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UNIVERSITY OF SOUTHAMPTON CENV2006
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SEMESTER 1 FINAL ASSESSMENT 2022/23
SOIL MECHANICS
DURATION – 8 Hours (Online Open-Book) including up/download
time
We recommend that you spend 120 minutes on this paper.
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This paper contains 4 questions
Answer ALL questions.
Each question carries 25 marks out of a total of 100 marks for the exam paper.
Note that marks will only be awarded when appropriate working is given.
All sources used to answer the questions should be referenced.
An outline marking scheme is shown in brackets to the right of each question.
You may submit either a handwritten or a typed submission, or a combination of
handwritten and typed answers. Your graphs and diagrams may be drawn using
software.
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QUESTION 1
Q1 A new building, which is square in plan view, is being
constructed. The ground conditions are summarised in Figure
Q1 and comprise a layer of compressible clay, sandwiched by
sand and gravel layers that can be assumed to be
incompressible and highly permeable relative to the clay.
Table Q1 shows results from three compression stages of an
oedometer test on a sample from the mid-depth of the clay layer.
The building settlement requires assessment. Assume that the
properties of the clay sample represent the full clay layer.
Figure Q1: Ground conditions and planned building
Table Q1: Oedometer test data for three loading stages Stress
increment
Time, t
minutes 0 0.5 1 2 4 8 16 32 64
60-120 kPa
Settle_xfffe_ment, ρ
mm
0 0.104 0.151 0.210 0.260 0.279 0.281 0.281 0.281
120-180 kPa 0 0.178 0.252 0.361 0.521 0.696 0.805 0.829 0.830
180-240 kPa 0 0.153 0.216 0.313 0.441 0.555 0.604 0.609 0.609
At the start of first stage: sample height, h = 25 mm.
At end of final stage: moisture content, w = 49%
Specific gravity of clay: = 2.65
Sand and gravel
Water table
New building
Clay
Sand and gravel
10 m
6 m M C
20 m
γ = 20 kN/m3
γ = 17 kN/m3
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a For each oedometer test stage, plot the settlement, ρ, against
the square root of time, t. Find the one-dimensional modulus, 0
′
,
and consolidation coefficient, cv, for each stage. State the units
you have used.
[8 marks]
b Using the sample height, h, at the start and end of the stages,
develop a figure showing the specific volume of the sample, v, at
different effective vertical stresses,
′
, and estimate the one dimensional virgin compression stiffness, 0, the unload-reload
stiffness, 0, and the intercept of the one-dimensional normal
compression line, 0, for the clay.
[5 marks]
c Calculate the in situ vertical total and effective stresses, and

′ , at the mid-depth of the clay layer (i.e. points M and C),
before construction of the building.
[2 marks]
d Estimate the over-consolidation ratio of the clay, before
construction of the building.
[2 marks]
e The building will apply a vertical stress of 100 kPa to the ground
surface. Estimate the increment of vertical effective stress, Δ
′
that this will cause at the mid-depth of the clay layer at points M
and C, which are under the middle and the corner of the building
respectively. State any assumptions involved in your approach.
[4 marks]
f Estimate the long term settlement of the building above points M
and C due to compression of the clay layer.
[4 marks]
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QUESTION 2
Q2 A specimen of saturated Kimmeridge Clay having an initial
overconsolidation ratio (based on average effective stress p′) of
2 is subjected to an undrained shear test in a triaxial cell from an
effective cell pressure of 100 kPa.
a Explain briefly how the Cam clay model can be used to
determine the state paths followed during shear.
[6 marks]
b Using the Cam clay model with Γ = 2.50, Μ = 1.2, λ = 0.16 and
κ = 0.05, calculate and plot these state paths in the q vs. p and
p′ and v vs. ln p′ planes. Your axes should extend from 0 to 200
kPa for p, p′ and q on the q vs p, p′ plot, and the scales for the
q and p, p′ axes should be the same.
[8 marks]
c A second, identical specimen is subjected to a drained (rather
than an undrained) test from an effective cell pressure of 100
kPa. Calculate the values of q and p’ and the specimen volume
change at failure if the volume of dry solids in the specimen was
875 ml (millilitres).
[4 marks]
d A third specimen having the same previous stress history as the
first two was subjected to an undrained shear test from an
effective cell pressure of 50 kPa. Use the Cam clay model to
calculate the volume of water taken into the specimen on
reducing the cell pressure from 100 kPa to 50 kPa, and the
theoretical values of q and p′ at yield. Sketch the stress path (q
vs. p′) on your graph from part (b).
[5 marks]
e Why is the calculated value of q at yield unlikely to be achieved
in reality
[2 marks]
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QUESTION 3
Q3 Figure Q3 shows a cross section through one half of a canal
embankment. The embankment is underlain by permeable
chalk, with a discontinuous layer of clay between the
embankment and the chalk as indicated. The canal is lined with
a low permeability material such that there is a 0.5 m head drop
across it.
Figure Q3: Cross section through one half of a canal
embankment (NOT TO SCALE)
a Construct a flownet for seepage from water from the canal into
the underlying chalk. Assume that the embankment material
remains saturated so there is no need to find the phreatic surface
(top flowline) while drawing the flownet. Label the head value of
each equipotential. Calculate the rate of leakage from the canal,
in litres per hour per metre length of the embankment.
[15 marks]
b Explaining your reasoning, determine the position of the line of
zero gauge pore water pressure within the embankment.
Calculate the maximum negative pore water pressure (suction)
Embankment fill, permeability k = 10-6 m/s
Impermeable clay layer
Permeable fractured chalk
Retaining wall
(impermeable)
Canal 2 m 1 m
1 m
6.5 m
10 m
3.5 m
1.5 m
2 m
GWL in
chalk
1.5 m
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within the embankment, according to your flownet. Using a
quantitative argument, discuss whether the assumption that the
soil above this line remains saturated is reasonable. Take the
surface tension of water T = 7×10-5 kN/m.
[6 marks]
c Comment on the assumption that the flow regime is symmetrical
about the centreline of the embankment, with reference to the
likely continuity of the clay layer. What would be the effect on the
flow if there were no discontinuity in the clay layer on the other
side of the embankment, and what might be the consequences
[4 marks]
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QUESTION 4
Q4 Figure Q4 shows a cross section through the foundation of a
bridge abutment, located on stiff clay overlying bedrock on the
side of a valley. A potential failure mechanism, consisting of two
sliding blocks, B and C, is shown. In this question you will
develop an upper bound plasticity solution for this mechanism.
The bridge abutment, A, is subjected to a vertical load per unit
length (into the page), , from the bridge. The bridge structure
constrains the abutment to move straight downwards if the
foundation fails.
Figure Q4: Foundation of bridge abutment
a Calculate the length RS and the angles and then construct
a hodograph (velocity diagram) showing the movement of the
abutment, A, and blocks B and C, based on the mechanism
shown. Scale the diagram such that the vertical movement of the
abutment is one unit.
[5 marks]
b Derive an expression for the energy dissipated on the failure
planes for a unit movement of the abutment as a function of
Stiff
clay
Bedrock
Abutment, A
B
C
V
Distances
PQ = w
PR = QR = 5w/6
QS = 2w
P Q
R
S
α α
β α
w
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and . Assume that the clay-abutment (PQ) and clay-bedrock
(RS) interfaces mobilise the full shear strength of the clay, . It
is recommended to begin by listing the failure planes and
tabulating their parameters.
[4 marks]
c Calculate the vertical load, , that will cause the failure
mechanism to occur, for = 50 and = 6 . Assume that
the soil is weightless.
[3 marks]
d Now consider that the influence of the soil weight. Calculate the
potential energy released by the movement of the clay blocks, B
and C, for a unit movement of the abutment as a function of soil
unit weight γ.
[4 marks]
e Recalculate the vertical load, , that will cause the failure
mechanism to occur, allowing for the influence of the soil weight.
Assume that = 50 , = 6 and = 20 / 3.
[3 marks]
f Unexpectedly, the bridge abutment collapses under a vertical
load of = 600 / . Subsequent investigations suggest that
this is caused by a weakening of the clay at the clay-bedrock
interface (RS), so that the available shear strength on this plane
is , = , where 0 < < 1. To assess the credibility of this explanation, calculate the apparent reduction factor on shear strength, , by extending the solution developed in part (e). [3 marks] g The upper bound failure mechanism developed in this question may not be optimal, and so could over-estimate the foundation capacity. Sketch two simple alternative failure mechanisms that could be considered, indicating their geometry and kinematics. [3 marks] END OF PAPER