure 2
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CN215 Soil Mechanics
Question 3
a)
The soil profile at a site for a proposed office building consists of a
layer of fine sand 11.0 m thick above a layer of soft normally
consolidated clay 2.2 m thick. Below the soft clay is a deposit of coarse
sand. The ground water table was observed at 2.9 m below ground
level. The void ratio of the sand is 0.78 and the water content of the
clay is 38%.
The building will impose a vertical stress increase of 150 kPa at the
middle of the clay layer.
Estimate the primary consolidation settlement of the clay, assuming the
soil above the water table to be saturated.
f
H0

Cc log( ' ) ; Cc = 0.3; and Gs = 2.7 for both the
1  e0
z
'
[Take:
 pc
clay and sand].
(18 marks)
b)
Define the terms total stress, effective stress and pore pressure and
state the relationship that is assumed to exist between them.
(7 marks)
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CN215 Soil Mechanics
SECTION B: Attempt ONE question from this section
Question 4
a)
What types of laboratory tests are best suited to determine soil strength
parameters for the following construction problems?
i)
the long term stability of a slope in stiff fissured clay
ii)
the initial stability of a footing on saturated clay.
Give reasons for your choice of test.
(6 marks)
b)
The results of an undrained direct shear box test are given in the
following table:
Normal Stress (kPa)
Shear Stress (kPa)
i)
200
113
300
141
400
167
Find the apparent cohesion (cu) and angle of shearing
resistance (u).
(7 marks)
ii)
What value of cu would be expected from an unconfined
compression test on the same soil?
(6 marks)
iii)
If another specimen of this soil is subjected to an undrained
triaxial test with lateral pressure 275 kPa, find the total axial
pressure at which failure would be expected.
(6 marks)
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CN215 Soil Mechanics
Question 5
a)
For the site profile shown in the following table draw total stresses,
pore water pressures and effective vertical stresses against depth for
the following conditions:
i)
water table at the ground surface, and
(6 marks)
ii)
water table at a depth of 2.5m assuming the silty sand stratum
above the water table to remain saturated with capillary water
(i.e. negative pore pressures are present).
(9 marks)
Saturated unit weights of silty sand = 18.5 kN/m3
Saturated unit weights of clay = 17.7 kN/m3
Depth (m)
0-5
5-9
>9
b)
Stratum
Silty sand
Peaty clay
Rock (impermeable)
A fully saturated clay sample has a volume of 185 ml and weighs 331
g. The specific gravity of the soil particles is 2.67. Determine the clay’s:
i)
void ratio,
ii)
porosity,
iii)
moisture content, and
iv)
bulk unit weight.
(10 marks)
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CN215 Soil Mechanics
FORMULAE SHEET AND DESIGN CHARTS
PHASE RELATIONSHIPS
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CN215 Soil Mechanics
PERMEABILITY AND FLOW
The quantity of flow through a given area in a unit time is therefore obtained
as
Q = kAi
Properties of a flow net:
Flow nets are constructed so that the intervals between adjacent
equipotentials represent a constant difference in head (h) and the intervals
between adjacent flow lines represent a constant flow quantity (q).
So, the total head loss,
H = h x no. equipotential intervals
= h x Ne
and the total seepage flow, q = q x no. of flow intervals (channels)
= q x Nf
Isotropic material
q = k h
per flow channel per unit length
H
Ne
per flow channel per unit length
qk
H = total head difference
Qk
H
N f Total flow
Ne
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CN215 Soil Mechanics
Anisotropic model
kh  kv
k  kx
ky
kx
 kxky
Seepage quantity derived from a transformed flow nets;
Q  Ak
Nf
Ne
A
Nf
Ne
kxky
Seepage through earth dams
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CN215 Soil Mechanics
SHEAR STRENGTH
Coulomb’s equation
  c'( n  u ) tan 
  c' n ' tan 
Shear stress

 = c’ + n’ tan ()

'3
c’
'1
Normal eff. stress (
n’)

MOHR CIRCLE OF EFFECTIVE STRESS

C
u
3
1
Normal total stress (
n)
MOHR CIRCLE OF TOTAL STRESS
Deviator stress:
q = 1-3
Undrained shear strength: su = q/2
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CN215 Soil Mechanics
STRESS DISTRIBUTION
Fadum Chart
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CN215 Soil Mechanics
Newmark chart
For a uniform loading intensity of q the stress at the required depth below the
point in question is computed as
v= N x IN x q
N is the number of segments or part segments, IN is the chart influence value
per field
DETACH AND SUBMITT CHART WITH ANSWER BOOK
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