Geotechnical Mechanics

Instructions:
1. This examination consists of FIVE pages. Make sure you have all the pages.
2. Answer ALL Questions.
3. This examination is closed book. You are not allowed to have any unauthorized material on the desk or in
your pockets.
4. This examination question paper MAY NOT be taken from the examination room.
5. Do not ask any questions. Make assumptions when required. (In case of missing data, or if you think
there is an error in the question). Assumptions must be reasonable, and clearly stated.
6. In addition to this question paper, students require an examination booklet.
Question # 1 Short Answer questions (15 marks)
1.1 Which of the following unit weights will have the lowest value in soil?
a) Bulk unit weight b) Buoyant unit weight c) Saturated unit weight d) Dry unit weight
1.2 Which of the following soils would have lower hydraulic conductivity?
a) SM b) GC c) GP d) CH
1.3 What is the optimum water content of a soil?
a) The water content at which soil will have the highest permeability b) The water content at which the
soil will have the highest dry density c) Swelling water content d) Shrinkage water content

1.4 How the excess pore water pressure can affect the shear strength of a fine-grained soil?
a) Increases effective stress b) Decreases effective stress c) Increases friction angle
d) Decreases cohesion
1.5 Which of the following factors will decrease the effective stress in soil?
a) Downward seepage b) Upward seepage c) External loading d) Drop in ground water table
Name : ID No. : 2
Question #2 (15 marks)
a) The dry density of a soil is 1780 kg/m3
. Given GS=2.68, what would be the moisture content of the soil
when saturated? (5 marks)
b) In its natural state, a soil has a bulk density of 2.15 Mg/m3
and a water content of 12% (GS = 2.65).
Would it be possible to compact the above soil at a water content of 13% to dry density of 2.0 Mg/m3? (10
marks)
Question #3 (30 marks)
A layer of sand of 18 m thick overlies
impermeable rock, and a long
cofferdam is formed by driving sheet
piling to a depth of 9 m below ground
surface.
a) If the flow of water through
underneath the cofferdam is 0.3 m3
/hr
per unit length of the dam, what is the
coefficient of permeability of the sand?
b) If the specific gravity of the soil
solids is 2.65 and e=0.7, do you
expect piping downstream of the
cofferdam?
c) Calculate pore water pressures at
points b and f.
Figure 1
Question #4 (10 marks)
Determine the increase in vertical stress at
a depth of 3 m below point X on the Lshaped foundation shown in Figure 2 (plan
view), when the foundation is subjected to a
uniform pressure of 200 kPa.
Figure 2: Plan view
Name : ID No. : 3
Question #5 (20 marks)
A building with the net foundation pressure (uniformly distributed) of 330 kN/m2 is supported on a 40 m  30 m
mat foundation located at a depth of 3 m from ground surface. The soil profile is given in the figure below. The
following values were measured from consolidation test for the clay layer: Cc=0.15, Cr=0.03, e0=0.96, p
’=130
kPa).
a) Determine the total settlement under the
center of the foundation due to the
consolidation of the clay.
b) If the water table is lowered 5 m after
the settlement calculated in part (a) is
complete, will the clay layer continue to
consolidate, remain at the same
thickness, or rebound? If the thickness
of the clay layer does change, calculate
the magnitude of the change.

Figure 3
Question # 6 (10 marks)
A sandy soil has a drained friction angle of 34. In a drained triaxial test on the same soil, the deviator stress at
failure was measured at 255 kPa. What is the cell pressure of the test sample?
s z   q I Appendices:
CIVE 3208: Formula Sheet
Name : ID No. : 4
1. Phase relationships:
e
n
n

1
, n
e
e

1
,  
w
s
w
s
e
G eS
e
G w
  






1 1
1
,
e
wG S
s  ,
      s a t w ,
w
d 

1

 ,
max min
max
e e
e e Dr 


2. Uniformity and curvature coefficients:
10
60
D
D
UC  Cu  ,
60 10
2
30
D .D
D
CC  Cc 
3. Consistency of soil: PI = LL – PL , LI w PL
PI
n 

, % finer than 2 m, by weight
PI A 
4. Compaction:
5. Flow of water in soil: v  ki  k(h / L) , q  Aki (1D flow) ,
n
v
vs 
u z (no flow) w w   , u (H Z) (with flow) w    , (2D flow)
N
N
q k H L
D
F   D
1 2
1 1 2 2
( )
z z
k z k z
k ave x 

 ,
( / ) ( / ) 1 1 2 2
1 2
( )
z k z k
z z
k ave z 

 ,
( )
ln( / )
2
1
2
2
2 1
h h
q r r
k pump



6. Stress in soil:
 ‘   u   ‘Z ,
w
c
i

 
 ,      h o v K ,  1 sin() Ko
5
3
2
3
L
Qz

  (point load),
(B z)(L z)
Q
 
  (approximate method)
7. Settlement: i s
I
E
q B
S
.
 , o
o
H
e
e
s



1
, m H0 Sc  v ,
‘
0
‘
z
p OCR




  



zo
zo
o
o
c c
e
H
s C

 
log
1
,

  



zo
zo
o
o
c r
e
H
s C

 
log
1
,

  







p
zo
o
o
c
zo
p
o
o
c r
e
H
C
e
H
s C

 


log
1
log
1
2
dr
v
v H
c t
T  For a given degree of consolidation U, Tv may be approximated by:
Tv  1.781 0.933log(100 U) for U  60% , ) 60%
100
(
4
2
 for U 
U
Tv
