Q2.1
a Solve for the unknown soil parameters in the table
below.
Soil Yt Y„ Gs e n s u>
kN’m’ kHm1
1 165 063 000
2 268 047 033
Q.2.2
A soil has a voids ratio of 0 7 Assume that the solid material occupies 1
m3. aid Gs = 2.65.
a Calculate the dry and saturated unit weight of the
material
a Find the moisture content for a fully saturated sample
Q2.3
Given the moist (bulk) density (p,) of a soil is 1 76 Mg/m3 and its
moisture content is 10% Assume the Specific Gravity (G3) for the solids
Is 2 65 Find.
a Void Ratio – e
a Porosity – n
a Degree of saturation – s
a The saturated density – ps
0.2.4
Standard proctor compaction tests earned out on the following sample of
sandy day yielded the following results: Gs = 2.73
Bulk density (kgfrn1) 2058 2125 2152 2159 2140
Water Content (%) 129 14 3 15.7 169 179
a Plot the relationship between dry density and water
content.
a Estimate the optimum water content and determine
the air voids percentage for the maximum dry
density.
a Calculate the moisture content necessary for
complete saturation at this MDD if Gs = 2 73
EFFECTIVE STRESS AND FLOW OF WATER THROUGH SOILS
Q3.1
Effective Stress
A soil profile consists of a 3 m thick layer of gravel, overlying a 5| m thick
clay layer overlying permeable rock The water table is 1 m below the
soil surface The properties of the gjravel are y^ = 18 kN/m3, y^. = 22
kN/m3, and for the clay y*« = 16 kN/m3
x Determine the effective vertical stress 6 m below the
soil surface if the pore pressure at this depth = 60
kPa.
£ Explain how the pore pressure can be greater than
the hydrostatic value.
Q3.2
Effective Stress
A borehole on a mine site has the profile shown below
i: Find the effective stress at the bottom of the clay
layer 2 under normal conditions.
s If the groundwater is lowered by 2.4m
£ If the groundwater is lowered by 2.4m and that
capillarity results in the sand layer 1 being saturated
with water up to the original WT level).
Gl
Sod Lay« 1, p, = 1930kg/m\ Gs = 2.72. e = 0.515
v WT
Soil Ljyw 2. » 2010 k»’m / .
4.8m
3.6m
2.4m
Q3.3
Effective Stress
The following table provides information on a layered deposit of soils.
Soil Thickness
(m) Gz e
U)
(%)
Capillary
Rise (mm)
1 2 265 04 10 0
2 4 27 05 15 500
3 4 26 045 5 800
4 5 2.65 0.55 10 0
Calculate the dry. bulk and saturated unit weights for
each of the materials.
Plot the vertical total stress profiles from surface to
the base of Soil 4 .
If a water table is located 5 m below surface, plot the
variations with depth below surface of the vertical
total stress, the pore water pressure and thus the
vertical effective stress.
Q3.4
Pumping from a Confined Aquifer
A well has been installed to penetrate a layejr of fine sand that is
estimated to be 4m thick and confined between two impermeable clay
layers Two monitoring bores are located 5m and 10m from the well
After 2 days of pumpinq at a constant rate of 20 litres per minute, the
heights of the water in these wells are measured to be stable and 6m
and 5m. respectively, below the ground surface.
& Estimate the in situ permeability. Express your
answer in units of cm/s.
Q.3.5
Pumping from an Unconfined Aquifer
A well has been installed to penetrate a saturated, uniform silty sand
layer that is 10m thick between the surface and an underlying
impermeable fresh rock layer Two momtonng bores are located 3m
and 6m from the well After 2 days of pumping at a constant rate of 100
litres per hour, the heights of the water in these wells are measured to
be stable and 6 0m and 6.5m, respectively, above the impermeable
layer.
Estimate the in situ permeability. Express your
answer in units of cm/s.
Q3.6
04.11 Flow wider an Embankmeht
A tailings dam has been constructed over a uniform semi-impermeable
layers as shown in the sketch. The layers has the permeability as Layer
Type 2 in the previous question o ool crr\ -5
s Use a “flow net” to estimate the flow rate (expressed
as nr per day per m strike length (width) of the
embankment).
DESIGN OF FOUNDATIONS IN SOIL
Q4.1
Stress below an irregularfooting
An irregular shaped concrete small house slab has been constructed
with the dimensions as shown in the diagram below. When the house is
completed, it is estimated that a uniform stress of about 250kPa will be
applied over the area of the slab
m Estimate the vertical stress at a depth of 2m below
the corner C.
■*—— 5m —►
5m
C
A
▼
3m
———————————————————————————►
12m
Q4.2
Strip footing ultimate bearing capacity
A stnp footing is 2m wide and founded at 3m depth in a soil of unit
weight 19 3kN/m3 and a cohesion of 10kPa
s Determine the variation in the ultimate bearing
capacity of the foundation for friction values of 25°
and 30°.
£ Given a FOS = 3.00, what are the safe bearing
capacities?
Q.4.3
Foundation on Sand
A footing 2 5m square is located 1m below surface in sand The load on
the footing is equivalent to a vertical pressure of 400kPa. The saturated
unit weight of the sand below the water table is 20kN/m3 and above the
water table its unit weight is 17kN/m3
The design parameters for the strength of the soil obtained from testing
are c’ = 0 and = 35°
s Determine the factor of safety with respect to bearing
failure for the following cases:
The water table is 5m below ground surface.
The water table is 1m below ground surface.
The water table is at the ground surface.
Comment on the effects of water.
Q4.4
Buried rigid footing
A ngid footing of plan dimensions 1.5m x 1.5m shown below is
constructed in soil of cohesion 30kN/m2, angle of fnction 25 degrees,
total unit weight 20kN/m3, Youngs Modulus 8400kPa and Poissons
ratio of 0.35.
1.5m
In a plate bearing test in the same soil, using plate dimensions 0 3m
x 0 3m and a bearing pressure of 400kN/m2, the settlement of the
plate is 4 5mm
a Calculate the greatest load that may be applied to
the footing, if the factor of safety against general
shear failure is to be at least 3.0 and settlement
according to the theory of linear elasticity must not
exceed 30mm.