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CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Autumn Examinations 2010/
Module Title: Geotechnical Engineering
Module Code: CIVL
School: School of Building and Civil Engineering
Programme Title: Bachelor of Engineering (Honours) in Structural Engineering
Programme Code: CSTRU_8_Y
External Examiner(s): Mr. J. O Mahony, Dr. M. Richardson Internal Examiner(s): Mr. D. Cadogan
Instructions: Answer four (4) out of five (5) questions
Duration: 2 hours
Sitting: Autumn 2011
Requirements for this examination: Graph paper
Note to Candidates: Please check the Programme Title and the Module Title to ensure that you have received the correct examination paper. If in doubt please contact an Invigilator.
Q1. (a) Calculate the factor of safety for each of the following embankments using Taylor’s stability numbers method (each to be constructed in homogenous soils): (4 marks)
(i) slope = 32.5; cu = 35.8 kPa; H = 7.6m; very deep hard layer; =19.6 kN/m^2 (ii) =20.3 kN/m^2 ; cu = 31.7 kPa; H = 6.2 m; slope = 28; hard layer 8.9m below surface
(b) In regard to compaction and consolidation , describe the key difference between these soil conditions and the causes of each. (3 marks)
(c) As part of the design process for a foundation scheme to be placed over a 3.5m layer of clay, a core sample was taken from the soil and an oedometer test was carried out on a specimen of this – the readings obtained are presented in the table below. Each load increment was held for a 24-hour period, prior to the subsequent load increment being applied. The load was removed once the required load cycle was completed, and the sample was allowed to expand over a further 24-hour period. The thickness of the sample was recorded at 17.11mm at this point – in addition, the specific gravity of the soil was found to be 2.56, while the water content was calculated to be 29.8%.
Applied Stress (kN/m^2 ) 0 25 50 100 200 400 800 0
Thickness (mm) 18.79 1 8.41 1 8.14 1 7.79 1 7.30 1 6.87 1 6.41 1 7.
(i) Plot the e/ curve and calculate the coefficient of volume compressibility ( mv ) for the material, for an effective stress range of 220 to 340 kN/m^2. (8 marks)
(ii) Plot the e/log curve and calculate the compressibility index ( Cc ). (4 marks)
(iii) Calculate and compare the values for consolidation settlement ( sc ) using data from parts (i) and (ii) above for the 3.5 metre thick layer of clay, when the expected average stress to be applied changes from 220 to 340 kN/m^2 , and comment on the result in terms of acceptable settlement values. (6 marks)
Q2. As part of works to support a block of soil, it is intended that a reinforced concrete gravity retaining wall is to be installed. The sloped back face of the wall is to be formed at an angle of 81 to the horizontal plane internally within the wall, while it is expected to have a surface which slopes up from the top of the 7.2m high wall at an angle of 11.9 to the horizontal plane.
It assumed that the interface friction angle between the wall and soil is approximately 19, while tests which were undertaken on the cohesionless soil showed it to have a bulk density of 20.2 kN/m^3 and an internal friction angle of 31.
(a) Using Rankine’s theory for a smooth-faced wall, calculate the maximum active thrust on the back of the wall, on the basis of a vertical virtual support face. (6 marks)
(b) Using Coulomb’s method and trial slip failure plane angles of 48, 50, 52, 54, 56, 58 and 60, calculate the maximum active thrust on the wall. (13 marks)
(c) In addition, calculate the equivalent maximum active thrust on the wall using the simplified Ka method. (6 marks)
Q5. (a) A project feasibility study is being undertaken on behalf of an investor at a potential development site. As part of the technical aspect of this process, an examination is to be carried out into the possible construction of a cutting to form an embankment at the back of the sloped site, in order to gain further area for construction rather than stepping the site. Calculate the maximum permissible slope angle so as to check it for a possible shallow depth failure, where a factor of safety of 1.6 has been specified previously in the area for such works. The soil has a c´ value of 0 kN/m^2 and an internal friction angle ´of 32.5, while the bulk weight of the material is 20.3 kN/m^3 – you are expected to carry out your checks for both cases where the soil is fully saturated and where the soil is dry. (6 marks)
(b) Calculate the factors of safety for each individual slope below, using the Bishop and Morgenstern method of design: (12 marks)
(i) H = 13.6 m; ´ = 23; = 19.8 kN/m^2 ; ru = 0.35; c´ = 15.2 kN/m^2 ; slope angle = 18.9 (ii) = 17.9 kN/m^2 ; slope angle = 17.8; H = 12.8 m; ru = 0.37; c´ = 11.1 kN/m^2 ; ´ = 35 (iii) ´ = 33; = 18.3 kN/m^2 ; ru = 0.29; slope angle = 21; c´ = 10.2 kN/m^2 ; H = 7.7 m
(c) It is anticipated that a raft foundation will suffice to support a unit for light commercial usage, in an area where there has been a history of minor subsidence. The unit is to be supported by a 21 metre by 10 metre slab which is assumed to be flexible and is to be located at a depth of 2.1m below the finished surface level.
Calculate the immediate settlement likely to take place under the centre of a concrete raft foundation, given that the soil at the location is generally anticipated to be saturated clay with a bulk weight of 22.1 kN/m^3 and an undrained elastic modulus Eu of 39.8 MN/m^2. It is expected to resist a uniform contact pressure of 240 kN/m^2. (7 marks)
21 m
2. 1 m
Useful Formulae and Charts Geotechnical Engineering Autumn 2011
1. F =
2. F =
W sin
c l tan W(cos rusec )
3. Ka =
Sin
Sin
= tan^2 (45 - /2) 4. Kp =
Sin
Sin
= tan^2 (45 + /2)
5. qA = 2
B
Ve
B
V
6. Nq = exp^ ^ tan^ ^ tan^2 (45+ /2)
7. N = 1.8 (Nq-1) tan 8. s = 1 - 0.4
L
B
9. qULT = (½) x (B) x ( ) x (N ) x (s ) 10.
11. e = ( e )
h
h 0 0
12. mv = ( 1 )
e 0
e
13. Cc =
log
e =
0
1
0 1
log
e e
14. sc = mv Δ H 0
tan
tan 1
z
wh
p u
i I E
qB( 1 ) s
^2
