CC9115 Semester 2 2016 Page 1 of 6

THE UNIVERSITY OF SYDNEY

FACULTY OF ENGINEERING & IT

(School of Civil Engineering)

CIVL 2410/CIVL 9410 SOIL MECHANICS

November 2016 Time allowed: Three hours

Candidates should attempt FOUR questions.

Question 1 is compulsory and is worth 40%. The remaining questions are each
worth 20%.

Only non-programmable calculators may be used.

____________________________________________________________________________
Question 1

(i) A soil specimen with a volume of 1000 cm3 is dried in an oven and the mass of water is
determined to be 200 g and the dry mass 1500 g. If the specific gravity, Gs = 2.65
determine the degree of saturation.

(ii) A long flexible structure 10 m wide is constructed on a silty clay layer (cv = 10 m2/yr)
that is 10 m thick. Assuming the clay layer is elastic the initial settlement under the
centre of the footing has been estimated to be 13.5 mm and the final settlement 27 mm.

If the flexible structure is permeable and the clay layer is underlain by impermeable rock
determine the time after construction when the settlement will be 20 mm.

(iii) A clay specimen is set up in an oedometer apparatus with an effective vertical stress of
50 kPa with a void ratio of 1.2. The vertical effective stress is increased to 200 kPa and
the void ratio reduces to 1.12. Determine the over-consolidation ratio if the clay has Cc
= 0.35 and Cr = 0.02.

(iv) The immediate settlement of a rigid circular foundation with diameter of 8.0 m,
subjected to a force of 1 MN, is 5.4 mm. Determine the ultimate settlement if the
foundation is on the surface of a 10 m thick soil layer. Assume the soil layer is elastic
with ν′ = 0.2.

(v) A triaxial test has been performed and at failure a deviator stress of 100 kPa recorded.
If the soil properties are c′ = 0 and φ′ = 25o and the confining (cell) pressure = 100 kPa,
determine the pore pressure at failure.

(Question 1 continued over page)

CC9115 Semester 2 2016 Page 2 of 6

(vi) Figure 1 shows a flow net for the flow of water into an inclined drain behind a
retaining wall. Determine the flow through the drain if the wall is 5 m high and the
permeability is isotropic with k = 1 × 10-6 m/s.

Figure 1

(vii) Classification tests to determine the particle size distribution and plastic and liquid
limits of a soil have given the following information.

Particle Size % finer than Liquid Limit Plastic Limit

(mm)
6 100 32% 26%
2 60
0.6 30
0.2 15
0.075 10
0.02 4
0.002 2

Use the Unified soil classification system to describe the soil.

(viii) Using Rankine’s method, determine the horizontal force required to prevent active
failure of the 6 m high wall, shown in Figure 2, immediately after construction. The
water table is at the surface of the clay.

4m Dry Sand c’=0, φ’ = 32o, γdry = 18 kN/m3

Retaining
6m Wall
Water Table

2m Clay cu = 20 kPa, φu = 0, γsat = 16 kN/m3

Figure 2
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Question 2

It is proposed to build a large structure, 50 m × 80 m in plan, adjacent to an elevated roadway as

shown in Figure 3. The roadway is supported by two piers which sit on square 2 m × 2 m
foundations. Site investigations have shown the soil profile consists of a 5 m thick layer of
gravel which overlies 2 m of clay, which is underlain by impermeable shale rock, and that the
water table is 1 m below the gravel surface. Each of the bridge foundations support a load of 1
MN (it may be assumed that the foundations subject the ground to a uniform pressure) and the
proposed load from the new building is 700 kPa.

(i) Use the 1-D settlement method to estimate the settlement under the centre of each
bridge pier, and hence the differential settlement between them due to the proposed
building.

(ii) If the large structure could be built rapidly how long would it take for 80% of the
settlements to occur?

(iii) Discuss the accuracy of the 1-D settlement calculation.

(iv) For the bridge structure it is required that the differential settlements be kept below 5
mm. Suggest and discuss briefly one method of how this could be achieved.

Assume that the deformations are one-dimensional, that the gravel and rock layers are
incompressible, and use a single layer for the clay. For the gravel γdry = 17 kN/m3, γsat = 20
kN/m3, and for the clay γ sat = 18 kN/m 3 and Gs = 2.6. Oedometer tests have been used to
determine the following clay properties: Over-consolidation ratio, OCR = 1.2, Compression
Index, Cc = 0.5, Re-compression Index, Cr = 0.05, Coefficient of Consolidation, cv = 3 m2/yr.

1 MN 1 MN 700 kPa
10m 10m 40m Proposed
Building

Gravel 80m

Clay

Shale Rock 50m

(a) (b)

Figure 3 (a) Elevation, (b) Plan

CC9115 Semester 2 2016 Page 4 of 6

Question 3

Figure 4 shows a section through a natural dam created by a rock slide into a river valley.
Because of the size of the dam, failure would be catastrophic to downstream inhabitants. To
ensure overtopping does not occur it is desirable that the water level does not exceed that shown
in Figure 4.

Water

12 m

Impermeable rock

Figure 4 (drawn to scale)

a. Draw the flow net for the situation shown in Figure 4. Mark clearly the boundary
conditions on your flow net.

b. Hence determine the maximum allowable flow of rivers feeding into the water behind
the dam. Assume that the dam material is isotropic with permeability, k = 5 × 10-5 m/s
and that the dam is 30 m wide

c. From your flow net determine the pore water pressure at point X.
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Question 4

At a construction site the soil profile consists of 10 m of highly over-consolidated clay

overlying impermeable shale. Construction activities involve initially a 2 m layer of sand being
placed on the surface of the clay. A year later the sand is to be rapidly removed and a further 6
months later 2 m of clay is to be excavated. The areas affected by sand placement and
excavation are large so that 1-D conditions can be expected.

(i) Use a numerical method (∆z = 2m, ∆t = 0.25 years) to determine the excess pore
pressures in the clay layer for a period of 2 years from the initial application of the sand.
Assume the clay is saturated with a unit weight γsat = 15 kN/m3, a coefficient of
consolidation cv = 8 m2/year, a coefficient of volume compressibility mv = 0.0001 m2/kN,
and that the bulk unit weight of the sand is 20 kN/m3.

(ii) Calculate the time settlement behaviour of a point 6 m above the base of the clay for a
period of two years.

(iii) Discuss whether you would you expect the displacements of a marker placed in the
ground 6 m above the clay base to agree with the values predicted by the numerical
method in (ii).
CC9115 Semester 2 2016 Page 6 of 6

Question 5

Two triaxial tests have been performed on clayey soil specimens obtained from behind the
retaining wall shown in Figure 5. The specimens were fully consolidated to identical conditions
with axial stress, σa = σr = 200 kPa and pore pressure, u = 100 kPa.

Specimen 1 was tested without allowing drainage by increasing the axial stress while adjusting
the cell pressure so that ∆σa = -2 ∆σr. Specimen 2 was tested fully drained by increasing the axial
stress while maintaining the cell pressure and pore pressure constant (∆σr = 0, ∆u = 0).

1. When the axial stress reached 250 kPa (∆σa = 50 kPa) the axial strains for the two
specimens were: undrained test εa = 0.0025; drained test εa = 0.002. Assuming the soil is
responding elastically calculate the elastic properties Eu, E′, ν′.
2. The axial stresses and pore pressures at failure for the two specimens were: undrained test
σa = 300 kPa, u = 83.7 kPa: drained test σa = 417.3 kPa, u = 100 kPa. Determine the
effective strength parameters c′ and φ′.
3. Use Coulomb’s method for the assumed failure plane shown in Figure 5 to determine the
horizontal force needed in the long term to prevent failure of the retaining wall supporting
the soil and foundation if the force, F on the strip foundation is 100 kN/m. Take the
saturated unit weight of the clay as 18 kN/m3, assume that the wall is frictionless and note
that the water level is the same on both sides of the wall.
4. Assuming that sufficient force is provided to ensure stability of the wall discuss how you
could calculate the width of the footing to ensure the settlements are less than a stated
value. No calculations are required, just a description of the process.
F

Water Clayey Soil

4 m

Assumed failure plane

40o

Rock

Figure 5