THE UNIVERSITY OF HONG KONG
BACHELOR OF ENGINEERING: LEVEL 3 EXAMINATION
DEPARTMENT OF CIVIL ENGINEERING
EARTH RETAINING SYSTEMS CIVL303 l/313 l
DATE: 14th December 2015 TIME: 14:30-17:30 (3 hours)
Instructions:
Answer all questions.
Additional Materials Provided:
Graph Papers
Use of Electronic Calculators:
Only approved calculators as announced by the Examinations Secretary can be used in this
examination. It is candidates' responsibility to ensure that their calculator operates
satisfactorily, and candidates must record the name and type of the calculator used on the
front page of the examination script.
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QUESTION 1 (50 marks)
(a) A concrete wall is installed to retain silty sand. It is assumed that the water table is deep
beneath the wall base. Details of tbe wall geometry, soil/wall friction and the soil properties
are given in Figure la.
(a-i) Determine tbe maximum force acting on the wall by using Coulomb's wedge
analysis by the graphical method.
[10 marks]
(a-ii) Determine the point of application of the force.
[5 marks]
(a-iii) What width of tbe wall base is required if a factor of safety FS=2.0 is used
against overturning and a factor of safety FS=l .5 is used against sliding? The concrete
has a unit weight of 24kN/m3 . What would you do to reduce the risk of sliding?
[15 marks]
(b) The same wall as above is being considered, but with water behind the wall. Drainage was
arranged to lower the water table, with a drain connected to tbe atmosphere in point A
(Figure lb).
(b-i) Determine the force resulting from the pore water on tbe plane AB.
[10 marks]
(b-ii) Using Coulomb's wedge analysis with the failure plane as AB, determine the
force on the wall and its point of application. Details of the wall geometry, soil/wall
friction and the soil properties are given in Figure I b. You will assume that the unit
weight of the soil is uniform and equal to y for the whole wedge.
[10 marks]
Page2 of5
.l
. ~-.;;,r---
/
;i
/.:
.l'
.. y=20kN/m3
../
.l
..! c'=OkPa
..
Sm
~
(\.
<j>'=2S 0
"7'--
8'=<j>'
,../
.../ drawLng to
..:./ scale (except
/
.....
the base of
// the wall)
.::/'
...................................\?\
, • J...........................
(a)
..
.....
/'
..
/
/' y=20kN/m 3
..1
.....
... c'=OkPa
Sm .
~ .. <j>'=2S 0
(\.
;--. . 8'=<j> '
_../;
\.':.
.:/ drawing to .
/
. scale (except . . ·.
......·. \~~
/ the hase of ·.
l
... / the wall)
.:'(................................)?)·······.................... A ·.
~i equipotentials
(b)
Figure 1
Page 3 of 5
QUESTION 2 (50 marks)
(a) Demonstrate, using Mohr's circle, that the active horizontal effective stress on a retaining
wall built in soil of cohesion c' and friction angle <// is: O'h '= K 0 0';-2c' /K; , with
K 0 = l-s'.n¢'. Show that there is a layer of soil where cracks are likely to develop behind
l+sm¢'
the wall and determine the depth of cracks as a function of the cohesion, unit weight, pore
water pressure and friction angle of the soil.
[10 marks]
(b) A cantilever wall is designed for a 6m deep excavation (Figure 2a).
(b-i) Determine the depth of embedment (d) required for the cantilever wall. Details
of the wall geometry, soil/wall friction and the soil properties are given in Figure 2a.
You will assume that the water table is deep beneath the wall.
[10 marks]
(b-ii) What would be the depth of embedment if a uniform surcharge of 50kN/m2
surcharge was added at the back of the wall? [10 marks]
(c) Consider the cantilever wall in Figure 2b. The water table is at ground level behind the
wall (retaining side) and it is kept at excavation level in front of the wall. The pore water
distribution due to seepage is shown on the figure. It increases linearly with depth on both
sides of the wall, with the pore pressure at the bottom of the wall equal tour= 5lkN/m2 . A
strut is installed at the top of the wall.
(c-i) Calculate the total active force on the retaining side of the wall and the total
passive force on the resisting side of the wall. [6 marks]
(c-ii) Determine the force P, in the strut (in kN/m). [7 marks]
(c-iii) Determine the factor of safety against piping. [7 marks]
Page 4 of5
6m
y=21kN/m 3
c'=OkPa
4>'=33°
0':QO
(a)
W.T.
6m
y=21kN/m3
c'=OkPa
4>'=33°
...
W.T.
0':QO
3.Sm
(b)
Figure 2
-END OF PAPER-
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