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Porosity, Degree of Saturation, Void Ratio and - most

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MINISTRY OF SCIENCE AND TECHNOLOGY
DEPARTMENT OF
TECHNICAL AND VOCATIONAL EDUCATION
Sample Questions & Worked Out Examples
for
CE-04015
GEOTECHNICAL ENGINEERING
B.Tech. (Second Year)
Civil Engineering
MINISTRY OF SCIENCE AND TECHNOLOGY
DEPARTMENT OF
TECHNICAL AND VOCATIONAL EDUCATION
CE-04015
GEOTECHNICAL ENGINEERING
Sample Questions
B.Tech. (Second Year)
Civil Engineering
PART - I
1
CHAPTER ( 1 ) Soil and Rocks
1.* Define: (a) Effective size, (b) Uniformity Coefficient, (c) Coefficient of Gradation.
2.* The Atterberg limits of a soil are LL = 74, PL = 27 and the soil contains 43% by weight
of clay. The water content of the soil is П‰ = 65.1%. Calculate the plasticity index 0f the soil.
3.* For a soil suppose that D10 = 0.08mm, D30 = 0.22mm, and D60 = 0.41mm. Calculate the
uniformity coefficient and the coefficient of gradation.
4.* A liquid limit test carried out on a sample of inorganic soil taken from below the water
table gave the following results:
Penetration (mm)
15.6 18.2 21.4 23.6
Moisture content ( % )
34.6 40.8 48.2 53.4
A plastic limit test gave a value of 33%. Determine the liquid limit and plasticity
index of this soil.
5.** Following are the results of a sieve analysis.
U.S sieve no.
4
10
20
40
60
100
200
Pan
Mass of soil retained
28
42
48
128
221
86
40
24
( a ) Determine the percent finer than each sieve and plot a grain-size distribution curve.
( b ) Determine D10, D30 and D60 from the grain-size distribution curve.
( c ) Calculate the uniformity coefficient, Cu.
( d ) Calculate the coefficient of gradation, Cc.
2
6.** Following are the results of a sieve analysis.
Opening size (mm)
4.76
2.00
1.19
0.59
0.42
0.25
0.149
0.074
Pan
Mass of soil retained
10
30
52
80
141
96
105
85
51
( a ) Determine the percent finer each sieve and plot a grain-size distribution curve.
( b ) Determine D10, D30 and D60 from the grain-size distribution curve.
( c ) Calculate the uniformity coefficient, cu.
( d ) Calculate the coefficient of gradation, cc.
3
CHAPTER ( 2 ) Soil Composition
1.* Define:- Porosity, Degree of Saturation, Void Ratio and Water Content.
2.* A cylinder of undisturbed saturated soil is 38mm in diameter and 78mm long and its mass
is 142 g. after oven drying its mass is 86 g. Calculate the water content and unit weight of the
soil.
3.* Calculate the dry unit weight, the saturated unit weight and the buoyant unit weight of a
soil having a void ratio of 0.70 and a value of Gs is 2.72. Calculate also the unit weight and
water content at a degree of saturation of 75%.
4.* A soil specimen is 38mm in diameter and 76mm long and in its natural condition weights
168.0g. When dried completely in an oven the specimen weights 130.5g. The value of Gs is
2.73. What is the degree of saturation of the specimen?
5.** A soil has a bulk density of 1.91 Mg/m3 and a water content of 9.5%. The value of Gs is
2.70. Calculate the void ratio and degree of saturation of the soil. What would be the values
of density and water content if the soil were fully saturated at the same void ratio?
6.** For a soil in natural state, given e = 0.8, П‰ = 24% and Gs = 2.68.
( a ) Determine the moist unit weight, dry unit weight, and degree of saturation.
( b ) If the soil is made completely saturated by adding water, what would its moisture
content be at the time? Also find the saturated unit weight.
7.** A laboratory test carried out on an undisturbed sample of soil weighing 1.74 kg and
having a volume of 1/1000 m3 determined the specific gravity of the soils to be 2.7 and the
dry density of the soil to be 1500kg/m3. Calculate;
( a ) The void ratio and porosity.
( b ) The critical hydraulic gradient.
( c ) The critical hydraulic gradient.
( d ) The saturated and effective unit weight.
( e ) The degree of saturation of the soil.
8.** A sample of soil is prepared by mixing a quantity of dry soil (Gs = 2.7) with 10.5% by
weight of water. Find the weight of this wet mixture which will be required to produce, by
static compaction, a cylindrical specimen 150mm diameter by 125mm deep with 5% air
voids.
9.*** Soil has been compacted in an embankment at a bulk density of 2.15 Mg/m3 and a
water content of 12%. The value of Gs is 2.65. Calculate the dry density, void ratio, degree of
saturation and air content. Would it be possible to compact the above soil at a water content
of 13.5% to a dry density of 2.00 Mg/ m3?
10.*** A sample of soil weighing 30.6 kg had a volume of 0.0183 m3. When dried out in an
oven its weight was reduced to 27.2 kg. The specific gravity of the solids was found to be
2.65. Determine the following:
( a ) Bulk density
( b ) Dry density
( c ) Percentage moisture content
4
( d ) Void ratio
( e ) Porosity
( f ) Degree of saturation
( g ) Critical hydraulic gradient.
11.*** In order to measure the insitu density of a soil the following sand replacement test
was carried out 4.56 kg of soil were extracted from a hole at the surface of the soil. The hold
was then just filled with 3.54 kg of loose dry sand. ( a ) If the took 6.57 kg the same sand to
fill a container 0.0042 m3 in volume, determine the bulk density of the soil. ( b ) In a water
content determination 24 g of the moist soil weighted 20g after drying in an oven at 15В°c. If
the specific gravity of the particles was 2.68, determine the water content, the dry density and
the degree of saturation of the soil.
12.*** In a British standard compaction test a maximum dry density of 1.83 g/ml was
produced. After compaction by field plants an undisturbed sample of the same soil, obtained
by core cutter, weighted 2072g. The core cutter was 127mm long with a diameter of 102mm.
Laboratory tests for water content and specific gravity yield a dry mass of 1806g and 2.67
respectively. Determine for the field compacted soil sample.
( a ) water content
( b ) bulk density
( c ) void ratio
( d ) air content
( e ) degree of saturation
5
CHAPTER ( 3 ) Classification of Soil
1.** The particle-size characteristics of a soil are given as follows:
Sizes
0.425
0.033
0.018
0.010
0.0062
0.0035
0.0018
0.0010
% finer
100
90
80
70
60
50
40
35
Draw a particle-size distribution curve and determine the percentages of gravel, sand,
silt, and clay, using AASHTO system.
6
CHAPTER ( 4 ) Flow of Water in Soil
1.* In a falling head permeability test the initial head of 1.00 m dropped to 0.35 m in 3h, the
diameter of the standpipe being 5mm. The soil specimen was 200mm long by 100mm in
diameter. Calculate the coefficient of permeability of the soil.
2.* For a constant head permeability tests, the following values are given.
L = 300mm
A = specimen area = 32 cm2
k = 0.0244 cm/sec
The head differences was slowly changed in steps to 800, 700, 600, 500and 400 mm.
Calculate and plot the rate of flow, q, through the specimen, in cm3/sec, against the head
different.
3.** A deposit of soil is 16m deep and overlies an impermeable stratum: the coefficient of
permeability is 10-6 m/s. A sheet pile wall is driven to a depth of 12.00m in the deposit. The
difference in water level between the two sides of piling is 4.00m. Draw the flow net and
determine the quantity of seepage under the piling.
4.** The section through part of a cofferdam is shown in Figure, the coefficient of
permeability of the soil being 2.0 x 10-6 m/s. Draw the flow net and determined the quantity
of seepage.
5.** Refer to Figure. Fine the flow rate in m3/sec/m length (at right angle to the cross section
shown) through the permeable soil layer. Given: H = 4m, H1=2m, h = 3.1m, L = 30m, О± =
14В°,
k = 0.05 cm/sec.
7
6.** For the flow net drawn in Figure. Calculate the up lift force at the base of the weir per
foot length (measured along the axis) of the structure.
7.** The section through part of a sheet pile wall is shown in the Figure. The saturated unit
weight of the soil being 19 kN/m3 and coefficient of permeability is 2.5x10-5 m/s. The length
of the sheet pile wall is 30m. Determine the quantity of seepage per day and pore water
pressure at end of the sheet pile wall.
8
8.*** A homogeneous isotropic earth dam section is detailed in figure, the coefficients of
permeability is 4.5 x 10-8. Draw the first flow line and determine the quantity of seepage
through the dam.
9.*** An embankment dam is shown in section in Figure, the coefficient of permeability in
the horizontal and vertical directions being 7.5 x 10-6 and 2.7 x 10-6 m/s respectively.
Construct the top flow line and determine the quantity of seepage through the dam.
10.*** The flow net for seepage under the proposed dam shown in the figure below is 100m
long and 25.5m wide. To decrease the seepage loss, sheet piles were driven in at the heel and
at the toe of the dam to a depth of 6.3. The coefficient of permeability of the soil is 0.05 cm/s.
The saturated unit weight of the soil is 20 kN/m2.
( a ) Find the quantity of water that will be lost per day per seepage.
( b ) Plot the distribution of uplift pressure on the base of the dam.
9
CHAPTER ( 5 )Effective Stress
1.* The bed of a river 5 m deep consists of saturated unit weight 19.5 kN/m3 . Calculate the
effective vertical stress 5 m below the surface of the sand.
2.** A layer of clay 4 m thick lies between two layers of sand each 4 m thick, the top of the
upper layer of sand being ground level. The water table is 2 m below ground level but the
lower layer of sand is under artesian pressure, the piezometric surface being 4 m above
ground level. The saturated unit weight of the clay is 20 kN/m3 and that of the sand 19 kN/m3
: above the water table the unit weight of the sand is 16.5 kN/m3 . Calculate the effective
vertical stresses at the top and bottom of the clay layer.
3.** In a deposit of fine sand the water table is 3.5 m below the surface but sand to a height
of 1.0 m above the water is saturated by capillary water: above this height the sand may be
assumed to be dry. The saturated and dry unit weights, respectively, are 20 kN/m3 and 16
kN/m3 . Calculate the effective vertical stress in the sand 8 m below the surface.
4.** Refer to figure. Calculate Пѓ, u and Пѓ/ at A, B, C and D for the following cases, and plot
the variations with depth.
For soil layer I, H1 = 2 ft, Оіd = 115 lb/ft3
II, H2 = 4 ft, Оіsat = 118 lb/ft3
III, H3 = 6 ft, Оіsat = 130 lb/ft3
5.** Refer to Figure. For the given data, calculate and plot Пѓ, u and Пѓ/ with depth.
Given: H1 = 6 ft, H2 = 4 ft, H3 = 9 ft
Degree of saturation in capillary rise zone, s (%) = 50%
10
6.*** Refer to the soil profile shown in Figure.
( a ) Calculate and plot the variation of Пѓ, u and Пѓ/ with depth.
( b ) If the water table rises to the top of the ground surface, what is the change in the
effective stresses at the bottom of the clay layer?
( c ) How many feet must the ground water table rises to decrease the effective stress by 300
lb/ ft2 at the bottom of the clay layer?
7.*** A layer of sand extends from ground level to a depth of 9 m and overlies a layer of
clay, of very low permeability, 6m thick. The water table is 6m below the surface of the sand.
The saturated unit weight of the sand is 19 kN/m3 and that of the clay 20 kN/m3 : the unit
weight of the sand above the water table is 16 kN/m3 . Over a short period of time the water
rises by 3m and is expected to remain permanently at this new level. Determine the effective
vertical stress at depth of 8m and 12m below ground level ( a ) immediately after the rise of
the water table, ( b ) several years after the rise of the water table.
8.*** A stratum of sand 2.4m thick overlies a stratum of saturated clay 3.0m thick. The water
table being 0.9m below the ground surface. The saturated unit weight of the clay and sand
are 18.5 kN/m3 and 20.6kN/m3 respectively. Above the water table the unit weight of the
sand is 17.4 kN/m3.
11
( a ) Calculate total vertical stress and effective vertical stress at against depth.
( b ) If sand to a height of 0.9m above the water table is saturated with capillary water, how
are the above stress affected?
( c ) If the water table rise to the ground surface, what is the effect on the stresses?
9.*** The soil stratum is shown in Figure. Plot the total stress, pore water pressure and
effective stress with depth.
( a ) Assume that zone of capillary rise is s = 100%.
( b ) If water table rise to 2m above the old water table.
12
CHAPTER ( 6 ) Stresses in Soil Mass
1.* For the stressed soil element shown in Figure, determine
( a ) Major principal stress
( b ) Minor principal stress
( c ) Normal and shear stress on the plain AE.
2.* Using the equation, for the soil mass is shown in Figure. Determine the following,
( a ) Maximum and minimum principal stresses.
( b ) Normal and shear stress on the plain AB.
3.* Using the principal of Mohr’s circles, for the soil element shown in Figure, determine the
following.
( a ) Maximum and minimum principal stresses.
( b ) Normal and shear stresses on the plain AB.
13
4.* Calculate the vertical stress in a soil mass of 5m vertically below a point load of 5000 kN
acting near the surface. Plot the variation of vertical stress with radial distance (up to 10m) at
a depth of 5m.
5.* Three point loads, 10,000 kN, 7500 kN and 9000 kN, act in line 5m apart near the surface
of a soil mass. Calculate the vertical stress at a depth of 4m vertically below the center (
7500kN ) load.
6.** Determine the vertical stress at a depth of 3m below the center of a shallow foundation
2m x 2m carrying a uniform pressure of 250 kN/m2. Plot the variation of vertical stress with
depth ( up to 10m ) below the center of the foundation.
7.** A shallow foundation 25m x 18m carries a uniform pressure of 175 kN/m2. Determine
the vertical stress at a point 12m below the mid-point of one of the longer sides by using
influence factors.
8.** Consider a point load p = 10000 lb. Plot the variation of the vertical stress increase, with
depth causes by the point load below the ground surface with x = 3 ft and y = 4 ft. z is
consider up to 20 ft.
9.** Consider a circularly loaded flexible area on the ground surface. Given that the radius of
the circular area R = 6 ft and that the uniformly distributed load q = 3500 lb / ft2. Calculate
the vertical stress increase, ∆p at points 1, 2, 3, 6, 9 and 12 ft below the ground surface (
immediately below the center of the circular area.)
10.** A strip footing 2m wide carries a uniform pressure of 250 kN/m3 on the surface of a
deposit of the sand. The water table is at the surface. The saturated unit weight of the sand is
20 kN/m3 and Ko = 0.40. Determine the effective vertical and horizontal stresses at a point
3m below the center of the footing before and after the application of the pressure.
11.*** Refer to Figure. Given q1= 750 lb / ft, x1 = 8 ft, x2 = 4 ft and z = 3 ft. If the vertical
stress increase at point A due to the loading is 35 lb / ft2, determine the magnitude of q2.
14
12.*** Point load of magnitude 2000, 4000 and 6000 lb act at A, B and C respectively shown
in Figure. Determine the increase in vertical stress at a point of 10 ft below point D.
13.*** The plan of a flexible rectangular area is shown in Figure. The uniformly distributed
load on the flexible area q is 1800 lb/ft2. Determine the vertical stress increase, ∆p, at a depth
of z = 5 ft below.
( a ) Point A, ( b ) Point B, ( c ) Point C
15
14.***Refer to previous problem. Calculate and plot the stress increase at z = 0, 5, 10, 15, 20
and 25 ft below the center of the loaded area.
15.*** A rectangular foundation 6m x 3m carries a uniform pressure of 300 kN/m2 near the
surface of a soil mass. Determine the vertical stress at a depth of 3m below a point ( A ) on
the center line 1.5m outside a long edge of the foundation, using influence factors.
PART - II
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