2 - Soil Mechanics Laboratory Manual by Engr. Yasser M.S. - Compressed

SOIL MECHANICS LABORATORY MANUAL 96
Definition
A stress increase caused by the construction of structures or other loads compresses
soil layers. This compression is offered by three different causes, these are: (a)
Deformation of soil particles, (b) Relocations of soil particles and (c) Expulsion of
water or air from the void spaces. However, the soil settlement caused by loads may
be divided into three broad categories, these are: (1) Elastic settlement (immediate
settlement), (2) Primary consolidation settlement and (3) Secondary consolidation
settlement. The three different settlements may be defined at a glance as follows:
(1) Elastic settlement (Se ), which is the settlement caused, immediately, by the
elastic deformation of soil, regardless of whether it is dry, moist or saturated,
without any change in the moisture content. Elastic settlement calculations are
generally based on equations derived from the theory of elasticity and they
will be extensively discussed in Foundation Engineering course in the
semester, ahead of you.
(2) Primary consolidation settlement (Sc ), which comes as a result of a volume
change in saturated cohesive soils due to the expulsion of water that occupies
the void spaces existing between soil particles.
(3) Secondary consolidation settlement (Sp ), which is observed in saturated
cohesive soils and is the result of plastic adjustment of soil fabrics. It is an
additional form of compression that occurs at constant effective stress.
Therefore, the total settlement can be expressed as the sum of the three components
as follows:
ST = Se + Sc + SP
Where:
ST = total settlement of soil.
Se = elastic settlement of soil.
Sc = primary consolidation settlement of soil.
Sp = secondary consolidation settlement of soil.
Further, there are some informative terms that are really important. These are:
Over Consolidation Ratio (OCR): It is a ratio that results when dividing the pre-
consolidation pressure over the present effective vertical pressure that a soil
experiences. Therefore, this ratio is:
Engr. Yasser M. S. Almadhoun

σ′c
OCR =
σ′
Where:
OCR = over consolidation ratio.
σ′c = pre-consolidation pressure.
σ′ = present effective vertical pressure.
Pre-consolidation pressure is the maximum effective vertical overburden stress

(pressure) that a soil has sustained in the past. Basically, this ratio results in two
definitions of clay depending upon its stress history, which are as follows:
Normally consolidated clay: The clay is said to be normally consolidated when its
present pressure is the maximum pressure that the soil has been subjected to during
its geological life. Thus, the over consolidation ratio is equal to one.
Over Consolidated Clay: The clay is said to be over consolidated when the present
pressure is less than the maximum pressure that the soil was subjected to during its
geological life. Thus, the over consolidation ratio is greater than one.
Under consolidated clay: The clay is said to be under consolidated when its present
pressure is greater than the maximum pressure that the soil has been subjected to
during its geological life. Thus, the over consolidation ratio is less than one.
OCR > 1.0 → Over Consolidated Clay (OCC)
Over Consolidation Ratio (OCR) OCR = 1.0 → Normally Consolidated Clay (NCC)
OCR < 1.0 → Under Consolidated Clay (UCC)
Figure 11.01: Over consolidation ratio of clay.
Significance
 The consolidation properties determined from the consolidation test are used
to estimate the magnitude and the rate of both primary and secondary
consolidation settlements of a structure or an earth fill.

 Estimates of this type are of key importance in case of designing engineering

structures and evaluating their performance.
Purpose
Determination of some factors used in settlement calculations of a soil, which are:
(1) Coefficient of consolidation, Cv .
(2) Compression index, Cc .
Standard Reference
ASTM D2435 ─ Standard Test Method for One-Dimensional Consolidation
Properties of Soils.
Equipment and Materials

(1) Odometer apparatus (porous stones and loading device).
(2) Trimmer and Extruder.
(3) Stopwatch.
(4) Metal ring (of 2-cm height and 6.21-cm in diameter).
(5) Glass plate.
Figure 11.02: Consolidation apparatus and dial gages.

Procedure
(1) Prepare a soil sample from the field where soil is to tested.
(2) Put the porous stone below the ring, then put filter paper and soil sample above
it. Use glass plate to compress the sample and level its surface, then put
another porous stone above the sample.
(3) Put the sample in a vessel of the device which is fully filled with water to
ensure that the soil is fully saturated with water.
(4) Put the loads on the sample, then from the dials record the value of
deformation of the sample and the value of the load. Start the stop watch to
record the elapsed time for each deformation value for the same vertical load
until the values of deformations being constant, then increase the loads to the
double in each time and continue until 16-kg load at which it is expected that
total consolidation is occurred to the soil.
(5) Dry the sample and measure its dry mass Ms and its specific gravity, Gs .
Data Analysis
The result of Lab work will be the values of applied loads and the reading of
deformation. Cv can be determined by two methods:
(1) Determination of coefficient of consolidation, Cv :

a. Logarithmic Time Method.

Figure 11.03: Log time versus deformation plot.
2
0.197 Hdr
Cv =
t 50
Where:
Hdr = height of drainage which equals the thickness of soil layer if one way drainage
or one half the thickness of soil layer for two-way drainage.
t 50 : time required for 50% consolidation.
b. Square Root Method.
OC = 1.15 × OB
2
0.848 Hdr
Cv =
t 90

Figure 11.04: Square root of time versus deformation plot.
(2) Determination of compression index, Cc :

Draw a relation between the applied stresses in log scale on x-axis versus the
values of void ratio, e, on y-axis to obtain Cc .
Ms
Cv =
ρw Gs A
Hi − Hs
eo =
Hs
∑ ∆H
ei = eo −
Hs
Where:
Hs = height of the soil solids in a specimen which is constant.

Figure 11.05: Pre-consolidation pressure.
Figure 11.06: Pressure versus deformation plot.

Measurements
Measurements of the testing are shown as given as under:
(1) Factor of consolidation, 𝐂𝐯

Table 11.01: Testing measurements.
Normal Stress, 𝛔 = 𝟏𝟎𝟎 𝐤𝐏𝐚

Elapsed Time (min) Dial Readings (0.02 mm)
00.00 57.5
00.10 64.5
00.25 66.5
00.50 68.0
01.00 68.5
02.00 70.5
04.00 71.5
08.00 73.5
15.00 76.5
30.00 78.5
60.00 82.0
120.0 87.0
256.0 92.5
420.0 95.5
1417 96.5

Normal Stress, 𝛔 = 𝟐𝟎𝟎 𝐤𝐏𝐚

Elapsed Time (min) Dial Readings (0.02 mm)
00.00 096.5
00.10 108.0
00.25 110.5
00.50 112.0
01.00 114.5
02.00 116.0
04.00 118.5
08.00 122.0
15.00 125.5
30.00 131.0
60.00 136.5
120.0 142.0
256.0 146.5
420.0 149.5
1417 150.5
Height of specimen, Hi = 2.0 cm
(2) Factor of compression, 𝐂𝐜 , and pre-consolidation pressure, ′𝐜

Pressure (kPa) Displacement, H (0.001 mm)

00.00 00.0
25.00 34.0
50.00 29.0
100.0 41.0
200.0 56.0
400.0 73.0
800.0 69.0
1600 73.0

Computation
(1) Factor of consolidation, 𝐂𝐯

(A) For normal stress, σ = 100 kpa
Table 11.04: Testing results.
Dial Readings Deformation, H

Elapsed Time (min)
(0.02 mm) (mm) √𝐭
00.00 57.5 1.15 00.00
00.10 64.5 1.29 00.32
00.25 66.5 1.33 00.50
00.50 68.0 1.36 00.71
01.00 68.5 1.37 01.00
02.00 70.5 1.41 01.41
04.00 71.5 1.43 02.00
08.00 73.5 1.47 02.83
15.00 76.5 1.53 03.87
30.00 78.5 1.57 05.48
60.00 82.0 1.64 07.75
120.0 87.0 1.74 10.95
256.0 92.5 1.85 16.00
420.0 95.5 1.91 20.49
1417 96.5 1.93 37.64

(a) Logarithmic Time Method
Logarithm of Time Method

1.00
1.10
d0 = 1.3 mm
1.20
← Deformation, ΔH (mm)
1.30 t1 = 1 sec
1.40
t2 = 4 sec
1.50 d50 = 1.91 mm
1.60 t50 = 44 sec
1.70
1.80 d100 = 1.92 mm
1.90
2.00
0.1 1 10 100 1000 10000
Log(t)
Figure 11.07: Logarithm of time method.
Consequently, final results of the testing are shown as given as under:

Item Data
t1 (minutes) 1.00
t2 (minutes) 4.00
d0 (millimetres) 1.30
t50 (millimetres) 44.0
Hi (millimetres) 20.0
Initial reading (millimetres) 1.15
Final reading (millimetres) 1.93
Davg (millimetres) 0.39
Hdr (centimetres) 0.9805
Cv (square centimetres per minute) 0.0043044

(b) Square Root of Time Method
Square Root of Time Method

1.00
1.10
1.20
1.30
1.40
1.50
1.60
1.70 t90 = 19 sec
1.80
1.90
OB
2.00
0 5 10 15 20 25 30 35 40
OC t ^ 0.5
Figure 11.08: Square root of time method.

Item Data
OB 20.0
OC 23.0
t 90 (minutes) 19.0
Cv (square centimetres per minute) 0.04290792

(B) For normal stress, σ = 200 kpa

Dial Reading Deformation, H

Elapsed Time (min)
(0.02 mm) (mm) √𝐭
00.00 096.5 1.93 00.0000
00.10 108.0 2.16 00.3162
00.25 110.5 2.21 00.5000
00.50 112.0 2.24 00.7071
01.00 114.5 2.29 01.0000
02.00 116.0 2.32 01.4142
04.00 118.5 2.37 02.0000
08.00 122.0 2.44 02.8284
15.00 125.5 2.51 03.8730
30.00 131.0 2.62 05.4772
60.00 136.5 2.73 7.74597
120.0 142.0 2.84 10.9545
256.0 146.5 2.93 16.0000
420.0 149.5 2.99 20.4939
1417 150.5 3.01 37.6431

(a) Logarithmic Time method.
Logarithm of Time Method

2.00
2.10 d0 = 2.22 mm
2.20
2.30
t1 = 1 sec
2.40
d50 = 2.6 mm t2 = 4 sec
2.50
2.60 t50 = 29 sec
2.70
2.80
d100 = 2.98 mm
2.90
3.00
3.10
3.20
0.1 1 10 100 1000 10000
Log(t)
Figure 11.09: Logarithm of time method.

Item Data
t1 (minutes) 1.00
t 2 (minutes) 4.00
t 50 (minutes) 29.0
Cv (cubic centimetres per minute) 0.006431228

(b) Square Root of Time Method
Square Root of Time Method

1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
t90 = 11.5 sec
2.6
2.7
2.8
2.9
3
3.1
OB
3.2
0 5 10 15 20 25 30 35 40
OC t ^ 0.5
Figure 11.10: Square root of time method.

Item Data
OB 17
OC 19.55
t 90 (minutes) 11.5
Hi (millimetres) 20
Cv (cubic centimetres per minute) 0.069810973

(2) Factor of compression, 𝐂𝐜 , and pre-consolidation pressure, ′𝐜

Dial Readings Deformation, ΔH

Pressure (kPa) 𝐞𝐢 = 𝐞𝐨 − ∑ ∆𝐇 /𝑯𝒔
(0.001 mm) (mm)
0.00 0.0 0.000 0.820210
25.0 34 0.034 0.789264
50.0 29 0.029 0.762870
100 41 0.041 0.725553
200 56 0.056 0.674583
400 73 0.073 0.608141
800 69 0.069 0.545340
1600 73 0.073 0.478898
90.0
Hs = π = 1.0987 cm
1.0 × 2.7 × × 6.2152
4
2.0 − 1.0987
e0 = = 0.82021
1.0987

Item Data
𝐇𝐬 (centimetres) 1.09870
𝐞𝐨 (ratio) 0.82021

Void Ratio Versus Effective Stress Plot

0.90
0.80
0.70
Void Ratio, e
0.60
0.50 Ϭ'c =175 Kpa
0.40
0.30
1 10 100 1000 10000
Effective Stresses, σ (kpa) ─ Log
Figure 11.11: Void ratio versus effective stress plot.
From the graph drawn above: σ′c = 175 kpa
Void Ratio Versus Effective Stress Plot

0.90
Slope = Cc
0.80
0.70
Void Ratio, e
0.60
Ϭ′𝐶 = 175 𝐾𝑝𝑎
0.50 σ'c = 175 Kpa
0.40
0.30
1 10 100 1000 10000
Effective Stresses, σ (kpa) ─ Log
Figure 11.12: Void ratio versus effective stress plot.

Cc = slope

Item Data
eo 0.8202
0.4 eo 0.3281
σ′c (kilopascals) 175.00
σ (kilopascals) 7200.0
0.8202 − 0.3281
Cc = = 7.0049×10−4
7200.0 − 175.00
Results and Discussion

After all calculations have been evaluated once, the results were as follows:
Cv = ?!
(A) For stress, σ = 100 kpa

a. Logarithmic Time method, Cv = 4.3044×10−3 mm²/min
b. Square Root of Time Method, Cv = 42.9079×10−3 mm²/min
(B) For stress, σ = 200 kpa

a. Logarithmic Time Method, Cv = 6.4312×10−3 mm²/min
b. Square Root of Time Method, Cv = 69.8110×10−3 mm²/min
Cc = ?!
Cc = 7.0049×10−4

Conclusion
 The results were not obtained exactly, since they are based on graphs, so
entrapped approximations are created.
 The value of Cv is smaller than one, which means that this method of
approximations, which is based on the graphs shown earlier, is close to be true
and, thus it is highly acceptable.

TEST NO. 12
DIRECT SHEAR TEST ON SAND
(ASTM D2216)
Introduction
This test method covers the determination of the consolidated-drained shear
strength of a sandy soil. The shear strength is one of the most important engineering
properties of a soil, since it is required whenever a structure is dependent upon the
shearing resistance of soil. The shear strength is needed for engineering situations,
such as determining the stability of slopes or cuts, finding the bearing capacity for
foundations and calculating the pressure exerted by a soil on a retaining wall. in
addition, in many engineering problems, for instance, design of foundation, retaining
walls, slab bridges, pipes and sheet piling, the value of cohesion and angle internal
friction of the soil involved are required for the design. Direct shear test is used to
predict these parameters quickly. However, this test is performed to cover the
laboratory procedure for determining these values for a cohesionless soil.
Page 115 of 202

Definition
There are several laboratory test methods now attainable to determine the shear
strength parameters (i.e. c, ∅, c′and ∅′) of various soil specimens in the laboratory.
They are as follows: (1) Direct shear test, (2) Triaxial test. (3) Direct simple shear
test, (4) Plane strain triaxial test and (5) Torsional ring shear test. The direct shear
test and the triaxial test are the two commonly used tests for determining the shear
strength parameters. The direct shear test will be described in detail in the
experiment that follows.
Shear strength is a term used in soil mechanics to describe the internal resistance per
unit area that a soil mass can develop to resist failure and sliding along any plane
inside it or it is the magnitude of the shear stress that a soil mass can sustain.
Moreover, the shear resistance of soil is a result of friction and interlocking of
particles and, probably, cementation or bonding at particle contacts. However, shear
strength is defined as the internal resistance per unit area that a soil mass can offer
to resist failure in shear.
The strength of a soil is dependent upon its resistance to shearing stresses. It is,
basically, made up of the following two components: (1) Frictional, which is offered
due to friction between individual particles. (2) Cohesive, which is offered due to
adhesion between the soil particles. The two components are, then, combined in
Mohr-Coulomb’s shear strength equation, which comes as follows:
τf = c + σ tan ∅
Where:
τf = shearing resistance of soil at failure.
c = cohesion of soil.
σ = total normal stress on the failure plane.
∅ = angle of soil shearing resistance or angle of internal friction.
The total normal stress at a point, in saturated soils, is the sum of the effective stress
(σ′ ) and pore water pressure (u). This may be expressed as:

σ = σ′ + u
Where:
σ = total normal stress at a point.
σ′ = cohesion of soil.
u = cohesion of soil.
A diagram of the direct shear testing machine is shown in Figure 12.01. The testing
machine used in direct shear test consists of a metal shear box in which a soil
specimen is placed. The soil specimens may be square or circular in plan. The size
of the specimens generally used is about 51 mm × 51 mm or 102 mm × 102 mm
(2 in. × 2 in. or 4 in. × 4 in.) across and about 25 mm (1 in.) high. The box is split
horizontally into halves. Normal force on the specimen is applied from the top of the
shear box. The normal stress on the soil specimens can be as great as 1050 kN/m2
(150 lb/in.2 ). Shear force is applied by moving one half of the box relative to the
other to cause failure in the soil specimen.
Figure 12.01: Drained direct shear test apparatus.

Significance
 The direct shear test is one of the oldest strength test for soils. In this
laboratory test, a direct shear device will be used to determine the shear
strength of a cohesionless soil (i.e. angle of internal friction or angle of repose,
∅). From the plot of shear stress versus its corresponding horizontal
displacement, the maximum shear stress is obtained for a specific vertical
confining stress. After the experiment is run several times for various vertical-
confining stresses, a plot of the maximum shear stresses versus the vertical
(normal) confining stresses for each of the tests performed is produced. From
the plot, a straight-line approximation of the Mohr-Coulomb failure envelope
curve can be drawn, ∅ may be determined and for cohesionless soils (c = 0),
the shear strength can be computed from the following equation:
τf = c + σ tan ∅
 In addition, knowing these information helps in determination of the bearing
capacity of soil, as well, lateral earth pressure coefficient.
Purpose
Determination of the shear strength parameters of soil (sand), which are:
 Cohesion, c.
 Angle of internal friction, ∅.
Those parameters are known as Shear Strength Parameters.
Standard Reference
ASTM D 3080 ─ Standard Test Method for Direct Shear Test of Soils Under
Consolidated Drained Conditions.

(1) Drained direct shear test apparatus.
(2) Metal shear box with square section (51 mm × 51 mm) or (102 mm × 102
mm) and height of 25 mm, the box is divided into two parts.

(3) Porous stones and filter papers.

(4) Motor generates horizontal force.
(5) Dial gages for horizontal displacement, vertical displacement, if required, and
shear force.
Figure 12.02: Drained direct shear testing machine.
Procedure
(1) Prepare soil sample from the field and ensure, during the test, that it has the
same field density, ρfield .
(2) Prepare shear box by putting porous stone and filter paper on its bottom, then
fill it with soil on 3 layers, each layer is compacted 20 blows, then put filter
paper and porous stone over the sample. Porous stone is used to allow water
to drain, thus sand is preferred in this test, since it has high coefficient of
permeability.
(3) Disconnect the bolts that joining the two parts of the box and make a little
space of 0.6 mm between the two parts.
(4) Adjust the dials at zero reading.
(5) Put vertical load, which cause vertical stress, σ, above the sample.
(6) Turn on a motor, which generates horizontal force causing shear stress, τ, then
take readings from horizontal displacement and shear force dial gages.

(7) Continue in taking readings until the sample fail or the horizontal
displacement become equal to 15% of the box’s dimension if the box is square
in shape, or of the box’s diameter if the box is circular in cross section.
(8) Prepare other samples from the same soil and expose it to other vertical
stresses, then make the same procedure and calculations.
Data Analysis
(1) Compute the cross-sectional area of the specimen.
For square box: A = D × D
For circular box: A = (π/4)D2
(2) Compute the shear stress value from the dial readings obtained at each
pressure increment.
(3) Draw the shear stress on the y-axis and the corresponding displacement on the
x-axis and obtain the value of shear stress at the peak displacement.
(4) Draw the normal stresses (pressure increments) on the x-axis and their
corresponding shear stresses, then develop the equation, which defines these
points in virtue of linear regression.
(5) Evaluate the values of soil internal friction, ∅ and cohesion, c by equating the
equation obtained from the last step with the following equation:
τ = c + σ tan ∅

Measurements
Shear box inside dimensions are 51 mm × 51 mm

Normal Stress, σ = 13.89 𝐤𝐏𝐚

Horizontal Dial Reading (0.00254 mm) Horizontal shear force (N)
00.0 00.00
10.0 26.04
16.0 26.44
26.0 27.10
33.0 27.36
41.0 30.01
48.0 31.33
54.0 38.59
60.0 40.57
67.0 43.21
73.0 45.86
81.0 47.17
88.0 49.82
97.0 50.48
104 51.14
111 51.80
119 53.78
126 54.44
134 55.10
142 56.43
149 57.08
157 57.75
176 53.78

Normal Stress, σ = 29.48 kPa

Horizontal Dial Reading (0.00254 mm) Horizontal Shear Force (N)
00.0 00.00
04.5 31.33
11.0 36.61
14.0 38.59
20 41.23
27.0 42.55
34.0 45.19
41.0 47.18
47.0 51.14
53.0 54.44
59.0 59.07
67.0 62.37
74.0 64.35
79.0 68.32
85.0 72.28
91.0 76.24
98.0 78.88
105 84.17
112 85.49
118 92.09
124 95.40
133 96.72
138 100.0
145 102.0
152 102.7


Horizontal Dial Reading (0.00254 mm) Horizontal Shear Force (N)
00.0 000.00
01.0 041.89
05.0 049.82
08.0 056.42
13.0 061.71
19.0 065.67
26.0 068.32
32.0 074.92
37.0 075.58
40.0 077.56
49.0 082.85
59.0 082.36
66.0 092.09
72.0 094.74
80.0 097.38
86.0 101.34
92.0 103.98
99.5 109.25
107 115.87
113 119.83
120 123.80
126 129.08
131 130.42
136 129.96
140 128.47

Computation
After all calculations have been evaluated once, the results were arranged in the
following tables:
Area = 51.0×10−3 × 51.0×10−3 = 0.002601 m2


Horizontal Dial Horizontal
Horizontal Shear
Reading (0.00254 Displacement, ΔH Shear Stress, 𝛕 (kPa)
Force (N)
mm) (mm)
00.0 00.000 0.000 00.000
10.0 26.040 0.025 10.012
16.0 26.440 0.041 10.165
26.0 27.100 0.066 10.419
33.0 27.360 0.084 10.519
41.0 30.010 0.104 11.538
48.0 31.330 0.122 12.045
54.0 38.590 0.137 14.837
60.0 40.570 0.152 15.598
67.0 43.210 0.170 16.613
73.0 45.860 0.185 17.632
81.0 47.170 0.206 18.135
88.0 49.820 0.224 19.154
97.0 50.480 0.246 19.408
104 51.140 0.264 19.662
111 51.800 0.282 19.915
119 53.780 0.302 20.677
126 54.440 0.320 20.930
134 55.100 0.340 21.184
142 56.430 0.361 21.696
149 57.080 0.378 21.945
157 57.750 0.399 22.203
176 53.780 0.447 20.677

ΔH-Displacement Versus Shear Stress Plot

25.00
τf = 22.203 kPa
20.00
Shear Stress, τ (kPa)
15.00
10.00
5.00
0.00
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
ΔH-Displacement (mm)
Figure 12.03: ΔH-displacement versus shear stress plot.


Horizontal Dial Horizontal
Horizontal Shear
Reading (0.00254 Displacement, ΔH Shear Stress, τ (kPa)
Force (N)
mm) (mm)
00.0 000.000 0.000 00.000
04.5 031.330 0.011 12.045
11.0 036.610 0.028 14.075
14.0 038.590 0.036 14.837
20.0 041.230 0.051 15.852
27.0 042.550 0.069 16.359
34.0 045.190 0.086 17.374
41.0 047.180 0.104 18.139
47.0 051.140 0.119 19.662
53.0 054.440 0.135 20.930
59.0 059.070 0.150 22.710
67.0 062.370 0.170 23.979
74.0 064.350 0.188 24.740
79.0 068.320 0.201 26.267
85.0 072.280 0.216 27.789
91.0 076.240 0.231 29.312
98.0 078.880 0.249 30.327
105 084.170 0.267 32.361
112 085.490 0.284 32.868
118 092.090 0.300 35.406
124 095.400 0.315 36.678
133 096.720 0.338 37.186
138 100.020 0.351 38.454
145 102.000 0.368 39.216
152 102.660 0.386 39.469


45.0
τf = 39.469 kPa
40.0
35.0
30.0
25.0
20.0
15.0
10.0
5.0
0.0
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45


Horizontal Dial
Horizontal Shear Horizontal
Reading (0.00254 Shear stress, τ (kPa)
Force (N) Displacement (mm)
mm)
00.0 00.000 0.000 00.000
01.0 41.890 0.003 16.105
05.0 49.820 0.013 19.154
08.0 56.420 0.020 21.692
13.0 61.710 0.033 23.725
19.0 65.670 0.048 25.248
26.0 68.320 0.066 26.267
32.0 74.920 0.081 28.804
37.0 75.580 0.094 29.058
40.0 77.560 0.102 29.819
49.0 82.850 0.124 31.853
59.0 82.360 0.150 31.665
66.0 92.090 0.168 35.406
72.0 94.740 0.183 36.424
80.0 97.380 0.203 37.439
86.0 101.340 0.218 38.962
92.0 103.980 0.234 39.977
99.5 109.250 0.253 42.003
107 115.870 0.272 44.548
113 119.830 0.287 46.071
120 123.800 0.305 47.597
126 129.080 0.320 49.627
131 130.420 0.333 50.142
136 129.960 0.345 49.965
140 128.470 0.356 49.393


55.00
τf = 50.142 kPa
50.00
45.00
40.00
35.00
30.00
25.00
20.00
15.00
10.00
5.00
0.00
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
Normal Stress, 𝛔𝐟 (kPa) Shear Stress, 𝛕𝐟 (kPa)

13.89 22.203
29.48 39.469
44.90 50.142

Normal Stress Versus Shear Stress Plot

60.0
50.0
shear Stress, τ (kPa)
40.0 y = 1.2097x
30.0
20.0
10.0
0.0
0.0 10.0 20.0 30.0 40.0 50.0
Normal Stress, Ϭ (kPa)
Figure 12.06: Normal stress versus shear stress plot.
τ = c + σ tan ∅
y = 0.0 + 1.2097x
Comparing the two past equations, one to another, leads to the results that follow:
c = 0.0
Slope = 1.2097
tan ∅ = 1.2097
∅ = tan−1 (1.2097) = 50.421˚

After all calculations have been evaluated once, all results were arranged in the
previous tables, for more details refer to the past section of computation.

Conclusion
 Sandy soil since cohesion, c = 0.0; and for clay, Ø = 0.0.
 Since the soil is sand, then c = 0.0, and Ø = 50.421˚ which is larger than
expected (Ø ≥ 45˚).

TEST NO. 13
UNCONFINED COMPRESSION TEST
(ASTM D2216)
Introduction
This test method covers the determination of the unconfined compression
strength, which is then used to calculate the unconsolidated undrained shear strength
of the clay under unconfined conditions. It is not always possible to conduct the
bearing capacity test in the field. Sometimes, it is cheaper to take the undisturbed
soil sample for testing its strength in the laboratory. In addition, to choose the best
material for the embankment, one has to conduct strength tests on the samples
selected. Under these conditions, it is easy to perform the unconfined compression
test on undisturbed and remoulded soil samples. Furthermore, in this test method,
the unconfined compression strength is taken as the maximum load attained per unit
area or the load per unit area at 15% axial strain, whichever takes place first during
the performance of a test.
Page 132 of 202

Definition
The unconfined compression test is a special type of unconsolidated-undrained test,
that is commonly used for clay specimens. The unconfined compression strength,
qu , is defined as the compressive stress, at which an unconfined cylindrical specimen
of soil will fail in a simple compression test.
With respect to shear strength, cohesive soil can fail under conditions of rapid
loading, where excess pore pressures do not have time to dissipate. Under these
conditions, the state of stress in a soil element can be demonstrated in virtue of a
Mohr circle, with minor and major total principal stress (σ3 and σ1 ), respectively. If
identical specimens of cohesive soil are subjected to different states of stress and
rapidly loaded to failure without excess pore pressure dissipation, the Mohr circles
of each specimen possess the same diameter, thus producing a ‘total stress envelope’
with a friction angle of zero and cohesion, c, equal to the undrained shear strength,
cu (see Figure 13.01). It is important to note, however, that if pore pressure is
measured within each specimen during shearing and total stresses are converted to
effective stresses, each Mohr circle overlaps one another and is tangent to the
effective stress envelope with an effective cohesion, c′, and effective friction angle,
∅′. This points out an important point regarding the strength of soil, which is: even
under rapid undrained loading, the strength of soil is still controlled by effective
stress.
Figure 13.01: Total stress Mohr-Coulomb failure envelope.
As demonstrated in Figure 13.02, the undrained shear strength, cu , is defined as the

intercept of the total stress failure envelope and it is half of the diameter of the Mohr

circle. The unconfined compression strength, cu , is defined as σ1 at failure. By

inspection, cu is equal to one half of qu .
Figure 13.02: Mohr circle from an unconfined compression test.
cu of clays is commonly determined from an unconfined compression test. cu of a

cohesive soil is equal to one half of the qu when the soil is under the ∅ = 0 condition.
The most critical condition for the soil usually occurs immediately after
construction, which represents undrained conditions, when the undrained shear
strength is basically equal to the cohesion, c. However, this is expressed as:
σ1 qu
τ=c= =
2 2
Then, as time passes, the pore water in the soil slowly dissipates and the intergranular
stress increases, so that the drained shear strength, τ, given by the following equation
must be used.
τ = c + σ′ tan ∅
Where:
σ′ = intergranular pressure acting perpendicular to the shear plane and σ′ = ( σ − u).

σ = total pressure.
u = pore water pressure.
c and ∅′ = drained shear strength parameters.
A typical configuration for the unconfined compressive strength testing is shown in

Figure 13.03. Axial deformation, ΔL, is measured using a deformation indicator and
applied load, P, is measured using a load cell.
Figure 13.03: Typical configuration for an unconfined compression test.
Generally speaking, the unconfined compression strength is determined by applying

an axial stress to a soil specimen that is cylindrical in shape with no confining
pressure and, thereafter, observing the axial strains at various stress levels. The
stress, at which failure in the soil specimen takes place, is referred to as the
unconfined compression strength (see Figure 13.04). For saturated clay specimens,
the unconfined compression strength decreases with the increase in water content.
For unsaturated soils, with constant dry unit weight, the unconfined compression
strength decreases with the increase in the degree of saturation. Furthermore, Table

13.01 illustrates the relationships of consistency and unconfined compression

strength of clays.
Figure 13.04: Definition of unconfined compression strength.
Table 13.01: General relationship of consistency and unconfined compression strength of clays.
Unconfined Compression Strength, qu

Consistency
𝐤𝐍/𝐦𝟐 (𝐭𝐨𝐧/𝐟𝐭 𝟐 )
Very soft 0 - 25 (0 - 0.25)
Soft 25 - 50 (0.25 - 0.5)
Medium 50 - 100 (0.5 - 1)
Stiff 100 - 200 (1 - 2)
Very stiff 200 - 400 (2 - 4)
hard > 400 (> 4)
Significance
 The undrained shear strength, cu , is necessary for the estimation of the bearing
capacity of spread footings, foundations, dams and other structures when
placed on deposits of cohesive soil.

Purpose
Determination of the unconfined compression strength of a cohesive soil in the
undisturbed or remoulded conditions at its natural water content. The applying load
rate is fast, so pore water is not allowed to dissipate and test considered being
undrained test shear.
Standard Reference
ASTM D2166 ─ Standard Test Method for Unconfined Compressive Strength of
Cohesive Soil.

(1) Unconfined compression device.
(2) Load and deformation dial gauges.
(3) Trimming equipment.
(4) Balance sensitive to an accuracy of 0.01 gm.
(5) Oven and moisture can.
Figure 13.05: Unconfined compression device.

Procedure
(1) Cut a soil specimen such that the ratio L/d is approximately between 2 and
2.5 so that:
2.0 ≤ L/d ≤ 2.5
Where:
L = length of the soil specimen.
d = diameter of the soil specimen.
(2) Measure the exact diameter of the top of the specimen at three locations
and then make the same measurements on the bottom of the specimen.
Take the average of the measurements and record it as the diameter.
(3) Measure the exact length of the specimen at three locations and then take
the average of the measurements and record the it as the length.
(4) Weigh the sample and record the mass.
(5) Calculate the deformation, ΔL, corresponding to 15% strain, ε.
ΔL
ε=
Lo
Where:
Lo = average length of the soil specimen.
(6) Carefully, place the specimen in the unconfined compression device and
centre it on the bottom plate. Adjust the device so that the upper plate just
makes contact with the specimen and set the load and deformation dials to
zero.
(7) Apply the load so that the device produces an axial strain at a rate of 0.5%
to 2.0% per minute and then record the load and deformation dial readings
onto the data sheet at every 20 to 50 divisions on deformation the dial.
(8) Keep applying the load until either (1) the load (i.e. load dial) decreases on
the specimen significantly or (2) the load holds constant for at least four
deformation dial readings; the deformation is significantly past the 15%
strain, which was determined in step 5.
(9) Draw a sketch to depict the sample failure.
(10) Remove the sample from the unconfined compression device. Obtain a
sample for water content measurement and measure the water content.

Data Analysis
(1) Convert the dial readings to the appropriate load and length units and
record these values onto the data sheet in the deformation and total load
columns.
(2) Compute the cross-sectional area of the specimen, Ao :
π
Ao = D2
4
(3) Compute the strain, ε:
∆L
ε=
Lo
(4) Compute the corrected area, A′:
Ao
Ao =
1−ε
(5) Compute the specimen stress:
P
σ= ′
A
(6) Plot the stress versus strain. Show qu as the peak stress or as the stress at
15% strain of the test. The strain is plotted on the abscissa.
(7) Draw Mohr-Coulomb’s circle using qu from obtained the last step and
compute the undrained shear strength, cu .
qu
cu = c =
2
Measurements
Diameter, D = 7.3 cm
Length, L = 14.5 cm
Mass of sample = 1221.4 gm
Percent water content = 35 %
Deformation-dial readings: each reading = 0.01 mm
Load-dial readings: each reading = 1.403 N

Deformation Dial Reading Load Dial Reading

0000.0 00.0
020.0 04.0
040.0 09.0
060.0 12.0
080.0 19.0
100.0 21.0
120.0 24.0
140.0 26.0
160.0 29.0
180.0 33.0
200.0 36.0
250.0 45.0
300.0 54.0
350.0 64.0
400.0 74.0
450.0 84.0
500.0 93.0
550 102
600.0 112
650.0 120
700.0 129
750.0 138
800.0 144
850.0 152
900.0 160
950.0 166
* *
* To be continued.

Deformation Dial Reading Load Dial Reading

* *
1000 171
1100 182
1200 192
1300 202
1400 209
1500 217
1600 223
1700 229
1800 234
1900 240
2000 243
2200 250
2400 253
2600 255
2800 256
3000 254
Computation
After all calculations have been evaluated once, the results were arranged in the
following table:
π
Area = × 7.3 = 41.854 cm2
4

Deformation,
Dial Reading
Deformation
Stress (𝐤𝐏𝐚)
Load (𝐤𝐍)
Corrected
Load Dial
𝚫𝐋 (mm)
Strain, 𝛆
%Strain
Reading
Area, 𝐀′
Sample
(𝐜𝐦𝟐)
000.0 00.0 0.0 0.000000 0.000000 41.83265 0.000000 0.000000
020.0 04.0 0.2 0.001379 0.137931 41.89043 0.005612 1.339685
040.0 09.0 0.4 0.002759 0.275862 41.94837 0.012627 3.010129
060.0 12.0 0.6 0.004138 0.413793 42.00647 0.016836 4.007954
080.0 19.0 0.8 0.005517 0.551724 42.06473 0.026657 6.337138
100.0 21.0 1.0 0.006897 0.689655 42.12315 0.029463 6.994490
120.0 24.0 1.2 0.008276 0.827586 42.18174 0.033672 7.982601
140.0 26.0 1.4 0.009655 0.965517 42.24049 0.036478 8.635790
160.0 29.0 1.6 0.011034 1.103448 42.29940 0.040687 9.618812
180.0 33.0 1.8 0.012414 1.241379 42.35848 0.046299 10.93028
200.0 36.0 2.0 0.013793 1.379310 42.41772 0.050508 11.90729
250.0 45.0 2.5 0.017241 1.724138 42.56656 0.063135 14.83207
300.0 54.0 3.0 0.020690 2.068966 42.71644 0.075762 17.73603
350.0 64.0 3.5 0.024138 2.413793 42.86738 0.089792 20.94646
400.0 74.0 4.0 0.027586 2.758621 43.01939 0.103822 24.13377
450.0 84.0 4.5 0.031034 3.103448 43.17249 0.117852 27.29794
500.0 93.0 5.0 0.034483 3.448276 43.32667 0.130479 30.11517
550.0 102 5.5 0.037931 3.793103 43.48197 0.143106 32.91158
600.0 112 6.0 0.041379 4.137931 43.63838 0.157136 36.00867
650.0 120 6.5 0.044828 4.482759 43.79592 0.168360 38.44194
700.0 129 7.0 0.048276 4.827586 43.95460 0.180987 41.17590
750.0 138 7.5 0.051724 5.172414 44.11443 0.193614 43.88904
800.0 144 8.0 0.055172 5.517241 44.27543 0.202032 45.63072
* * * * * * * *
* To be continued.

Deformation,
Dial Reading
Deformation
Stress (kPa)
Load (kN)
Corrected
Load Dial
𝚫𝐋 (mm)
Strain, 𝛆
%Strain
Reading
Area, 𝐀′
Sample
(𝐜𝐦𝟐)
* * * * * * * *
850.0 152 8.5 0.058621 5.862069 44.43761 0.213256 47.98998
900.0 160 9.0 0.062069 6.206897 44.60099 0.224480 50.33072
950.0 166 9.5 0.065517 6.551724 44.76557 0.232898 52.02615
1000 171 10 0.068966 6.896552 44.93136 0.239913 53.39544
1100 182 11 0.075862 7.586207 45.26667 0.255346 56.40927
1200 192 12 0.082759 8.275862 45.60702 0.269376 59.06459
1300 202 13 0.089655 8.965517 45.95253 0.283406 61.67364
1400 209 14 0.096552 9.655172 46.30331 0.293227 63.32743
1500 217 15 0.103448 10.34483 46.65949 0.304451 65.24953
1600 223 16 0.110345 11.03448 47.02120 0.312869 66.53787
1700 229 17 0.117241 11.72414 47.38855 0.321287 67.79845
1800 234 18 0.124138 12.41379 47.76169 0.328302 68.73752
1900 240 19 0.131034 13.10345 48.14075 0.336720 69.94490
2000 243 20 0.137931 13.79310 48.52587 0.340929 70.25716
2200 250 22 0.151724 15.17241 49.31491 0.350750 71.12453
2400 253 24 0.165517 16.55172 50.13004 0.354959 70.80765
2600 255 26 0.179310 17.93103 50.97256 0.357765 70.18777
2800 256 28 0.193103 19.31034 51.84388 0.359168 69.27876
3000 254 30 0.206897 20.68966 52.74552 0.356362 67.56252

Axial Stress Versus Percent Axial Strain Plot

80.0
70.0
60.0
Axial Stress (kPa)
50.0
40.0
30.0
20.0
10.0
0.0
25.0 20.0 15.0 10.0 5.0 0.0
%Axial Strain
Figure 13.06: Axial stress versus percent axial strain plot.
From the graph drawn above: At 15% strain, the value of qu is 72.0 kPa.
Therefore, the value of qu can be computed from as follows:

72.0
c=τ= = 36.0 kPa
2
Consequently, Mohr’s circle of the tested specimen can be drawn as given as under:
Figure 13.07: Unconfined compression device.


After all calculations have been evaluated once, the results were as follows:
 Unconfined compression strength, qu = 72.0 kPa

 Cohesion, c = 36.0 kPa
Conclusion
 For Sandy soils, the value of cohesion, c is 0.0, while the value of angle of
friction, ∅ is 0.0.
 The results in this experiment are convincing to an extent since the value of
cohesion, c is 0.0 and the value of angle of friction, ∅ is 50.405˚, which means
that the soil specimen tested is sand. Hence, this is totally true.
 Unconfined compression test is dependent upon making the soil specimen,
that is to be tested, exposed to header compression only, therefore, the value
of σ3 is 0.0.

REFERENCES
Soil Mechanics Laboratory Manual, 9th Edition, by B. M. Das, Oxford University

Press, 2015.
Principles of Geotechnical Engineering, 8th Edition, by B. M. Das & K. Sobhan, CL

Engineering, 2013.
American Society for Testing and Materials, 1995 Annual Book of ASTM Standards
- Vol. 04.08, Philadelphia, PA, 1995.
BS 1377 - British Standard Methods of Test for Soils for Civil Engineering Purposes,
1990.
Page 146 of 202

APPENDICES
Appendix A: Weight-Volume Relationships
Appendix B: Laboratory Data Sheets
Page 147 of 202

APPENDIX A
Weight-Volume Relationships
A-1
Weight-Volume Relationships
𝑊 = 𝑊𝑠 + 𝑊𝑤
𝑉 = 𝑉𝑠 + 𝑉𝑣 = 𝑉𝑠 + 𝑉𝑤 + 𝑉𝑎
𝑉𝑣
𝑛=
𝑉
𝑉𝑣
𝑒=
𝑉𝑠
𝑉𝑤
𝑆=
𝑉𝑣
𝑉𝑣
𝑉𝑣 𝑉𝑣 𝑉𝑠 𝑒
𝑛= = = =
𝑉 𝑉𝑣 + 𝑉𝑠 𝑉𝑣 + 1 𝑒 + 1
𝑉𝑠
𝑉𝑣
𝑉𝑣 𝑉𝑣 𝑛
𝑒= = = 𝑉 =
𝑉𝑠 𝑉 − 𝑉𝑣 1 − 𝑉𝑣 1 − 𝑛
𝑉
𝑀𝑤
𝑤=
𝑀𝑠
A-2
𝑊 𝑊𝑠 + 𝑊𝑤
𝛾= =
𝑉 𝑉
𝑊𝑑 𝑊𝑠 𝛾
𝛾𝑑 = = =
𝑉 𝑉 1+𝑤
𝛾𝑠𝑎𝑡 > 𝛾 > 𝛾𝑑
𝑊𝑠 = 𝛾𝑠 𝑉𝑠 = 𝐺𝑠 𝛾𝑤 𝑉𝑠
𝑊𝑤
𝑤=
𝑊𝑠
𝑊𝑤 = 𝑤𝑊𝑠 = 𝑤𝐺𝑠 𝛾𝑤 𝑉𝑠
𝐺𝑠 𝛾𝑤 𝑉𝑠
𝑊𝑠 𝐺𝑠 𝛾𝑤 𝑉𝑠 𝑉𝑠 𝐺𝑠 𝛾𝑤
𝛾𝑑 = = = =
𝑉 𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣 1 + 𝑒
𝑉𝑠 𝑉𝑠
(𝑤 + 1)𝐺𝑠 𝛾𝑤 𝑉𝑠
𝑊𝑤 + 𝑊𝑠 𝑊𝑤 + 𝑊𝑠 𝑤𝐺𝑠 𝛾𝑤 𝑉𝑠 + 𝐺𝑠 𝛾𝑤 𝑉𝑠 (𝑤 + 1)𝐺𝑠 𝛾𝑤 𝑉𝑠 𝑉𝑠
𝛾𝑠𝑎𝑡 = = = = =
𝑉 𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣 𝑉𝑠 𝑉𝑣
+
𝑉𝑠 𝑉𝑠
(𝑤 + 1)𝐺𝑠 𝛾𝑤 𝑉𝑠
𝑉𝑠 (𝑤 + 1)𝐺𝑠 𝛾𝑤
𝛾𝑠𝑎𝑡 = = = (𝑤 + 1)𝛾𝑑
𝑉𝑠 𝑉𝑣 1 + 𝑒
+
𝑉𝑠 𝑉𝑠
A-3
𝛾𝑠𝑎𝑡
𝛾𝑑 =
(𝑤 + 1)
𝑊𝑠
𝛾𝑑 =
𝑉
𝑊𝑠
𝑉=
𝛾𝑑
𝑊𝑠 𝐺𝑠 𝛾𝑤 𝑉𝑠
𝑉𝑣 𝑉 − 𝑉𝑠 𝑉 𝛾 𝛾𝑑 𝐺𝑠 𝛾𝑤
𝑒= = = −1= 𝑑 −1= −1= −1
𝑉𝑠 𝑉𝑠 𝑉𝑠 𝑉𝑠 𝑉𝑠 𝛾𝑑
𝑊𝑠 𝐺𝑠 𝛾𝑤 𝑉𝑠 𝑉𝑠 𝐺𝑠 𝛾𝑤
𝛾𝑑 = = = =
𝑉 𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣 1 + 𝑒
𝑉𝑠 𝑉𝑠
𝑊𝑠
𝛾𝑠 =
𝑉𝑠
𝑊𝑠
𝑉𝑠 =
𝛾𝑠
𝑊𝑤
𝛾𝑤 =
𝑉𝑤
𝑊𝑤
𝑉𝑤 =
𝛾𝑤
A-4
𝑊𝑤
𝑉𝑤 𝑉𝑣 𝑉𝑤 𝛾 𝑊𝑤 𝛾𝑠 𝑤𝐺𝑠 𝛾𝑤 𝑉𝑠 𝛾𝑠 𝛾𝑠
𝑆𝑒 = . = = 𝑤 = . = . =𝑤 = 𝑤𝐺𝑠
𝑉𝑣 𝑉𝑠 𝑉𝑠 𝑊𝑠 𝑊𝑠 𝛾𝑤 𝐺𝑠 𝛾𝑤 𝑉𝑠 𝛾𝑤 𝛾𝑤
𝛾𝑠
𝐺𝑠 𝛾𝑤 𝑉𝑠 𝛾𝑤 𝑉𝑣
𝑊𝑠 + 𝑊𝑤 𝑊𝑠 + 𝑊𝑤 𝐺𝑠 𝛾𝑤 𝑉𝑠 + 𝛾𝑤 𝑉𝑣 + 𝐺𝑠 𝛾𝑤 + 𝛾𝑤 𝑒
𝑉𝑠 𝑉𝑠
𝛾𝑠𝑎𝑡 = = = = =
𝑉 𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣 𝑉𝑠 𝑉𝑣 1+𝑒
+
𝑉𝑠 𝑉𝑠
(𝐺𝑠 + 𝑒)𝛾𝑤
=
1+𝑒
𝐺𝑠 𝛾𝑤 𝑉𝑠 𝑤𝐺𝑠 𝛾𝑤 𝑉𝑠
𝑊 𝑊𝑠 + 𝑊𝑤 𝐺𝑠 𝛾𝑤 𝑉𝑠 + 𝑤𝐺𝑠 𝛾𝑤 𝑉𝑠 + 𝐺𝑠 𝛾𝑤 + 𝑤𝐺𝑠 𝛾𝑤
𝑉𝑠 𝑉𝑠
𝛾= = = = =
𝑉 𝑉𝑣 + 𝑉𝑠 𝑉𝑣 + 𝑉𝑠 𝑉𝑣 𝑉𝑠 1+𝑒
+
𝑉𝑠 𝑉𝑠
𝐺𝑠 𝛾𝑤 (1 + 𝑤) 𝐺𝑠 𝛾𝑤 (1 + 𝑤) 𝐺𝑠 𝛾𝑤 (1 + 𝑤) 𝐺𝑠 𝛾𝑤 (1 + 𝑤)
= = 𝑛 = =
1+𝑒 1+ 1−𝑛 𝑛 1−𝑛+𝑛
1−𝑛 +
1−𝑛 1−𝑛 1−𝑛
𝐺𝑠 𝛾𝑤 (1 + 𝑤)
= = 𝐺𝑠 𝛾𝑤 (1 + 𝑤)(1 − 𝑛)
1
1−𝑛
𝛾𝑤 𝑉𝑣
𝑊𝑤 𝛾𝑤 𝑉𝑤 𝛾𝑤 (𝑉𝑤 = 𝑉𝑣 𝑖𝑓 𝑆 = 1) 𝛾𝑤 𝑉𝑣 𝛾𝑤 𝑉𝑣 𝑉
𝑤= = = = = =
𝑊𝑠 𝐺𝑠 𝛾𝑤 𝑉𝑠 𝐺𝑠 𝛾𝑤 𝑉𝑠 𝐺𝑠 𝛾𝑤 𝑉𝑠 𝐺𝑠 𝛾𝑤 (𝑉 − 𝑉𝑣 ) 𝐺 𝛾 (𝑉 − 𝑉𝑣 )
𝑠 𝑤 𝑉 𝑉
𝛾𝑤 𝑛 𝑛
= =
𝐺𝑠 𝛾𝑤 (1 − 𝑛) 𝐺𝑠 (1 − 𝑛)
𝑊𝑠 + 𝑊𝑤 + (𝐺𝑠 + 𝑤𝐺𝑠 )𝛾𝑤 (𝐺𝑠 + 𝑆𝑒)𝛾𝑤
𝑉𝑠 𝑉𝑠
𝛾= = = =
𝑉𝑠 + 𝑉𝑣 𝑉𝑠 𝑉𝑣 1+𝑒 1+𝑒
+
𝑉𝑠 𝑉𝑠
A-5
𝑊𝑤
𝑉𝑤 𝑉𝑣 𝑉𝑤 𝛾 𝑊𝑤 𝛾𝑠
𝑆𝑒 = . = = 𝑤 = . = 𝑤𝐺𝑠
𝑉𝑣 𝑉𝑠 𝑉𝑠 𝑊𝑠 𝑊𝑠 𝛾𝑤
𝛾𝑠
𝑊𝑠 + 𝑊𝑤 𝐺𝑠 𝛾𝑤 𝑉𝑠 + 𝑤𝐺𝑠 𝛾𝑤 𝑉𝑠 + (𝐺𝑠 + 𝑤𝐺𝑠 )𝛾𝑤
𝑉𝑠 𝑉𝑠
𝛾= = = =
𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣 𝑉𝑠 𝑉𝑣 1+𝑒
+
𝑉𝑠 𝑉𝑠
(1 + 𝑤 )𝐺𝑠 𝛾𝑤
=
𝑤𝐺𝑠
1+
𝑆
𝑊 𝑊𝑠 + 𝑊𝑤 𝐺𝑠 𝛾𝑤 𝑉𝑠 + 𝑤𝐺𝑠 𝛾𝑤 𝑉𝑠 + 𝐺𝑠 𝛾𝑤 + 𝑤𝐺𝑠 𝛾𝑤
𝑉𝑠 𝑉𝑠
𝛾= = = = =
𝑉 𝑉𝑣 + 𝑉𝑠 𝑉𝑣 + 𝑉𝑠 𝑉𝑣 𝑉𝑠 1+𝑒
+
𝑉𝑠 𝑉𝑠
𝐺𝑠 𝛾𝑤 (1 + 𝑤) 𝐺𝑠 𝛾𝑤 (1 + 𝑤) 𝐺𝑠 𝛾𝑤 (1 + 𝑤) 𝐺𝑠 𝛾𝑤 (1 + 𝑤)
= = 𝑛 = =
1+𝑒 1+ 1−𝑛 𝑛 1−𝑛+𝑛
1−𝑛 +
1−𝑛 1−𝑛 1−𝑛
𝐺𝑠 𝛾𝑤 (1 + 𝑤)
= = 𝐺𝑠 𝛾𝑤 (1 + 𝑤)(1 − 𝑛) = 𝐺𝑠 𝛾𝑤 (1 − 𝑛) + 𝑤𝐺𝑠 𝛾𝑤 (1 − 𝑛)
1
1−𝑛
𝑤𝐺𝑠 𝛾𝑤 𝑤𝐺𝑠 𝛾𝑤 𝑉𝑠
= 𝐺𝑠 𝛾𝑤 (1 − 𝑛) + = 𝐺𝑠 𝛾𝑤 (1 − 𝑛) +
1+𝑒 𝑉𝑠 + 𝑉𝑣
𝑊𝑤 𝛾𝑤 𝑉𝑤
= 𝐺𝑠 𝛾𝑤 (1 − 𝑛) + = 𝐺𝑠 𝛾𝑤 (1 − 𝑛) +
𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣
𝛾𝑤 𝑉𝑤 𝛾𝑤 (𝑉𝑤 = 𝑉𝑣 𝑖𝑓 𝑠𝑎𝑡)
𝑉𝑣 𝑉𝑣
= 𝐺𝑠 𝛾𝑤 (1 − 𝑛) + = 𝐺𝑠 𝛾𝑤 (1 − 𝑛) +
𝑉𝑠 𝑉𝑣 𝑉𝑠 𝑉𝑣
+ +
𝑉𝑣 𝑉𝑣 𝑉𝑣 𝑉𝑣
𝛾𝑤 𝑆 𝛾𝑤 𝑆𝑒
= 𝐺𝑠 𝛾𝑤 (1 − 𝑛) + = 𝐺𝑠 𝛾𝑤 (1 − 𝑛) + = 𝐺𝑠 𝛾𝑤 (1 − 𝑛) + 𝛾𝑤 𝑆𝑛
1 1+𝑒
+1
𝑒
A-6
𝑊𝑠 + 𝑊𝑤 𝐺𝑠 𝛾𝑤 𝑉𝑠 + 𝑤𝐺𝑠 𝛾𝑤 𝑉𝑠 + 𝐺𝑠 𝛾𝑤 + 𝑤𝐺𝑠 𝛾𝑤
𝑉𝑠 𝑉𝑠
𝛾𝑠𝑎𝑡 = = = =
𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣 𝑉𝑣 𝑉𝑠 1+𝑒
+
𝑉𝑠 𝑉𝑠
𝐺𝑠 𝛾𝑤 (1 + 𝑤)
= = 𝛾𝑑 (1 + 𝑤)
1+𝑒
𝛾𝑠𝑎𝑡
𝛾𝑑 =
1+𝑤
𝑊𝑠 𝐺𝑠 𝛾𝑤 𝑉𝑠 𝑉𝑠 𝐺𝑠 𝛾𝑤 𝐺𝑠 𝛾𝑤 𝐺𝑠 𝛾𝑤 𝐺𝑠 𝛾𝑤
𝛾𝑑 = = = = = = =
𝑉 𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣 1 + 𝑒 1 + 𝑛 1−𝑛 𝑛 1−𝑛+𝑛
𝑉𝑠 𝑉𝑠 1−𝑛 1−𝑛+1−𝑛 1−𝑛
𝐺𝑠 𝛾𝑤
= = 𝐺𝑠 𝛾𝑤 (1 − 𝑛)
1
1−𝑛
𝑊𝑠 𝐺𝑠 𝛾𝑤 𝑉𝑠 𝑉𝑠 𝐺𝑠 𝛾𝑤 𝐺𝑠 𝛾𝑤 𝐺𝑠 𝛾𝑤 𝐺𝑠 𝛾𝑤
𝛾𝑑 = = = = = = =
𝑉 𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣 1 + 𝑒 1 + 𝑆𝑒 1 + 𝑤𝐺𝑠 1 + 𝑤𝐺𝑠
𝑉𝑠 𝑉𝑠 𝑆 𝑆 𝑆
𝑊𝑠 𝑉𝑤
𝛾𝑠 𝑉𝑠 𝑊𝑠 𝑉𝑤 1 𝑉𝑤 1 𝑉𝑣 1 𝑆 1 𝑆𝑒
𝐺𝑠 = = = . = . = . = . = . 𝑆𝑒 =
𝛾𝑤 𝑊𝑤 𝑊𝑤 𝑉𝑠 𝑤 𝑉𝑠 𝑤 𝑉𝑠 𝑤 1 𝑤 𝑤
𝑉𝑤 𝑉𝑣 𝑒
𝐺𝑠 𝛾𝑤 𝑉𝑠 𝑆𝑒
𝑊𝑠 𝐺𝑠 𝛾𝑤 𝑉𝑠 𝑉𝑠 𝐺𝑠 𝛾𝑤 𝛾𝑤 𝑒𝑆𝛾𝑤
𝛾𝑑 = = = = = 𝑤 =
𝑉 𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣 1 + 𝑒 1 + 𝑒 𝑤(1 + 𝑒)
𝑉𝑠 𝑉𝑠
A-7
𝛾𝑤 𝑉𝑤
𝑊𝑠 + 𝑊𝑤 𝑊𝑠 𝑊𝑤 𝑊𝑤 𝛾𝑤 𝑉𝑤 𝑉𝑠
𝛾𝑠𝑎𝑡 = = + = 𝛾𝑑 + = 𝛾𝑑 + = 𝛾𝑑 +
𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣 𝑉𝑠 𝑉𝑣
+
𝑉𝑠 𝑉𝑠
𝛾𝑤 (𝑉𝑤 = 𝑉𝑣 𝑖𝑓 𝑠𝑎𝑡 ) 𝛾𝑤 𝑉𝑣
𝑉𝑠 𝑉 𝛾𝑤 𝑒
= 𝛾𝑑 + = 𝛾𝑑 + 𝑠 = 𝛾𝑑 +
1+𝑒 1+𝑒 1+𝑒
𝛾𝑤 𝑒
𝛾𝑑 = 𝛾𝑠𝑎𝑡 −
1+𝑒
𝛾𝑤 𝑉𝑤
𝑊𝑠 + 𝑊𝑤 𝑊𝑠 𝑊𝑤 𝑊𝑤 𝛾𝑤 𝑉𝑤 𝑉𝑠
𝛾𝑠𝑎𝑡 = = + = 𝛾𝑑 + = 𝛾𝑑 + = 𝛾𝑑 +
𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣 𝑉𝑠 𝑉𝑣
+
𝑉𝑠 𝑉𝑠
𝛾𝑤 (𝑉𝑤 = 𝑉𝑣 𝑖𝑓 𝑠𝑎𝑡 ) 𝛾𝑤 𝑉𝑣
𝑉𝑠 𝑉 𝛾𝑤 𝑒
= 𝛾𝑑 + = 𝛾𝑑 + 𝑠 = 𝛾𝑑 + = 𝛾𝑑 + 𝛾𝑤 𝑛
1+𝑒 1+𝑒 1+𝑒
𝛾𝑑 = 𝛾𝑠𝑎𝑡 − 𝛾𝑤 𝑛 = 𝛾𝑠𝑎𝑡 − 𝑛𝛾𝑤
A-8
𝑊𝑠 + 𝑊𝑤 + 𝐺𝑠 𝛾𝑤 + 𝑤𝐺𝑠 𝛾𝑤 (𝐺𝑠 + 𝑤𝐺𝑠 )𝛾𝑤
𝑉𝑠 𝑉𝑠
𝛾𝑠𝑎𝑡 = = = =
+
𝑉𝑠 𝑉𝑠
𝑊𝑠
𝑉
(𝐺𝑠 + 𝑤 𝑊𝑠 ) 𝛾𝑤
𝛾𝑠 𝑤 𝑊 𝑉
(𝐺𝑠 + 𝑤 ) 𝛾𝑤 𝑉𝑤 (𝐺𝑠 + 𝑤 𝑠 . 𝑤 ) 𝛾𝑤
𝛾𝑤 𝑊𝑤 𝑉𝑠
= = =
1+𝑒 1+𝑒 1+𝑒
𝑉𝑤
𝑉
(𝐺𝑠 + 𝑉𝑣 ) 𝛾𝑤 (𝐺 + 𝑆 ) 𝛾
1 𝑉 𝑠 𝑠 1 𝑤
(𝐺𝑠 + 𝑤 . 𝑤 ) 𝛾𝑤 𝑉𝑣 (𝐺𝑠 + 𝑆𝑒)𝛾𝑤
𝑤 𝑉𝑠 𝑒
= = = =
1+𝑒 1+𝑒 1+𝑒 1+𝑒
(𝐺𝑠 + 𝑆𝑒)𝛾𝑤 (𝐺𝑠 + (𝑆 = 1 𝑖𝑓 𝑠𝑎𝑡)𝑒)𝛾𝑤 (𝐺𝑠 + 1. 𝑒)𝛾𝑤
= = =
1+𝑒 1+𝑒 1+𝑒
(𝐺𝑠 + 𝑒)𝛾𝑤
=
1+𝑒
A-9
𝑊𝑠 + 𝑊𝑤 + 𝐺𝑠 𝛾𝑤 + 𝑤𝐺𝑠 𝛾𝑤 (𝐺𝑠 + 𝑤𝐺𝑠 )𝛾𝑤
𝑉𝑠 𝑉𝑠
𝛾𝑠𝑎𝑡 = = = =
+
𝑉𝑠 𝑉𝑠
(𝐺𝑠 + 𝑤𝐺𝑠 )𝛾𝑤 (𝐺𝑠 + 𝑤𝐺𝑠 )𝛾𝑤 (𝐺𝑠 + 𝑤𝐺𝑠 )𝛾𝑤 (𝐺𝑠 + 𝑤𝐺𝑠 )𝛾𝑤
= 𝑛 = = =
1+ 1−𝑛 𝑛 1−𝑛+𝑛 1
1−𝑛 +
1−𝑛 1−𝑛 1−𝑛 1−𝑛
= (𝐺𝑠 + 𝑤𝐺𝑠 )𝛾𝑤 (1 − 𝑛) = ((1 − 𝑛)𝐺𝑠 + (1 − 𝑛)𝑤𝐺𝑠 )𝛾𝑤
𝑊𝑠
𝛾𝑠 𝑉
= ((1 − 𝑛)𝐺𝑠 + (1 − 𝑛)𝑤 )𝛾 = (1 − 𝑛)𝐺𝑠 + (1 − 𝑛)𝑤 𝑠 𝛾𝑤
𝛾𝑤 𝑤 𝑊𝑤
𝑉𝑤
( )
1 + 𝑤 𝑊𝑠 (𝑉𝑤 = 𝑉𝑣 𝑖𝑓 𝑠𝑎𝑡)
𝑊𝑠 = ( ) . 𝛾𝑤
1 + 𝑒 𝑊𝑤 𝑉𝑠
= (1 − 𝑛)𝐺𝑠 + (1 − 𝑛)𝑤 . 𝛾𝑤
𝑊𝑤 𝑉𝑠
( )
1 + 𝑤 𝑊𝑠 𝑉𝑣
𝑊𝑠 = ( ) . 𝛾
1 + 𝑒 𝑊𝑤 𝑉𝑠 𝑤
= (1 − 𝑛)𝐺𝑠 + (1 − 𝑛)𝑤 . 𝛾𝑤
𝑊𝑤 𝑉𝑠
( )
1
= ((1 − 𝑛)𝐺𝑠 + (1 − 𝑛)𝑤 . 𝑒) 𝛾𝑤 = ((1 − 𝑛)𝐺𝑠 + (1 − 𝑛)𝑒)𝛾𝑤
𝑤
𝑛
= ((1 − 𝑛)𝐺𝑠 + (1 − 𝑛). ) 𝛾 = ((1 − 𝑛)𝐺𝑠 + 𝑛 )𝛾𝑤
(1 − 𝑛) 𝑤
𝑊𝑠 + 𝑊𝑤 + 𝐺𝑠 𝛾𝑤 + 𝑤𝐺𝑠 𝛾𝑤 (1 + 𝑤)𝐺𝑠 𝛾𝑤
𝑉𝑠 𝑉𝑠
𝛾𝑠𝑎𝑡 = = = =
𝑉𝑠 + 𝑉𝑣 𝑉𝑠 𝑉𝑣 1 + 𝑒 1+𝑒
+
𝑉𝑠 𝑉𝑠
(1 + 𝑤)𝐺𝑠 𝛾𝑤 (1 + 𝑤)𝐺𝑠 𝛾𝑤 (1 + 𝑤)𝐺𝑠 𝛾𝑤
= = =
1 + (𝑆 = 1 𝑖𝑓 𝑠𝑎𝑡)𝑒 1 + 𝑆𝑒 1 + 𝑤𝐺𝑠
1+𝑤
=( )𝐺 𝛾
1 + 𝑤𝐺𝑠 𝑠 𝑤
A-10
𝑊𝑠 + 𝑊𝑤 + 𝐺𝑠 𝛾𝑤 + 𝑤𝐺𝑠 𝛾𝑤 (1 + 𝑤)𝐺𝑠 𝛾𝑤
𝑉𝑠 𝑉𝑠
𝛾𝑠𝑎𝑡 = = = =
+
𝑉𝑠 𝑉𝑠
𝑊𝑠
1+𝑤 1 + 𝑤 𝛾𝑠 1 + 𝑤 𝑉𝑠
=( )𝐺 𝛾 = ( ) 𝛾 =( ) 𝛾
1+𝑒 𝑠 𝑤 1 + 𝑒 𝛾𝑤 𝑤 1 + 𝑒 𝑊𝑤 𝑤
𝑉𝑤
1 + 𝑤 𝑊𝑠 (𝑉𝑤 = 𝑉𝑣 𝑖𝑓 𝑠𝑎𝑡) 1 + 𝑤 𝑊𝑠 𝑉𝑣
=( ) . 𝛾𝑤 = ( ) . 𝛾
1 + 𝑒 𝑊𝑤 𝑉𝑠 1 + 𝑒 𝑊𝑤 𝑉𝑠 𝑤
1+𝑤 1 𝑒 1+𝑤
=( ) . 𝑒 𝛾𝑤 = ( ) ( )𝛾
1+𝑒 𝑤 𝑤 1+𝑒 𝑤
𝑊𝑠 + 𝑊𝑤 + 𝐺𝑠 𝛾𝑤 + 𝑤𝐺𝑠 𝛾𝑤 (1 + 𝑤)𝛾𝑤 𝐺𝑠
𝑉𝑠 𝑉𝑠
𝛾𝑠𝑎𝑡 = = = =
+
𝑉𝑠 𝑉𝑠
𝑊𝑠
𝑉𝑠
𝛾𝑠 𝑊𝑤
𝐺𝑠 𝛾𝑤 𝑉
= (1 + 𝑤 )𝛾𝑤 = (1 + 𝑤)𝛾𝑤 = (1 + 𝑤)𝛾𝑤 𝑤
1+𝑒 1+𝑒 1+𝑒
𝑊𝑠 (𝑉𝑤 = 𝑉𝑣 𝑖𝑓 𝑠𝑎𝑡 ) 1
. 𝑒
𝑊𝑤 𝑉𝑠
= (1 + 𝑤 )𝛾𝑤 = (1 + 𝑤)𝛾𝑤 𝑤
1+𝑒 1+𝑒
1 𝑒 1 𝑛 (1 + 𝑤 )
= (1 + 𝑤 )𝛾𝑤 = (1 + 𝑤)𝛾𝑤 𝑛 = (1 + 𝑤)𝛾𝑤 = 𝑛 𝛾𝑤
𝑤1+𝑒 𝑤 𝑤 𝑤
𝑊𝑠 + 𝑊𝑤 𝑊𝑠 𝑊𝑤 𝑊𝑤 𝑤𝐺𝑠 𝛾𝑤 𝑉𝑠 𝑤𝐺𝑠 𝛾𝑤 𝑉𝑠
𝛾𝑠𝑎𝑡 = = + = 𝛾𝑑 + = 𝛾𝑑 + = 𝛾𝑑 +
𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣
𝑉
𝑤𝐺𝑠 𝑉𝑣 𝑤𝐺𝑠 𝑠 𝑤𝐺𝑠 𝑆𝑒
𝑉𝑠
= 𝛾𝑑 + 𝛾𝑤 = 𝛾𝑑 + 𝛾𝑤 = 𝛾𝑑 + 𝛾𝑤 = 𝛾𝑑 + 𝛾𝑤
𝑉𝑠 + 𝑉𝑣 𝑉𝑠 𝑉𝑣 1 + 𝑒 1 + 𝑒
+
𝑉𝑠 𝑉𝑠
(𝑆 = 1 𝑖𝑓 𝑠𝑎𝑡)𝑒 1. 𝑒 𝑒
= 𝛾𝑑 + 𝛾𝑤 = 𝛾𝑑 + 𝛾𝑤 = 𝛾𝑑 + ( )𝛾
1+𝑒 1+𝑒 1+𝑒 𝑤
A-11
𝑊𝑠 + 𝑊𝑤 𝑊𝑠 𝑊𝑤 𝑊𝑤 𝑤𝐺𝑠 𝛾𝑤 𝑉𝑠 𝑤𝐺𝑠 𝛾𝑤 𝑉𝑠
𝛾𝑠𝑎𝑡 = = + = 𝛾𝑑 + = 𝛾𝑑 + = 𝛾𝑑 +
𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣
𝑉
𝑤𝐺𝑠 𝑉𝑣 𝑤𝐺𝑠 𝑠 𝑤𝐺𝑠 𝑆𝑒
𝑉𝑠
= 𝛾𝑑 + 𝛾𝑤 = 𝛾𝑑 + 𝛾𝑤 = 𝛾𝑑 + 𝛾𝑤 = 𝛾𝑑 + 𝛾𝑤
𝑉𝑠 + 𝑉𝑣 𝑉𝑠 𝑉𝑣 1 + 𝑒 1 + 𝑒
+
𝑉𝑠 𝑉𝑠
(𝑆 = 1 𝑖𝑓 𝑠𝑎𝑡)𝑒 1. 𝑒 𝑒
= 𝛾𝑑 + 𝛾𝑤 = 𝛾𝑑 + 𝛾𝑤 = 𝛾𝑑 + 𝛾 = 𝛾𝑑 + 𝑛𝛾𝑤
1+𝑒 1+𝑒 1+𝑒 𝑤
1 𝛾𝑑 𝐺𝑠 𝛾𝑤 𝛾𝑤 𝐺𝑠 𝛾𝑤 𝛾𝑤 𝛾𝑤 (1 + 𝑒)
(1 − ) 𝛾𝑑 + 𝛾𝑤 = 𝛾𝑑 − + 𝛾𝑤 = − + 𝛾𝑤 = − +
𝐺𝑠 𝐺𝑠 1+𝑒 1+𝑒 1+𝑒 1+𝑒 1+𝑒
𝐺𝑠 𝛾𝑤 − 𝛾𝑤 + 𝛾𝑤 + 𝑒𝛾𝑤 𝐺𝑠 𝛾𝑤 + 𝑒𝛾𝑤 (𝐺𝑠 + 𝑒)𝛾𝑤
= = = = 𝛾𝑠𝑎𝑡
1+𝑒 1+𝑒 1+𝑒
𝑊𝑠 + 𝑊𝑤 𝑊𝑠 𝑊𝑤 𝑤𝑊𝑠 𝑊𝑠
𝛾𝑠𝑎𝑡 = = + = 𝛾𝑑 + = 𝛾𝑑 + 𝑤 = 𝛾𝑑 + 𝑤𝛾𝑑
𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣 𝑉𝑠 + 𝑉𝑣
= 𝛾𝑑 (1 + 𝑤)
A-12
APPENDIX B
Laboratory Data Sheets
Measurement of Water Content

Measurement of Specific Gravity
Measurement of Unit Weight
Mechanical Sieve Analysis
Mechanical Hydrometer Analysis
Measurement of Consistency Limits
Modified Proctor Compaction
Field Density by Sand Cone Method
Constant-Head Permeability
Falling-Head Permeability
Consolidation Test
Direct Shear Test on Sand
Unconfined Compression Test
B-1
Measurement of Water Content
(Data Sheet)
Sample Description: _______________________________________________
Sample Number: __________________________________________________
Location: ________________________________________________________
Tested By: _______________________________________________________
Testing Date: _____________________________________________________
Item / Trial Sample No. 1 No. 2 No. 3
Specimen number
Moisture can and lid number
MC = Mass of empty, clean can + lid (grams)
MWC = Mass of can + lid + moist soil (grams)
MDC = Mass of can + lid + dry soil (grams)
MS = Mass of soil solids (grams)
MW = Mass of pore water (grams)
WC = Water content (percent)
WCAVG = Water content (percent)
B-2
Measurement of Specific Gravity
(Data Sheet)
Sample Number: __________________________________________________
Location: ________________________________________________________
Tested By: _______________________________________________________
Testing Date: _____________________________________________________
Item / Trial Sample No. 1 No. 2 No. 3

Specimen number
Pycnometer bottle number
WP = Mass of empty, clean pycnometer (grams)
WPS = Mass of empty pycnometer + dry soil (grams)
WB = Mass of pycnometer + dry soil + water (grams)
WA = Mass of pycnometer + water (grams)
GS = Specific Gravity (ratio)
GS(AVG) = Specific Gravity (ratio)
B-3
Measurement of Unit Weight (Density)
(Data Sheet)
Sample Number: __________________________________________________
Location: ________________________________________________________
Tested By: _______________________________________________________
Testing Date: _____________________________________________________
Unit Weight Measurement

Item / Trial Sample No. 1
MS = Mass of soil sample (grams)
MSW/AIR = Mass of soil sample covered with wax (grams)
MSW/WATER = Mass of soil sample (grams)
WS = Bulk weight of soil sample (newtons)
MW = Mass of paraffin wax (grams)
VW = Volume of paraffin wax (cubic metres)
VSW = Volume of soil sample covered with wax (cubic metres)
VS = Volume of soil sample (cubic metres)
 = Unit weight of soil sample (kilonewtons per cubic metre)
B-4
Moisture Content Measurement
Specimen number
Density Measurement
Specimen number
 = unit weight of soil sample (kilonewton per cubic metres)
g = Gravity acceleration (metres per square second)
B = Bulk density of soil sample (kilonewton per cubic metres)
D = Dry density of soil sample (kilonewtons per cubic metre)
B-5
Mechanical Sieve Analysis
(Data Sheet)
Sample Number: __________________________________________________
Location: ________________________________________________________
Tested By: _______________________________________________________
Testing Date: _____________________________________________________
Item Data
MC = Mass of container (grams)
MCD = Mass of container + dry soil sample (grams)
MD = Mass of dry soil sample (grams)
Sieve Cumulative Percent Percent
Sieve No. Opening Retained Cumulative Cumulative
(mm) (grams) Retained Passing
4 4.75
10 2
16 1.18
30 0.6
40 0.425
50 0.3
100 0.15
200 0.075
Pan 0.00
B-6
From the grain-size distribution ogive:
Item Data
Percent gravel
Percent sand
Percent fines
D10 = Size of grains that accounts for 10% of the total (mm)
Cu = Uniformity coefficient
Cz = Coefficient of gradation
Classification of the soil according to USCS: _____________________________
B-7
Mechanical Hydrometer Analysis
(Data Sheet)
Sample Number: __________________________________________________
Location: ________________________________________________________
Tested By: _______________________________________________________
Testing Date: _____________________________________________________
Item Data
Hydrometer number
GS = Specific gravity of solids (ratio)
Mass of dispersing agent (grams)
Mass of soil sample (grams)
Zero correction factor
Meniscus correction factor
B-8
Classification of the soil according to USCS: ___________________________________________________
Adjusted Percent Finer

(%PA)
Percent Finer (%P)
a from Table 5.04
= f (GS)
RC = RACTUAL – Zero
Correction + CT
CT from Table 5.03
= f (T˚)
𝐋 (𝐜𝐦)
𝐃(𝐦𝐦) = 𝐊√
𝐓 (𝐦𝐢𝐧)
K from Table 5.02
= f (GS, T˚)
L from Table 5.01 (cm)
Hydrometer Corrected
for Meniscus = RACTUAL +
1.0
RACTUAL
Temperature (˚C)
Elapsed Time (min)
B-9
`
B-10
Measurement of Consistency (Atterberg) Limits
(Data Sheet)
Sample Number: __________________________________________________
Location: ________________________________________________________
Tested By: _______________________________________________________
Testing Date: _____________________________________________________
Liquid Limit Measurement

Item / Trial Sample No. 1 No. 2 No. 3 No. 4
B-11
LL = Liquid Limit (%): _______________________________________________
Plastic Limit Measurement

PL = Plastic Limit (percent): __________________________________________
PI = Plasticity Index (percent): ________________________________________
B-12
Modified Proctor Compaction
(Data Sheet)
Sample Number: __________________________________________________
Location: ________________________________________________________
Tested By: _______________________________________________________
Testing Date: _____________________________________________________
Water Content Measurement

V = Volume of Mould (cubic centimetres): _____________________________________
B-13
Density Measurement
WC = Assumed water content (percent)
MM = Mass of empty mould (grams)
MMS = Mass of compacted soil and mould (grams)
MS = Wet mass of soil in mould (grams)
ρW = Wet density (grams per cubic centimetre)
ρD = Dry density (grams per cubic centimetre)
Optimum Moisture Content (percent): ___________________________________
Maximum Dry Density (grams per cubic centimetre): _______________________
B-14
Field Density by Sand Cone Method
(Data Sheet)
Sample Number: __________________________________________________
Location: ________________________________________________________
Tested By: _______________________________________________________
Testing Date: _____________________________________________________
Density Measurement
Item No. 1
WC = In-field water content (percent)
M1 = Weight of the jar filled with Ottawa sand (percent)
M2 = Weight of Ottawa sand retained in the jar (grams)
M3 = Mass of compacted soil and mould (grams)
MF = Weight of the soil sample taken from field (grams)
ρFB = In-field bulk density of soil (grams per cubic centimetre)
ρFD = In-field dry density of soil (grams per cubic centimetre)
In-field Dry Density (grams per cubic centimetre): __________________________
Maximum Dry Density (grams per cubic centimetre): ________________________
Degree of Compaction (percent): _______________________________________
B-15
Constant-Head Permeability
(Data Sheet)
Sample Number: __________________________________________________
Location: ________________________________________________________
Tested By: _______________________________________________________
Testing Date: _____________________________________________________
Item / Trial Sample No. 1 No. 2

D = Diameter of soil specimen (centimetres)
L = Length of soil specimen (centimetres)
MS = Weight of soil specimen (grams)
MEC = Weight of container empty (grams)
MWC = Weight of container + water (grams)
H = Deference in head in manometers (centimetres)
t = test duration (minutes)
Q = Quantity of water discharged (cubic centimetres)
q = Rate of flow (cubic centimetres per second)
A = Cross-sectional area of specimen (square centimetres)
k = Coefficient of permeability (centimetres per second)
Coefficient of Permeability at LAB Temperature, KT ˚C (cm/sec): _______________
Relative-Temperature Viscosity of Water, ηT °C /η20 °C (factor): _________________
Coefficient of Permeability at 20 ˚C, K20 ˚C (cm/sec): ________________________
B-16
Falling-Head Permeability
(Data Sheet)
Sample Number: __________________________________________________
Location: ________________________________________________________
Tested By: _______________________________________________________
Testing Date: _____________________________________________________
Item / Trial Sample No. 1 No. 2

D = Diameter of soil specimen (centimetres)
H1 = Head across sample at the test beginning (centimetres)
H2 = Head across sample at the test end (centimetres)
t = Collection duration (minutes)
A = Cross-sectional area of specimen (square centimetres)
a = Cross-sectional area of the burette (square centimetres)
k = Coefficient of permeability (centimetres per second)
Coefficient of Permeability at LAB Temperature, KT ˚C (cm/sec): _______________
Relative-Temperature Viscosity of Water, ηT °C /η20 °C (factor): _________________
Coefficient of Permeability at 20 ˚C, K20 ˚C (cm/sec): ________________________
B-17
Consolidation Test
(Data Sheet)
Sample Number: __________________________________________________
Location: ________________________________________________________
Tested By: _______________________________________________________
Testing Date: _____________________________________________________
Part I: Factor of consolidation (CV)
Stress, σ (kPa): ___________ Stress, σ (kPa): ___________

Deformation
Deformation
Time (min)
Time (min)
, ΔH (mm)
, ΔH (mm)
t0.50 (min)
t0.50 (min)
Reading
Reading
Elapsed
Elapsed
(min)
(min)
Dial
Dial
Hi = Height of Specimen (centimetres): __________________________________
B-18
(1) Logarithmic Time Method
Item Data
t2 (minutes)
t2 (minutes)
d0 (millimetres)
d100 (millimetres)
d50 (millimetres)
t50 (millimetres)
Hi (millimetres)
Initial reading (millimetres)
Final reading (millimetres)
DAVG (millimetres)
Hdr (centimetres)
CV (square centimetres per minute)
B-19
(2) Square Root of Time Method
Item Data
OB
OC
t90 (minutes)
Hi (millimetres)
Initial reading (millimetres)
Final reading (millimetre)
DAVG (millimetres)
Hdr (centimetres)
CV (square centimetres per minute)
B-20
Part II: Factor of compression (CC) and pre-consolidation pressure (σ’c)
Pressure (kPa) ΔH (0.001 mm) ΔH Viod Ratio, ei
Item Data
HS (centimetres)
eo (viod ratio)
Pre-consolidation Pressure, σ’C (kilopascals): ____________________________
B-21
Item Data
𝐞𝐨 (void ratio)
0.4 𝐞𝐨 (void ratio)
𝛔′𝐜 (kilopascals)
𝛔 (kilopascals)
Compression Index, CC (slope): _______________________________________
B-22
Direct Shear Test on Sand
(Data Sheet)
Sample Number: __________________________________________________
Location: ________________________________________________________
Tested By: _______________________________________________________
Testing Date: _____________________________________________________
Shear Box Inside Dimensions (millimetres): _____________________________
Shear Box cross-sectional area (square millimetres): ______________________
B-23
Horizontal
Dial Reading
(0.00254 mm)
Horizontal
Shear Force
(N)
Horizontal
Displacement,
ΔH (mm)
Shear Stress,
Normal Stress, σ (kPa): __________
τ (kPa)
B-24
Horizontal
Dial Reading
(0.00254 mm)
Horizontal
Shear Force
(N)
Horizontal
Displacement,
ΔH (mm)
Shear Stress,
τ (kPa)
Peak Shear Stress (kilopascals): ______________________________________
B-25
Horizontal
Dial Reading
(0.00254 mm)
Horizontal
Shear Force
(N)
Horizontal
Displacement,
ΔH (mm)
Shear Stress,
τ (kPa)
B-26
Horizontal
Dial Reading
(0.00254 mm)
Horizontal
Shear Force
(N)
Horizontal
Displacement,
ΔH (mm)
Shear Stress,
τ (kPa)
B-27
Horizontal
Dial Reading
(0.00254 mm)
Horizontal
Shear Force
(N)
Horizontal
Displacement,
ΔH (mm)
Shear Stress,
τ (kPa)
B-28
Horizontal
Dial Reading
(0.00254 mm)
Horizontal
Shear Force
(N)
Horizontal
Displacement,
ΔH (mm)
Shear Stress,
τ (kPa)
B-29
Normal Stress, σf (kPa) Shear Stress, τf (kPa)
T = c + σ tan ∅
Y=a+bX
Comparing the two past equations, one to another, leads to the results that follow:
c = 0.0 (since the spacemen is sand)
tan ∅ = slope = b
tan ∅: ___________________________________________________________
Angle of Internal Friction, ∅: __________________________________________
B-30
Unconfined Compression Test
(Data Sheet)
Sample Number: __________________________________________________
Location: ________________________________________________________
Tested By: _______________________________________________________
Testing Date: _____________________________________________________
Diameter of Specimen (millimetres): ___________________________________
Cross-sectional Area of Specimen (square millimetres): ____________________
B-31
Deformation
*
Dial Reading
* To be continued.
Load Dial
*
Reading
Sample
*
Deformation,
ΔL (mm)
*
Strain, ε
B-32
*
%Strain
Corrected
*
Area, A'
(cm2)
*
Load (kN)
*
Stress (kPa)
Deformation
*
Dial Reading
Load Dial
*
Reading
Sample
*
Deformation,
ΔL (mm)
*
Strain, ε
B-33
*
%Strain
Corrected
*
Area, A'
(cm2)
*
Load (kN)
*
Stress (kPa)
From the graph drawn above: At 15% strain, the value of qu is ___________ kPa
Therefore, the value of cu which is equal to qu / 2 is ___________ kPa
Consequently, Mohr’s circle of the specimen tested can be drawn as under:
B-34

2 - Soil Mechanics Laboratory Manual by Engr. Yasser M.S. - Compressed

Uploaded by

Copyright:

Available Formats

2 - Soil Mechanics Laboratory Manual by Engr. Yasser M.S. - Compressed

Uploaded by

Document Information

Original Description:

Original Title

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

2 - Soil Mechanics Laboratory Manual by Engr. Yasser M.S. - Compressed

Uploaded by

Copyright:

Available Formats

SOIL MECHANICS LABORATORY MANUAL 96

Engr. Yasser M. S. Almadhoun

Pre-consolidation pressure is the maximum effective vertical overburden stress

OCR > 1.0 → Over Consolidated Clay (OCC)

OCR < 1.0 → Under Consolidated Clay (UCC)

Figure 11.01: Over consolidation ratio of clay.

Engr. Yasser M. S. Almadhoun

 Estimates of this type are of key importance in case of designing engineering

Equipment and Materials

Figure 11.02: Consolidation apparatus and dial gages.

Engr. Yasser M. S. Almadhoun

(1) Determination of coefficient of consolidation, Cv :

Engr. Yasser M. S. Almadhoun

Figure 11.03: Log time versus deformation plot.

b. Square Root Method.

Engr. Yasser M. S. Almadhoun

Figure 11.04: Square root of time versus deformation plot.

(2) Determination of compression index, Cc :

Engr. Yasser M. S. Almadhoun

Figure 11.05: Pre-consolidation pressure.

Figure 11.06: Pressure versus deformation plot.

Engr. Yasser M. S. Almadhoun

(1) Factor of consolidation, 𝐂𝐯

Normal Stress, 𝛔 = 𝟏𝟎𝟎 𝐤𝐏𝐚

Engr. Yasser M. S. Almadhoun

Table 11.02: Testing measurements.

Normal Stress, 𝛔 = 𝟐𝟎𝟎 𝐤𝐏𝐚

(2) Factor of compression, 𝐂𝐜 , and pre-consolidation pressure, ′𝐜

Pressure (kPa) Displacement, H (0.001 mm)

Engr. Yasser M. S. Almadhoun

(1) Factor of consolidation, 𝐂𝐯

Dial Readings Deformation, H

Engr. Yasser M. S. Almadhoun

(a) Logarithmic Time Method

Logarithm of Time Method

Figure 11.07: Logarithm of time method.

Consequently, final results of the testing are shown as given as under:

Engr. Yasser M. S. Almadhoun

(b) Square Root of Time Method

Square Root of Time Method

Figure 11.08: Square root of time method.

Consequently, final results of the testing are shown as given as under:

Engr. Yasser M. S. Almadhoun

(B) For normal stress, σ = 200 kpa

Dial Reading Deformation, H

Engr. Yasser M. S. Almadhoun

(a) Logarithmic Time method.

Logarithm of Time Method

Figure 11.09: Logarithm of time method.

Consequently, final results of the testing are shown as given as under:

Engr. Yasser M. S. Almadhoun

(b) Square Root of Time Method

Square Root of Time Method

Figure 11.10: Square root of time method.

Consequently, final results of the testing are shown as given as under:

Engr. Yasser M. S. Almadhoun

(2) Factor of compression, 𝐂𝐜 , and pre-consolidation pressure, ′𝐜

Dial Readings Deformation, ΔH