University of
Glasgow
Geotechnical Exam
Questions
1
GEOTECHNICAL ENGINEERING 3A
MEng and BEng degrees in Civil Engineering
And Civil Engineering with Architecture
time : :, ?? December 2009
Instructions
• Please attempt THREE questions.
• Time allowed 90 minutes.
• If an electronic calculator is used, appropriate intermediate steps in calculations should be
indicated.
• The marks allocated to each question or part question are to be used as a guide only.
Candidates to be issued with:
Data Sheet (attached)
1.
A clay deposit 10 m thick (  '  30,   18 kN / m ) overlies an aquifer. The aquifer is
under artesian pressure, such that the measured water pressure at a depth of 15 m below GL
2
reads 160 kN/m . Consolidation test data on a sample taken from a depth of 6m suggests that
the OCR at this depth is five (5).
3
(a)
Assuming that the ground has been subjected to a single cycle of deposition and
erosion, estimate, at a depth of 3 m:
(Assume
 zt , u,  z ' , OCR,  x ' .
 w  9.8 kN / m 3 . )
(12 marks)
(b)
Answers:
If the clay deposit is 100% saturated, and the quoted unit weight (above) is that of the
soil sample (taken from a depth of 6m), what would the unit weight of this sample have
been before erosion took place?
Assume λ = 0.2, κ = 0.04, Gs= 2.7
( 8 marks)
(a) 54kPa, 33kPa, 21kPa, 9, 32kPa
(b) 18.3 kN/m3
2
Continued overleaf /
2.
In a soil, principal total stresses ( 
t
z
 80 kN / m , 
2
t
x
 40 kN / m 2 ) act on horizontal
and vertical planes, respectively.
(a)
Determine graphically the normal total stress and shear stress acting on the plane:
  150 . (Also, draw a sketch of your answer).
(12 marks)
(b)
If the pore water pressure is 20 kN/m , what is the normal effective stress and shear
stress acting on the plane   150 .
(3 marks)
(c)
If the angle of internal friction of the soil is 30˚, establish whether this state of stress is,
(i) permissible, (ii), permissible but at the limit state, or, (iii) impossible. Assume the
cohesion intercept c΄ is zero.
( 5 marks)
2
Answers;
3.
a) Normal = 70, Shear = +17 (both approximate)
b) Normal = 50 Shear unchanged
c) At the limit state (failure).
For simplicity, in this question, assume that under undrained loading conditions p' = 0.
In addition to sketching the required plots, for each identified point (A, B, C etc.), calculate the
following quantities:
(a)
 z' ,  x'
and
u.
Plot on a q-p plot, the path followed (OA) by a clay soil which is normally (K o)
consolidated to
 'z  180 kN / m 2 , after deposition in water. Assume (ø' = 25o).
(4 marks)
(b)
Beginning from A, plot the path AB if (due to erosion)
 'z is reduced to 90 kN/m2.
(4 marks)
(c)
Estimate
 'z where the path AB (or AB extrapolated) crosses the p' axis.
(4 marks)
(d)
From B, the soil is removed from the ground under "undisturbed" conditions. Plot the
ESP from B-C' for this case, as well as the path BC (TSP). What pore water pressure is
developed during this process?
(4 marks)
(e)
In the laboratory, the soil is consolidated to B. It is then subjected to an undrained test,
where
 xt
is decreased, while
 z  0. Plot BD (the TSP) and BD' (the ESP),
t
where D' corresponds to the stress-state at failure.
(4 marks)
Answers:
A
B
C
D
q
76
17
0
0
77
p
129
79
60
79
79
t
p
129
79
0
39
3
4.
Continued overleaf /
A storage tank of 30 m diameter is founded 2 m below the surface of a deposit of clay 32 m
thick, overlying bedrock. The water table is at ground level. The gross weight of the tank (when
3
full) and its foundation is 70 MN. The unit weight of the clay is 18kN/m . The undrained
Young’s modulus of the soil can be taken to be equal to 1000  z where  z is the vertical
effective stress. Poisson’s ratio

may be taken to be 0.1.
Noting carefully any assumptions adopted, estimate the settlement underneath the
centre of the tank,
(a) in the short-term, and,
(14 marks)
(b) in the long-term.
(6 marks)
Hint: consider a single sub-layer only (i.e., 30m thick)
ANSWERS (using 2 sub-layers 10m + 20m)
(a) S = 4.1 + 2.9 = 7mm
(E1 = 65MPa, E2=185MPa)
(b) S = 7.5 + 3.2 = 10.7mm
(E1 = 86MPa, E2=191MPa)
NOTE: In 2010-11, problems such as this (involving a stress dependent modulus) have not been
considered - - and will not appear in examinations.
End of examination paper.
(+ Data Sheet)
4
Geotechnical Engineering 3A
Examination Data Sheet:
Ko = (1 – Sin φ΄) OCR0.5
 
G se
w
1 e
e  eo   loge  
M 
6Sin 
3  Sin 


u  B  rt  A at   rt 
L  z2  R2
cz/L
Stresses beneath circular foundation
 zt  q( 1  c 3 )
 xt 

q
1  2   2  2 c  c 3
2
