CN215 SOIL MECHANICS 2
School of Environment & Technology
Semester 2 Examinations June 2014
CN215
SOIL MECHANICS 2
Instructions to Candidates:
Time allowed: TWO hours
Attempt ALL questions in section A & ONE question from section B.
Formulae sheet, design charts and graph paper provided.
Items permitted: Any approved calculator. Calculators may be used provided they
are battery-operated, silent and not pre-programmed.
2–13 June 2014
Page 1 of 11
CN215 SOIL MECHANICS 2
SECTION A: Attempt ALL questions in this section
Question 1
a)
Indicate if the statements below are true or false:
i
ii
iii
iv
If a load is applied slowly on the surface of a cohesionless soil, excessive
pore water pressure will be generated.
The permeability of a soil is a function of its grain size.
An undrained direct shear test carried out on a sample of clay could take
several days to complete.
If there is no time for the water to drain from a fine soil, the undrained
shear strength should be used.
(8 marks)
b)
A sand layer 5m deep lies over a layer of clay which has a depth of 6m. The
saturated unit weights of both the sand and clay layers are given in Table 1
below. The water table is at the ground surface and the unit weight of water is
10 kN/m3.
i) Calculate the total stress, pore water pressure and effective vertical stress at
the centre of the clay layer.
(6 marks)
ii) A fill material of 4 m depth and of a bulk unit weight shown in Table 1 is
placed on the ground surface over an extensive area. Determine the effective
vertical stress and the pore water pressure at the centre of the clay layer
immediately after the fill has been placed, assuming this takes place rapidly
and the permeability of the clay is very low.
(6 marks)
iii) Determine the effective vertical stress and the pore water pressure at the
centre of the clay layer many years after the fill has been placed.
(5 marks)
Table 1
Soil
layer
sand
clay
fill
Bulk unit weight
(kN/m3)
Saturated unit weight
(kN/m3)
19
20
18
Page 2 of 11
CN215 SOIL MECHANICS 2
Question 2
Figure 1 shows the plan of a square raft foundation at a swallow depth in a soil
mass. The foundation carries a vertical load of 2000 kN. The soil profile and the
values of the drained Young’s modulus of each soil layer are listed in Table 2 below.
Figure 1
5.6 m
5.6 m
Table 2
Soil type
Sand
Alluvial Clay
Depth (m)
0-8
8 - 14
E' (MPa)
12
3
a)
Determine the vertical stress at a point 6 m below the centre of the foundation
assuming that the load acts as a point load at the centre of the foundation.
(4 marks)
b)
Assuming that the load is uniformly distributed over the foundation calculate
the following:
i)
The vertical stress at a point 4 m below the centre of the foundation
using Fadum’s (1948) chart.
(8 marks)
ii)
The vertical stress at a point 11 m below the centre of the foundation
using Newmark’s (1942) chart. Assume that the influence value for
Newmark’s chart (IN) is equal to 0.005.
(8 marks)
iii)
The elastic settlement under the centre of the foundation.
(5 marks)
Page 3 of 11
CN215 SOIL MECHANICS 2
Question 3
a) Indicate if the statements below are true or false:
i
iii
Excess pore water pressure is generated at the end of the consolidation
process of a fine material.
The distribution of pore water pressure in an oedometer sample at any
given time after an increase in external loading is represented by a line
called isochrone.
An excavation carried out in saturated clay will cause heave movements.
iv
The coefficient of volume compressibility mv has units of kN/m2.
ii
(8 marks)
b) The results obtained from an oedometer test on a sample of clay are given in
Table 3 below:
Table 3
v (kPa)
Void ratio e
50
100
200
400
800
600
400
1.191
1.165
1.138
0.983
0.830
0.842
0.857
i) Plot a graph of the specific volume against the natural logarithm of the
vertical effective stress. Indicate the one-dimensional normal compression line
on the graph.
(7 marks)
ii) Calculate the preconsolidation pressure and determine the slopes of the
one-dimensional normal compression and unloading/reloading lines.
(10 marks)
Page 4 of 11
CN215 SOIL MECHANICS 2
SECTION B: Attempt ONE question from this section
Question 4
Table 4 below lists data obtained from consolidated undrained triaxial tests on soft
clay.
Table 4
Tests
1
2
3
i)
Cell pressure
(kPa)
100
200
400
Deviator stress
(kPa)
62
120
230
Pore pressure
(kPa)
50
103
215
Draw the Mohr’s circles of effective stress for all tests and determine the value
of φ' at failure.
(12 marks)
ii)
Plot the critical state line and determine the critical state parameter M.
(9 marks)
iii)
Would failure occur on a plane within a mass of this soil at a point where the
shear stress is 70 kPa and the vertical effective stress is 200 kPa? Justify
your answer.
(4 marks)
Page 5 of 11
CN215 SOIL MECHANICS 2
Question 5
Figure 2 shows the cross section of a concrete dam founded on permeable soil,
below which there is an impermeable stratum.
i)
Draw a flow net on graph paper assuming the soil to be isotropic.
(10 marks)
ii)
Calculate the seepage rate under the dam if the permeability is:
k=12.5 ∙10-3 mm/s.
(5 marks)
iii)
Calculate the total uplift force per metre run of dam that acts on the base of
the dam.
(10 marks)
Impermeable
Figure 2
Page 6 of 11
CN215 SOIL MECHANICS 2
FORMULAE SHEET AND DESIGN CHARTS
Soil Physical Relations
TERM
SYMBOL
UNITS
Moisture content
w
%
Void ratio
(Partially saturated)
e
ratio
Void ratio
(Fully saturated)
e
ratio
Porosity
n
ratio
Specific volume
v
ratio
Degree of saturation
Sr
%
Specific Gravity
Gs
ratio
Bulk density
ρb
kg/m3
Dry density
ρd
kg/m3
Saturated density
ρsat
kg/m3
Submerged density
ρ
kg/m3
Bulk unit weight
b
kN/m3
Dry unit weight
d
kN/m3
Saturated unit weight
sat
kN/m3

kN/m3
Submerged unit weight
Page 7 of 11
FORMULAE
mw
ms
V
wGs
e v 
Vs
Sr
V
e  v  wGs
Vs
V
e
n v 
V 1 e
w
v 1  e
Vw
Vv
w
m
Gs  s  s
Vs w Vs  w
 (G  eS r )
b  w s
(1  e)
 G
b
d  w s 
(1  e) (1  w)
 (G  e)
 sat  w s
(1  e)
 (G  1)
  w s
(1  e)
 (G  eS r )
b  w s
(1  e)
 G
b
d  w s 
(1  e) (1  w)
 (G  e)
 sat  w s
(1  e)
 (G  1)
  w s
(1  e)
Sr 
CN215 SOIL MECHANICS 2
Soil strength
Mohr-Coulomb equation
τ  c'(σ n  u)tan φ  c'σn tanφ
Deviator stress
q = σ1 - σ3 = σ'1 - σ'3
Mean effective stress
p'= (σ'1+σ'2+σ'3) / 3
Mean effective stress in a
triaxial test
p'= σc + q/3 - u
Undrained shear strength
su = q / 2
Critical state line (q - p')
q = M p'
Critical state line (v - lnp')
v = Γ – λ (ln p')
Hydraulic permeability
Apparent velocity
v
Q
At
Flow rate
q
Q
t
 vA
Properties of flownets – Isotropic material
Total flow
q = k H Nf / Ne
Total head loss
H = Δh Ne
Flow per channel per unit length
Δq = k Δh = k H / Ne
Total seepage flow
q = Δq Nf
Page 8 of 11
CN215 SOIL MECHANICS 2
Consolidation
Consolidation settlement
ρc 
H
(e 0 - e1 )
1  e0
Consolidation settlement
ρc 
Δσv H
E
Consolidation settlement
ρ c  m v Δσv H
Consolidation settlement
for normally consolidated
soils
ρc 
      
H

Cc log  o

1  eo
σ
o


Consolidation settlement
for over-consolidated clays
for (σ'o + Δσ') ≤ σ'c
ρc 
 σo  Δσ 
H

C r log 

1  eo
σ
o


Consolidation settlement
for over-consolidated clays ρ  H C log  σo  Δσ   H Crlog  σc 
c
c
 σ 
 σ
 1 e
for σ'o < σ'c < σ'o + Δσ'
1  eo
c
o


 o
(e 0 - e1 )
log( σ1 /σ0 )
Compression index
Cc 
1-D normal compression
line
v = vo – λ ln σ'v
Page 9 of 11
CN215 SOIL MECHANICS 2
STRESS DISTRIBUTION
Fadum’s (1948) Chart
σv = k ∙ q
Page 10 of 11
CN215 SOIL MECHANICS 2
Newmark’s (1942) chart
For a uniform loading intensity of q the stress at the required depth below the point in
question is computed as σv = N ∙ IN ∙ q
DETACH AND SUBMITT CHART WITH ANSWER BOOK
Page 11 of 11