Das b. m._,soil_mechanics_laboratory_manual,_6th_ed,_2002

SOIL MECHANICS
LABORATORY MANUAL
Sixth Edition
Braja M. Das
Dean, College of Engineering and Computer Science
California State University, Sacramento
New York Oxford
OXFORD UNIVERSITY PRESS
2002

CONTENTS
I. Laboratory Test and Report Preparation
2. Determination of Water Content 5
3. Specific Gravity 9
4. Sieve Analysis 15
5. Hydrometer Analysis 23
6. Liquid Limit Test 35
7. Plastic Limit Test 41
B. Shrinkage Limit Test 45
9. Engineering Classification of Soils 51
10.. Constant Head Permeability Test in Sand 69
II. Falling Head Permeability Test in Sand 75
12. Standard Proctor CompactionTest 81
13. Modified Proctor Compaction Test 89
14. Determination of Field Unit Weight of
Compaction by Sand Cone Method 93
15. Direct Shear Test on Sand 99
16. Unconfined Compression Test 109
17. Consolidation Test I 17
lB. Triaxial Tests in Clay 129
References 145
Appendices
A. Weight-Volume Relationships· 147
B. Data Sheets for Laboratory Experiments 151
C. Data Sheets for Preparation of Laborat~ry Reports 215

PREFACE
Since the early 1940'sthe study ofsoil mechanics has made great progress all overthe world.
A course in soil mechanics is presently required for undergraduate students inmostfour-year
civil engineering and civil engineering technology programs. It usually includes some
laboratory procedures that are essential in understanding the properties of soils and their
behaviorunder stress and strain; the present laboratory manual is prepared for classroom use
by undergraduate students taking such a course.
The procedures and equipment described in this manual are fairly common. For a few
tests such as permeability, direct shear, and unconfined compression, the existing equipment
in a given laboratory may differ slightly. In those cases, it is necessary that the instructor
familiarize students with the operation ofthe equipment. Triaxial test assemblies are costly,
and the equipment varies widely. For that reason, only general outlines for triaxial tests are
presented.
For each laboratory test procedure described, sample calculation(s) and graph(s) are
inCluded. Also, blank tables for each test are provided at the end ofthe manual for student
use in the laboratory and in preparing the final report. The accompanying diskette contains
the Soil Mechanics LaboratoryTest Software, a stand-alone program that students can use
to collect and evaluate the data for each ofthe 18 labs presented in the book. For this new
edition, Microsoft Excel templates have also been provided for those students who prefer
working with this popular spreadsheet program.
Professor William Neuman ofthe Department ofCivil Engineering at California State
University, Sacramento, took inost ofthe photographs used in this edition. Thanks are due
to Professor Cyrus Aryarti of the Department of Civil Engineering at Califoruia State
UnIversity, Sacramento, for his assistance in taking the photographs. Last, I would like to
thank my wife, Janice F. Das, who apparently possesses endless energy and enthusiasm. Not·
only did she type the manuscript, she also prepared all ofthe tables, graphs, and other line
drawings.
BrajaM Das
dasb@csus.edu

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I
Laboratory Test and
Preparation of Report
Introduction
Proper laboratory testing of soils to detennine their physical properties is an integral part in
the design and construction ofstructural foundations, the placement and improvement ofsoil
properties, and the specification and quality control of soil compaction works. It needs to be
kept in mind that natural soil deposits often exhibit a high degree of nonhomogenity. The
physical properties ofa soil deposit can change to a great extent even within a few hundred
feet. The fundamental theoretical and empirical equations that are developed in soil
mechanics can be properly used in practice if, and only if, the physical parameters used in
those equations are properly evaluated in the laboratory. So, learning to perfonn laboratory
tests of soils plays an important role in the geotechnical engineering profession.
Use of Equipment
Laboratory equipment is never cheap, but the cost may vary widely. For accurate ex-
perimental results, the equipment shouldbe properly maintained. The calibration ofcertain
equipment, such as balances and proving rings, should be checked from time to time. It is
always necessary to see that all equipment is clean both before and after use. Better results
will be obtained when the equipment being used is clean, so alwa);'s maintain the equipment
as if it were your own.
Recording the Data
In any experiment, it is always a good habit to record all data in the proper table immediately
after it has been taken. Oftentimes, scribbles on scratch paper may later be illegible or even
misplaced, which may result in having to conduct the experiment over, or in obtaining in-
accurate results.
1

2 Soil Mechanics Laboratory Manual
Report Preparation
In the classroom laboratory, most experiments described herein will probably be conducted
in small groups. However, the laboratory report should be written by each. student
individually. This is one way for students to improve their technical writing skills. Each
report should contain:
1. Cover page-This page should include the title ofthe experiment, name, and date on
which the experiment was performed.
2. Following the cover page, the items listed below should be included in the body of
the report:
a. Purpose ofthe experiment
b. Equipment used
c. A schematic diagram ofthe main equipment used
d. A brief description ofthe test procedure
3. Results-This should include the data sheet(s), sample calculations(s), and the
required graph(s).
4. Conclusion-A discussion ofthe accuracy ofthe test procedure should be included
in the conclusion, along with any possible sources of error.
120r---~~---r-----'
120
0!:----''----'-~1;':5,--.-L-.,!25 800!;----'--!c-5-----:;1';;-0--~15
(a)
Figure 1-1.
(a) Apoorly drawn graph for
dry unit weight of soil vs.
moisture content
Moisture content, w (%)
(b)
(b) The results'given in (a),
drawn in amore presentable
manner

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Soil Mechanics Laboratory Manual 3
Graphs and Tables Prepared for the Report
Graphs and tables should be prepared as neatly as possible. Always give the units. Graphs
should be made as large as possible, and they should be properly labeled. Examples of a
poorly-drawn graph and an acceptable graph are shown inFig. 1-1. When necessary, French
curves and a straight edge should be used in preparing graphs.
Table 1-1. Conversion Factors
Length _1 in. 25.4 mm 1 mm 3.937 x 10-2 in.
1ft 0.3048 m 3.281 x 10-3ft
304.8 mm 1m 39.37 in.
3.281 ft
Area 1 in.2 6.4516 x 10-4m2 1 em2 0.155 in2
6.4516 em2
1.076 x 10-3
~
645.16 mm2 1 m2 1550 in2
1~ 929 x 1O-4m2
10.76 ft2
929.03 em2
92903 mm2
Volume 1 in3
16.387 em3 I em3 0.061 in.'
1 ft3 0.028317 m3 3.531 x 10-5 ft'
1ft' 28.3168 I I m3 61023.74 in3
35.315 ft3
Velocity 1 ftls 304.8 mll/s I em/s 1.969 ftlmin
0.3048 m/s 1034643.6 ftlyear
1 ftlmin 5.08 mm/s
0.00508 m/s
Foree I Ib 4.448 N IN 0.224821b
1 kN 0.22482 kip
Stress 1 Ib/in.2
6.9 kN/m2
I kN/m2
O.1451b/in2
I Ib/ft2 47,88 N/m2 2.089 x 10.2 Ib/W
Unit Weight Ilb/ft3 157.06 N/m3 1 kN/m 3
6.367 Ib/ft3
Coefficient of 1 in.2
/s 6.452 em2/s I em2
/s 0.155 in?/s
Consolidation I W/s 929.03 cm2/s 2.883 x 103ft2
/month
Mass 1 kg 2.20461b
2.2046 x W-3 kip

4 Soil Mechanics Laboratorv Manual
Units
It may be necessary to express the results of laboratory tests in a given system ofunits. At
this time in the United States, both the English and the SI system of units are used.
Conversion ofunits may be necessary in preparing reports. Some selected conversion factors
from the English to the SI units and from SI to English units are given in Table 1-1.
Standard Test Procedures
In the United States, most laboratories conducting tests on soils for engineering purposes
follow the procedures outline by the American Society for Testing and Materials (ASTM)
and the American Association of State Highway and Transportation Officials (AASHTO).
The procedures and equipment for soil tests may vary slightly from laboratory to laboratory,
but the basic concepts remain the same. The test procedures described in this manual may
not be exactly the same as specified by ASTM or AASHTO; however, for the .students, it is
beneficial to know the standard test designations and compare them with the laboratory work
actually done. For this reason some selected AASHTO and ASTM standard test designations
are given in Table 1-2.
Water content T-265 D-2216
Specific gravity T-IOO D-854
Sieve analysis T-87, T-88 D-421
Hydrometer ~alysis T-87, T-88 D-422
Liquid limit T-89 D-4318
Plastic limit T-90 D-4318
Shrinkage limit T-92 D-427
Standard Proctor compaction T-99 D-698
Modified Proctor compaction T-180 D-1557
Field density by sand cone T-191 D-1556
Permeability of granular soil T-215 D-24:34
Consolidation T-2l6 D-2435
Direct shear (granular soil) T-236 D-3080
Unconfined compression T-208 D-2166
Triaxial T-234 D-2850
AASHTO Soil Classification System M-145 D-3282
Unified Soil Classification System D-2487
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2
Determination of
Water Content
Introduction
Most laboratory tests in soil mechanics require the determination of water content. Water
content is defined as
weight of water present in a given soil mass
w =
weight of dry soil
(2.1)
Water content is usually expressed in percent.
For better results, the minimum size ofthe most soil specimens should be approximately
as given in Table 2-1. These values are consistent with ASTM Test Designation D-2216.
Table 2-1. Minimum Size of Moist Soil Samples to
Determine Water Content
0.425 40 20
2.0 10 50
4.75 4 100
9.5 3/8 in. 500
19.0 3/4 in. 2500
5

Equipment
1. Moisture can(s).
Moisture cans are available in various sizes [for example, 2-in. (50,S mm) diameter
and % in. (22.2 mm) high, 3.5-in. (S8.9 mm) diameter and 2 in. (50.S mm) high).
2. Oven with temperature control.
For drying, the temperature ofoven is generally kept between 105°C to 110°C. A
higher temperature should be avoided to prevent the burning oforganic matter in the
soil.
3. Balance.
The balance should have a readability of0.01 g for specimens having amass of200
g or less. Ifthe specimen has a mass of over 200 g, the readability should be 0.1 g.
Procedure
1. Determine the mass (g) ofthe empty moisture can plus its cap (WI)' and also record
. the number.
2. Place a sample ofrepresentative moist soil in the can. Close the can with its cap to
avoid loss ofmoisture.
3. Determine the combined mass (g) ofthe closed can and moist soil (Wz).
4. Remove the cap from the top ofthe can and place it on the bottom (ofthe can).
5. Put the can (Step 4) in the oven to dry the soil to a constant weight. In most cases,
24 hours ofdrying is enough.
6. Determine the combined mass (g) ofthe dry soil sample plus the can and its cap (W3)'
Calculation
1. Calculatethe mass of moisture = W2- W3
2. Calculate the mass of dry soil = W3 - WI
3. Calculate the water content
W2 - W3
w (%) = --''---'''- x 100
W3 - WI
(2.2)
Report the water content to the nearest 1% or 0.1% as appropriate based on the size
ofthe specimen.
A sample calculation ofwater content is given in Table 2-2.
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Table 2-2. Determination of Water Content
Description of sOil_----"B"'-fi"'Q"'"W,u.'f7'-'S""/Z"'~Vw.c!.""~,LV----- Sample No. __
4'--__
Location __~_____________-,-____________
Tested by_~_____________ Date __________
Can No. 42 3/ 54
Mass of can, WI /73/ /8.92 /6.07
Mass of can + wet soil, W2(g) 43.52 52./9 39.43
Mass of can + dry soil,.W3 (g) 39.86 47.6/ 36./3
Mass ofmoisture, W2- W3 (g) 3.66 4.58 3.30
Mass of dry soil, W3 - WI (g) 22.55 28.69 20.06
W-W
Moisture content, w(%) = 2 3 X 100
/6.2 16.0 16.5
w,-~
Average rnoisture content, W /6.2 %
General Comments
a. Most natural soils, which are sandy and gravelly in nature, may have water contents
up to about 15 to 20%. In natural fine-grained (silty or clayey) soils, water contents
up to about 50 to 80% can be found. However, peat and highly organic soils with
water contents up to about 500% are not uncommon.
Typical values of water content for various types ofnatural soils in a saturated state
are shown in Table 2-3.
b. Some organic soils may decompose during oven drying at 110°C. An oven drying
temperature of n0° may be too high for soils containing gypsum, as this material
slowly dehydrates. According to ASTM, 'a drying temperature of 60°C is more
appropriate for such soils.
c. Cooling the dry soil after oven drying (Step 5) ina desiccator is recommended. It
prevents absorption ofmoisture from the atmosphere.

Table 2-3. Typical Values of Water Content
in a,Saturated State
Loose uniforll sand
Dense uniform sand
Loose angular-grained silty sand
Dense angular-grained silty sand
Stiffclay ,
Soft clay
Soft organic clay
Glacial till
25-30
12-16
25
15
20
30-50
80-130
10

3
Specific Gravity of
Soil Solids
Introduction
The specific gravity of a given material is defined as the ratio of the weight of a given
volume ofthe material to the weight ofan equal volume ofdistilled water. In soil mechanics,
the specific gravity ofsoil solids (which is often referred to as the specific gravity ofsoil) is
an important parameter for calculation of the weight-volume relationship. Thus specific
gravity, G" is defined as
G = unit weight (or density) of soil solids only
, unit weight (or density) or water
or
G, = W, IV, W,
pz V,p"
where . W, = mass of soil solids (g)
.V, = volume of soil solids (cm3)
Pw = density ofwater (glcm3
).
(3.1)
The general ranges of the values of G, for various soils are given in Table 3-1. . The
procedure for determination of specific gravity, G" described here is applicable for soils
composed ofparticles smaller than 4.75 mm (No.4 U.S. sieve) in size.
9

10 Soil Mechanics Laboratorv Manual
Table 3-1. General Ranges of Gs for Various Soils
Equipment
Sand
Silts
Clay and silty clay
Organic soil
1. Volumetric flask (500 ml)
2.63-2.67
2.65-2.7
2.67-2.9
less than 2
2. Thermometer graduated in O.soC division scale
3. Balance sensitive up to 0.01 g
4. Distilled water
5. Bunsen bumer and a stand (and/or vacuum pump or aspirator)
6. Evaporating dishes
7. Spatula
8. Plastic squeeze bottle
9. Drying oven
The equipment for this experiment is shown in Fig. 3-1.
Figure 3-1. Equipment for conducting specific gravity test.
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Procedure
1. Clean the volumetric flask well and dry it.
2. Carefully fill the flask with de-aired, distilled water up to the 500 ml mark (bottom
ofthe meniscus should be at the 500 ml mark).
3. Determine the mass ofthe flask and the water filled to the 500 ml mark (Wi)'
4. Insert the thermometer into the flask with the water and determine the temperature
ofthe water T = Ti DC.
5. Put approximately 100 grams of air dry soil into an evaporating dish.
6. Ifthe soil is cohesive, add water (de-aired and distilled) to the soil and mix it to the
form of a smooth paste. Keep it soaked for about one-half to one hour in the
evaporating dish. (Note: This step is not necessary for granular, i.e., noncohesive,
soils.)
7. Transfer the soil (if granular) or the soil paste (ifcohesive) into the volumetric flask.
8. Add distilled water to the volumetric flask containing the soil (or the soil paste) to
make it about two-thirds full.
9. Remove the air from the soil-water mixture. This can be done by:
a. Gently boiling the flask containing the soil-water mixture for about 15 to 20
minutes. Accompany the boiling with continuous agitation of the flask. (If
too much heat is applied, the soil may boil over.) Or
b. Apply vacuum by a vacuum pump or aspirator until all ofthe entrapped air
is out.
This is an extremely important step. Most ofthe errors in the results ofthis test
are due to entrapped air which is not removed.
10. Bring the temperature ofthe soil-water mixture in the volumetric flask down to room
temperature, i.e., TiDC-see Step 4. (This temperature ofthe water is at room tem-
perature.)
II. Add de-aired, distilled water to the volumetricflask until the bottom ofthe meniscus
touches the 500 m1 mark. Also dry the outside ofthe flask and the inside ofthe neck
above.the meniscus.
12. . Determine the combined mass ofthe bottle plus soil plus water (W2).
13. Just as a precaution, check the temperature ofthe soil and water in the flask to see if
itis TiD.± 1DC or not.
14. Pour the soil and water into an evaporating dish. Use a plastic squeeze bottle and
wash the inside of the flask. Make sure that no soil is left inside.
15. Put the evaporating dish in a oven to dry to a constant weight.
16. Determine the mass ofthe dry soil in the evaporating dish (W,).
Calculation
1. Calculate the specific gravity
G = mass of soil, W,
S mass of equal volume of soil

where mass of soil = Ws
mass of equal volume ofwater, Ww = (WI + Ws) - W2
So
(3.2)
Specific gravityis generally reported on the value ofthe density ofwater at 20°C. So
G
[
Pw<"r,Oq]
;(at20°c) =Gs(atljoq
Pw(at20°C) (3.3)
= G,<" Tl"q A
(3.4)
Pw = density ofwater.
The values ofA are given in Table 3-2.
Table 3-2. Values ofA[Eq. (3.4)J
16 1.0007 24 0.9991
17 1.0006 25 0.9988
18 1.0004 26 0.9986
19 1.0002 27 0.9983
20 1.0000 28 0.9980
21 0.9998 29 0.9977
22 0.9996 30 0.9974
23 0.9993
At least three specific gravity tests should be conducted. Fot correct results, these values
should not vary by more than 2 to 3%. A sample calculation for specific gravity is shown
in Table 3-3.
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Table 3-3. Specific Gravity of Soil Solids
Description of soil Light brown sandySilt Sample No. 23
Volume of fiask at 20"C 500 ml Temperature of test 23 "C A 0.9993
(Table 3-2)
Location_______.,--____________________
Tested by _________________ Date_______
Volumetric flask No.
Mass of flask + water filled to mark, WJ (g)
Mass of flask + soil + water filled to mark,
W2 (g)
Mass of dry soil, Ws (g)
Mass ofequal volume ofwater as the soil
solids, Ww (g) = (WI + Ws) - W2
6 8
666.0 674.0
722.0 738.3
99.0 103.0
370 38.7
2.68 2.66
2.68 2.66
9
652.0
709.93
92.0
34.07
2.70
2.70
(2.68 + 2.66 + 2.70) = 2.68
3
Average Gs ______-c-_ _ _ _ _ __

=
4
Sieve Analysis
Introduction
In order to classifY a:soil for engineering purposes, one needs to know the distribution ofthe
size of grains in a given soil mass. Sieve analysis is a method used to deter mine the grain-
size distribution of soils. Sieves are made ofwoven wires with square openings. Note that.
as the sieve number increases the size ofthe openings decreases. Table 4-1 gives a list ofthe
U.S. standard sieve numbers with their corresponding size of openings. For all practical
purposes, the No. 200 sieve is the sieve with the smallest opening that should be used for the
test. The sieves that are most commonly used for soil tests have a diameter of 8 in. (203 mm).
A stack of sieves is shown in Fig. 4.-1.
The method of sieve analysis described here is applicable for soils that are mostly
granular with some or no fines. Sieve analysis does not provide information as to shape of
particles.
Table 4-1. U.S. Sieve Sizes
4 4.75 35 0.500
5 4.00 40. 0.425
6 3.35 45 0.355
7 2.80 50 0.300
8 2.36 60 0.250
10 2.00 70 0.212
12 1.70 80 0.180
14 1.40 100 0.150
16 1.18 120 0.125
18 1.00 l40 0.106
20 0.85 200 O.o?5
25 0.71 270 0.053
30 0.60 400 0.038
15

Figure 4-1. Astack of sieves with a pan at the
bottom and acover on the top.
Equipment
1.
2.
3.
4.
Sieves, a bottom pan, and a cover
Note: Sieve numbers 4, 10, 20, 40, 60, 140, and 200 are generally used for most
standard sieve analysis work.
A balance sensitive up to 0.1 g
Mortar and rubber~tipped pestle
Oven
5. Mechanical sieve shaker
Procedure
1. Collect a representative oven dry soil sample. Samples having largest particles ofthe
size ofNo. 4 sieve openings (4.75 rnm) should be about 500 grams. For soils having
largest particles of size greater than 4.75 rnm, larger weights are needed.
2. Break the soil sample into individual particles using a mortar and a rubber-tipped
pestle. (Note: The idea is to break up the soil into individual particles, not to break
the particles themselves.)
3. Determine the mass ofthe sample accurately to 0.1 g CW).

Figure 4-2. Washing of the soil retained on No. 200 sieve.
4. Prepare a stack ofsieves. A sieve with larger openings is placed above a sieve with
smaller openings. The sieve at the bottom should be No. 200. A bottom pan should
be placed under sieve No. 200. As mentioned before, the sieves that are generally
used in a stack are Nos. 4, 10,20,40,60, 140, and 200; however, more sieves can be
placed in between.
5. Pour the soil prepared in Step 2 into the stack of sieves from the top.
6. Place the cover on the top ofthe stack of sieves.
7. Run the stack of sieves through a sieve shaker for about 10 to 15 minutes.
8. Stop the sieve shaker and remove the stack of sieves.
9. Weigh the amount of soil retained on each sieve and the bottom pan.
10. Ifa considerable amount of soil with silty and clayey fractions is retained onthe No.
200 sieve, it has to be washed. Washing is done by taking the No. 200 sieve with the
soilretained on it and pouring water through the sieve from a tap in the laboratory
(Fig. 4-'-2).
When the water passing through the sieve is clean, stop the flow ofwater. Transfer the soil
retained on the sieve at the end ofwashing to a porcelain evaporating dish by back washing
(Fig. 4-'-3). Put it in the oven to dry to a constantweight. (Note: This step is not necessary
ifthe amount ofsoil retained on the No. 200 sieve is small.)
Determine the mass ofthe dry soil retained on.No. 200 sieve. The difference between
this mass and that retained on No. 200 sieve determined in Step 9 is the mass ofsoil that has
washed through.

Figure 4-3. Back washing to transfer the soil retained on
No. 200 sieve to an evaporating dish.
Calculation
1. Calculate the percent of soil retained on the nth sieve (counting from the top)
= massretained, w,. x 100 = R
total mass, W (Step 3) n
2. Calculate the cumulative percent of soil retained on the nth sieve
j"",n
=LRn
;=1
3. Calculate the cumulative percent passing through the nth sieve
i=n
=percent fmer =100 - L Rn
1=1
(4.1)
(4.2)
(4.3)
Note: If soil retained on No.200 sieve is washed, the dry unit weight determined after
washing (Step 10) should be used to calculate percent finer (than No. 200 sieve). The weight
lost due to washing should be added to the weight ofthe soil retained on the pan.
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A sample calculation of sieve analysis is shown in Table 4-2.
Table 4-2. Sieve Analysis
Description of soil _~s.""a,-"nd"-L!W::L!ltLJ.h-",so",m.!..!"'-eJ.LfinlJje",,5,--__ Sample No. _~2,,----_
Mass of oven dry specimen, W 500 g
Location_____________________
Tested by_________________ Date,_··________
4 4.750 0 0 0 /00.0
/0 2.000 40.2 8.0 8.0 92.0
20 0.850 84.6 /6.9 24.9 75.1
30 0.600 50.2 10.0 34.9 65. /
40 0.425 40.0 8.0 42.9 571
60 0.250 /06.4 2/.3 64.2 35.8
/40 0.106 /08.8 21.8 86.0 /4.0
200 0.075 59.4 11.9 979 2./
Pan 8.7
L 498.3 = W,
Mass loss during sieve analysis = w- w, x 100 = 0.34 % (OK.if less than 2%)
w
Graphs tJ.. 13;
The grain-size distribution obtained from the sieve analysis is plotted in a semi-logarithmic
graph paper with grain size plotted on the log scale and percent finer plotted on the natural
scale. Figure ~ is a grain-size distribution plot for the calculation shown in Table 4--2.

100
80
r---
""
""
lJ 60
"
'" I'
"
"
g 1
~ 40

20
1
~.
0
10 1 0.1
Grain size, D (mm)
Figure 4-4. Plot of percent finer vs. grain size from the
calculation shown in Table 4-2.
.
The grain-size distribution plot helps to estimate the percent finer than a given sieve size
which might not have been used during the test. .
Other Calculations
I.
2.
Determine D IO, D 30, and D60 (from Fig. 4-4), which are, respectively, the diameters
corresponding to percents finer of 10%, 30%, and 60%.
Calculate the uniformity coefficient (Cu) and the coefficient ofgradation (Cc
) using
11
7 - ..

D.;J,
C = D60
U
D10
the following equations:
(4.4)
(4.5)
As an example, from Fig. 4-4, D60 = 0.46 mm, D30 = 0.21 mm, and L10 = 0.098 mm.
So
c = 0.46 =4.69
u 0.098
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<-
and
C = (0.21)2 =0.98
, (0.46)(0.098)
General Comments
The diameter, DID' is generally referred to as effective size. The effective size is used for
several empirical correlations, such as coefficient of permeability. The coefficient of
gradation, Cu, is a parameter which indicates the range of distribution of grain sizes in a
given soil specimen. If Cu is relatively large, it indicates a well graded soil. If Cu is nearly
equal to one, it means that the soil grains are of approximately equal size, and the soil may
be referred to as a poorly graded soil.
Figure 4-5 shows the general nature of the grain-size distribution curves for a well
graded and a poorly graded soil. In some instances, a soil may have a combination oftwo or
more uniformly graded fractions, and this soil is referred to as gap graded. The grain-size
distribution curve for a gap graded soil is also shown in Fig. 4-5.
The parameter Cc is also referred to as the coefficient ofcurvature. For sand, if <;; is
greater than 6 and Cc is between I and 3, it is considered well graded. However, for a gravel
to be well-graded, Cu should be greater than 4 and Cc must be between I and 3.
The DIS and Dss sizes are used for design of filters. The DSD size is used for correlation
of the liquefaction potential of saturated granular soil during earthquakes.

22 Soil Mechanics LaboratoryManual
Well graded
Poorly graded Gap graded
Grain size (log scale)
Figure 4-5. General nature of grain-size distribution
of well graded, poorly graded and gap
.graded soil.

i'
5
'Hydrometer Analysis
Introduction
-Hydrometer analysis is the procedure generally adopted for determination ofthe particle-size
distribution in a soil for the fraction that is finer than No. 200 sieve size (0.075 mm). The
lower limit ofthe particle-size determined by this procedure is about 0.001 mm.
In hydrometer analysis, a soil specimen is dispersed in water. In a dispersed state in the
water, the soil particles will settle individually. It is assumed that the soil particles are
spheres, and the velocity ofthe particles can be given by Stoke's law as
where u = velocity (cm/s)
'U= Ys-Y" D2
181)
ys = specific weight of soil solids (g/cm3
)
yw = unit weight ofwater (g/cm3
) ,
11 = viscosity ofwater (:~~ )
D = diameter ofthe soil particle
(5.1)
If a hydrometer is suspended in water in which soil is dispersed (Fig. 5-1), it will
measure the specific gravity ofthe soil-water suspension at a depth L. The depth L is called
the effective depth. So, at a time t minutes from the beginning of the test, the soil particles'
that settle beyond the zone ofmeasurement (i.e., beyond the effective .depth L) will have a
diameter given by ,
L (cm) (Ys-Yw) g/cm
3
t (min) x 60
181) (:~~)
23

Hydrometer
Meniscus
correction
Figure 5-1. Hydrometer suspended in water in
which the soil is dispersed.
where A =
1800'1'
1----"--=
30'1'
60(Y8 -Yw)
o
~ r
60 L
1-1 1
L(cm)
t (min) (S.2)
(S.3)
In the test procednre described here, the ASTM152-Htype ofhydrometer will be used.
From Fig. S-1 it can be seen that, based on the hydrometer reading (which increases from
zero to 60 in the ASTM152-H type ofhydrometer), the value ofL will change. The mag-
nitude ofL can be given as .
1( VB)
L=L +- L--
I 2 2 A
c
(S.4)

where LI = distance between the top ofhydrometer bulb to the mark for a hydrometer
reading. For a hydrometer reading ofzero, LI = 10.5 cm. Also, for a Hydro-
meter reading of 50 glliter, LI = 2.3 cm. Thus, in general, for a given hydro-
meter reading
LI (cm) = 10.5 - (
1
0.55~2.3) x (hydrometer reading)
L2 =14cm
VB = volume ofthe hydrometer bulb = 67.0 cm3
Ac = cross-sectional area ofthe hydrometer cylinder = 27.8 cm2
Based on Eq. (5.4), the variation ofL with hydrometer reading is shown in Table 5-1.
For actual calculation purposes we al~o need to know the values ofA given by Equation
(5.3). An example ofthis calculation is shown below.
where Gs = specific gravity ofsoil solids
Thus
A=
3011
(Gs -l)y"
For example, ifthe temperature ofthe water is 25b
C,
and Gs = 2.7
11 = 0.0911 X 10-4 (;~~ )
A= 30(0.0911 X 10-4) '=0.0127 .
(2.7 -1)(1)
The variations ofA with Gs and the water temperature are shown in Table 5-2.
(5.5)

Table 5-1. Variation of Lwith hydrometer reading-
ASTM 152-H hydrometer
0 16.3 26 12.0
1 16.1 27 11.9
2 16·9 28 11.7
3 ,15.8 29 11.5
4 15.6 30 11.4
5 15.5 31 11.2
6 15.3 32 11.1
7 15.2 33 10.9
8 15.0 34 10.7
9 14.8 35 10.6
10 14.7 36 10.4
11 14.5 37 10.2
12 14.3 38 10.1
13 14.2 39 9.9
14 14.0 40 9.7
15 13.8 41 9.6
16 13.7 42 9.4
17 13.5 43 9.2
18 13.3 44 9.1
19 13.2 45 8.9
20 13.0 46 8.8
21 12.9 47 8.6
22 12.7 48 8.4
23 12.5 49 8.3
24 12.4 50 8.l
25 12.2 51 7.9
The ASTM152-Htype ofhydrometer is c:alibrated up to a reading of60 at a temperature
of20oe for soil particles having a Gs = 2.65. A hydrometer reading of, say, 30 at a given time
ofa test means thatthere are 30 g ofsoil solids (Gs = 2.65) in. suspension per 1000 cc ofsoil-
water mixture at a temperature of20oe at a depth where the specific gravity ofthe soil-water
suspension is measured (i.e., L). From this measurement, we can determine the percentage
ofsoil still in suspension at time t from the beginning ofthe test and all the soil particles will
have diameters smaller than D calculated by Equation (5.2). However, in the actual
experimental work, some corrections to the observed hydrometer readings need to be applied.
They are as follows:

Table 5-2. Variation of A with G
s
2.50 0.0149 0.0147 0.0145 0.0143 0.0141 0.0140 0.0138
2.55 0.0146 0.0144 0.0143 0.014) 0.0139 0.0137 0.0136
2.60 0.0144 0.0142 0.1040 0.0139 0.0137 0.0135 0.0134
2.65 0.0142 0.0140 0.0138 0.0137 0.0135 0.0133 0.0132
2.70 0.0140 0.0138 0.1036 0:0134 0.0133 0.0131 0.0130
2.75 0.0138 0.0136 0.0134 0.0133 0.0131 0.0129 0.0128
2.80 0.0136 0.0134 0.0132 0.0131 0.0129 0.0128 0.0126
2.50 .0.0137 0.0135 0.0133 0.0132 0.0130 0.0129 0.0128
2.55 0.0134 0.0133 0.0131 0.0130 0.0128 0.0127 0.0126
2.60 0.0132 0.0131 0.0129 0.0128 0.0126 0.0125 0.0124
2.65 0.0130 0.0129 0.0127 0.0126 0.0124 0.0123 0.0122
2.70 0.0128 0.0127 0.0125 0.0124 0.0123 0.0121 0.0120
2.75 0.0126 0.0125 0.0124 0.0122 0.Ol21 0.0120 0.0118
2.80 0.0125 0.0123 0.0122 0.0120 0.0119 0.0118 O.oI17
1. Temperature correction (FT)-The actual temperature ofthe test may not be 20°C.
The temperature correction (FT) may be approximated as
FT = -4.85 + 0.25T(for Tbetween 15°C and 28°C)
where FT = temperature correction to the observed reading
(can be either positive or negative)
T= temperature oftest inoC
(5.6)
2. Meniscus correction (Fm)-Generally, the upper level ofthe meniscus is taken as the
reading during laboratory work (Fm is always positive).
3. Zero correction (Fz)- A deflocculating agent is added to the soil-distilled water
suspension for performing experiments. This will change the zero reading (Fz can be
either positive or negative).

Figure 5-2. Equipment for hydrometer test.
Equipment
1. ASTM 152-Hhydrometer
2. Mixer
3. Two lOOO-cc graduated cylinders
4. Thermometer
5. Constant temperature bath
6. Deflocculating agent
7. Spatula
8. Beaker
9. Balance
11. Distilled water
12. No. 12 rubber stopper
The equipment necessary (except the balance and the constant temperature bath) is shown
in Fig. 5-2.

G·.
Procedure
Note: This procedure is used when more than 90 per cent of the soil is finer than No. 200
sieve.
1. Take 50 g of oven-dry, well-pulverized soil in a beaker.
2. Prepare a deflocculating agent. Usually a 4% solution ofsodium hexametaphosphate
(Calgon) is used. This can be prepared by adding 40 g of Calgon in 1000 cc of dis-
tilled water and mixing it thoroughly. ,
3. Take 125 cc ofthe mixture prepared in Step 2 and add it to the soil taken in Step 1.
This should be allowed to soak for about 8 to 12 hours.
4. Take a IOOO-cc graduated cylinder and add 875 cc ofdistilled water plus 125 cc of
deflocculating agent in it. Mix the solution well.
5. Put the cylinder (from Step 4) in a constant temperature bath. Record the temperature
ofthe bath, T (in 0c).
6. Put the hydrometer in the cylinder (Step 5). Record the reading. (Note: The top a/the
meniscus should be read.) This is the zero correction (Fz), which can be +ve or -ve.
Also observe the meniscus correction (Fm).
7. Using a spatula, thoroughly mix the soil prepared in Step 3. pour it into the mixer
cup.
Note: During this process, some soil may stick to the side ofthe beaker. Using the
plastic squeeze bottle filled with distilled water, wash all the remaining soil in the
beaker into the mixer cup.
8. Add distilled water to the cup to make it abouttwo-thirds full. Mix it for about two
minutes using the mixer.
9. Pour the mix into the second graduated 1000-cc cylinder. Make sure that all ofthe
soil solids are washed out ofthe mixer cup. Fill the graduated cylinder with distilled
water to bring the water level up to the 1000-cc mark.
10. Secure a No. 12 rubber stopper on the top ofthe cylinder (Step 9). Mix the soil-water
well by turning the soil cylinder upside down several,times.
11. Put the cylinder into the constant temperature bath next to the cylinder described in
Step 5. Record the time immediately. This is·cumulative time t= O. Insert the hydro-
meter into the cylinder containing the soil-water suspension.
12. Take hydrometer readings at cumulative times t = 0.25 min., 0.5 min., 1 min., and 2
min. Always read the upper level ofthe meniscus.
13. Take the hydrometer out after two minutes an<l put it into the cylinder next to it (Step
5).
14. Hydrometer readings are to be taken at time t =4 min., 8 min., 15 min., 30 min., 1
hr., 2 hr., 4 hr., 8 hr., 24 hr. and 48 hr. For each reading, insert the hydrometer into
the cylinder containing the soil-water suspension about 30 seconds before the reading
is due. After the reading is taken, remove the hydrometer and put it back into the
cylinder next to it (Step 5).

Calculation
Refer to Table 5-4.
.Column 2-These are observed hydrometer readings (R) corresponding to times given in
Column I.
Column 3-Rep = corrected hydro~_eter reading for calculation ofpercent fmer
oR
Column 4-Percentjiner-= ---.:!!. (I 00)
Ws
where Ws = dry weight of soil used for the hydrometer analysis
(5.7)
a = correction for specific gravity (since the hydrometer is calibrated for
Gs = 2.65)
= Gs (1.65) (S bl 5 3)
ee Ta e -
(Gs -I)2.65
Table 5-3. Variation of awith G
s [Eq.5.8]
2.50
2.55
2.60
2.65
2.70
2.75
2.80
1.04
1.02
1.01
1.00
0.99
0.98
0.97
(5.8)
Column 5-ReL = corrected reading for determination ofeffective length = R +Fm (5.9)
Column 6--Determine L (effective length) corresponding to.the values ofReL (Col. 5) given
in Table 5-1.
Column 7-Determine A from Table 5-2.
Column 8- DetermineD (mm) = A L (cm)
t (min)

Table 5-4. Hydrometer Analysis
Description of soil Brown siltyc!iJ,v Sample No.___
Location __________________________
Gs _---'2
...
.7.L>'S'---__ Hydrometertype ASTt1 /52-H
.Dry weight of soil, Ws _ _""50"--__ g Temperature of test, T_-!,.2",,8___oc
Meniscus correction, Fm_1_ Zero correction, Fs + 7 Temperature correction, Fr +2./5
[Eq. (5.6)]
Tested by Date,___________
0.25 51 46./5 90.3 52 7.8 0.0/2/ 0.068
0.5 48 43.15 84.4 49 8.3 0.049
I 47 42.15 82.4 48 8.4 0.035
2 46 41.15 80.5 47 8.6 0.025
4 45 40.15 78.5 46 8.8 0.018
8 44 39.15 76.6 45 8.95 0.013
/5 43 38.15 74.6 44 9.1 0.009
30 42 37./5 72.7 43 9.25 0.007
60 40 3515 68.8 41 9.6 0.005
120 38 33.15 64.8 ,39 9.9 0.0035
240 34 29.15 57.0 35 10.5 0.0025
480 32 27.15 53.1 33 10.9 0.00/8
1440 29 24.15 47.23 30 11.35 0.0011
2880 27 22.15 43.3 28 11.65 0.0008
'Table 5.3; tTable 5.1; *Table 5.2

Graph
Plot a grain-size distribution graph on semi-log graph paper with percent finer (Col.4, Table
5-4) on the natural scale and D (Col. 8, Table 5-4) on the log scale. A sample calculation
and the corresponding graph are shown in Table 5-4 and Fig. 5-3, respectively.
100
80 · .,..
I-
~
~ 60
;;
"
~ 40
20
00.1 0.01 0.001 0.0001
Grain size, D (mm)
Figure 5-3. Plot of percent finer vs. grain size
from the results given in Table 5-4.
Procedure Modification
When a smaller amount (less than about 90%) of soil is finer than No. 200 sieve size, the
following modification to the above procedure needs to be applied.
1. Take an oven-dry sample ofsoil. Determine its weight (WI)'
2. Pulverize the soil using a mortar and rubber-tipped pestle, as described in Chapter 4.
3. Run a sieve analysis on the soil (Step 2), as described in Chapter 4.
4. Collect in the bottom pan the soil passing through No. 200 sieve.
5. Wash the soil retained on No. 200 sieve, as described in Chapter 4. Collect all the
wash water and dry it in an oven.
6. Mix together the minus No. 200 portion from Step'4 and the dried minus No. 200
portion from Step 5.
7. Calculate the percent finer for the soil retained on No. 200 sieve and above (as shown
'in Table 4-1).
8. Take 50 g of the minus 200 soil (Step 6) and run a hydrometer analysis. (Follow
Steps 1 through 14 as described previously.)

9. Report the calculations for the hydrometer analysis similar to that shown in Table
5-4. Note, however, that the percent finer now calculated (as in Col. 8 ofTable 5-4)
is not the percentfiner based on the total sample. Calculate the percent finer based
on the total sample as
P
r
=(Col. 8 of Table S_4)(percent passing No. 200 Sieve)
100
Percent passing No. 200 sieve can be obtained from Step 7 above.
10. Plot a combined graph for percent finer versus grain-size distribution obtained from
both the sieve analysis and the hydrometer analysis. An example ofthis is shown in
Fig. 5-4. From this plot, note that there is an overlapping zone. The percent finer cal-
culated from the sieve analysis for a given grain size does not match that calculated
from the hydrometer analysis. The grain sizes obtained from a sieve analysis are the
least sizes of soil grains, and the grain sizes obtained from the hydrometer are the
diameters ofequivalent spheres ofsoil grains.
]00
r--.,
'"
80
Sieve
J 60
f.a
1::
"
Ii 40
~
~
eter
Hydrom
20 ....,
j'---,
0]0 ] 0.1 0.0]
Gmin size, D (mm)
Figure 5-4. Agrain-size distribution plot-combined results from
sieve analysis and hydrometer analysis.
General Comments
0.00]
A hydrometer analysis gives results from which the percent of soil finer than 0.002 mm in
diameter can be estimated. It is generally accepted that the percent finer than 0.002 mm in
size is clay or clay-size fractions. Most clay particles are smaller than 0.001 mm, and 0.002
mm is the upper limit. The.presence of clay in a soil contributes to its plasticity.

6
Liquid Limit Test
Introduction
When a cohesive soil is mixed with an excessive amount ofwater, it will be in a somewhat
liquid state and flow like a viscous liquid. However, when this viscous liquid is gradually
dried, with the loss of moisture it will pass into a plastic state. With further reduction of
moisture, the soil will pass into a semisolid and then into a solid state. This is shown in Fig.
6-L The moisture content (inpercent) at which the cohesive soil will pass from a liquid state
to a plastic state is called the liquidlimit ofthe soil. Similarly, the moisture contents (in per-
cent) at which the soil changes from a plastic to a semisolid state and from a semisolid state
to a solid state are referred to as the plastic limit and the shrinkage limit, respectively. These
limits are referred to as the Atterberg limits (1911). In this chapter, the procedure to deter-
mine the liquid limit ofa cohesivesoH will be discussed.
1. Casagrande liquid limit device
2. Grooving tool
3. Moisture cans
4. Porcelain evaporating dish
Solid . Liquid
Semisolid Plastic Moisture
----1----+-----,--1-'----- content
increasing
Shrinkage Plastic
limit, SL limit, PL
Figure 6-1. Atterberg limits.
35
Liquid
limit,LL
Equipment

5. Spatula
6. Oven
9. Paper towels
The equipment (except the balance and the oven) is shown in Fig. 6-2.
The Casagrande liquid limit device essentially consists ofa brass cup that can be raised
and dropped through a distance of 10 mth on a hard rubber base by a cam operated by a crank
(see Fig. 6-3a). Fig. 6-3b shows a schematic dil!gram ofa grooving tool.
,
Procedure
I. Determine the mass ofthree moisture cans (WI).
2. Put about 250 g ofair"dry soil, passed through No. 40 sieve, into an evaporating dish.
Add water from the plastic squeeze bottle and mix the soil to the form of a uniform
paste.
3. Place a portion of the paste in the brass cup of the liquid limit device. Using the
spatula, smooth the surface ofthe soil in the cup such that the maximum depth ofthe
soil is about 8 mm.
4. Using the grooving tool, cut a groove along the center line ofthe soil pat in the cup
(Fig. 6-4a).
5. Turn the crank ofthe liquid limit device at the rate ofabout 2 revolutions per second.
By this, the liquid limit cup will rise and drop through a vertical distance of 10 mm
once for each revolution. The soil from two sides of the cup will begin to flow
toward the center. Count the number ofblows, N, for the groove in the soil to close
through a distance of Yz in. (12.7 mm) as shown in Fig. 6-4b.
Figure 6-2. Equipment for liquid limit test.

(a)
'" 50 mm ---+I
(b)
'8
~mmto-
Figure 6-3. Schematic diagram of: (a) liquid limit device; (b) grooving tool.
Section
Plan
(a) (b)
Figure 6-4. Schematic diagram of soil pat in the cup of the liquid limit device at
(a) beginning of test, (b) end of test.

IfN = about 25 to 35, collect a moisture sample from the soil in the cup in a moisture
can. Close the cover ofthe can, and determine the mass ofthe can plus the moist soil
(W2)·
Remove the rest of the soil paste from the cup to the evaporating dish. Use paper
towels to thoroughly dean the cup.
Ifthe soil is too dry, Nwill be more than about 35. In that case, remove the soil with
the spatula to the evaporating dish. Clean the liquid limit cup thorollghly with paper
towels. Mix the soil in the evaporating dish with more water, and try again.
Ifthe soil is too wet, N will be It;ss than about 25. In that case, remove thesoil in the
cup to the evaporating dish. ,Clean the liquid limit cup carefully with paper towels.
Stir the soil paste with the spatula for some time to dry it up. The evaporating dish
may be placed in the oven for a few minutes for drying also. Do not add dry soil to
the wet-soil paste to reduce the moisture content for bringing it to the proper
consistency. Now try again in the liquid limit device to get the groove closure of Yz
in. (12.7 mm) between 25 and 35 blows.
6. Add more water to the soil paste in the evaporating dish and mix thoroughly. Repeat
Steps 3, 4 and 5 to get a groove closure of Yz in. (12.7 mm) in the liquid limit device
at a blow count N = 20 to 25. Take a moisture sample from the cup. Remove the rest
ofthe soil paste to the. evaporating dish. Clean the cup with paper towels.
7. Add more water to the soil paste in the evaporating dish and mix well. Repeat Steps
. 3, 4 and 5 to get a blow count N between 15 and 20 for a groove closure of Yz in.
(12.7 Illlh) in the liquid limit device. Take a moisture sample from the cup.
8. Put the three moisture cans in the oven to dry to constant masses (W3). (The caps of
the moisture cans should be removed from the top and placed at the bottom ofthe
respective cans in the oven.)
Calculation
Detennine the moisture content for each ofthe three trials (Steps 5, 6 and 7) as
w (%) = W; - W; (100)
W,-W;
(6.1)
Graph
Plot a semi-log graph between moisture content (arithmetic scale) versus number ofblows,
N (log scale). This wiII approximate a straight line, which is called theflow curve. From the
straight line, determine the moisture content w (%) corresponding to 25 blows. This is the
liquid limit ofthe soil.
The magnitude ofthe slope ofthe flow line is called theflow index, F], or
(6.2)

Typical examples ofliquid limit calculation and the corresponding graphs are shown in Table
~1 and Fig. ~5.
Table 6-1. Liquid LimitTest
Description of Soil _--'G."'ra"""v....
sl<U;!ty"-""C!.....
qV'--_____ Sample No! _4'--__
Location.___________________-,_ /
Tested by _______________ Date _---,".:..'_______
Can No. 8 21 25
Mass ofcan, WI (g) 15.26 17.01 15.17
Mass ofcan + moist soil, W2 (g) 29.30 3/.58 31.45
Mass ofcan + dry soil, W3 (g) 25.84 27.72 26.96
w-w
Moisture content, w (%) = 2. 3 X 100
w,-W; 32.7 36.04 38.1
Number ofblows, N 35 23 17
Liquid limit =_~1""'5"".2~__~----------...,....--
(37- 33,7)
= 18.74
Flow index = __--'('--lo""g_3_0_-_lo..;:g:...2_0"-)__________
, General Comments
Basedon the liquid limittests on several soils, the u.s. Army Waterways Experiment Station
(1949) observed that the liquid limit, LL, ofa soil can,be approximately given by
where wN (%) = moisture content, in percent, for 92 in. (12.7 mm) groove
closure in the liquid limit device at N number ofblows
(6.3)

40
r-..
'<t. 38
'-'
;t
ii,
.,
i:l
0
0
34
~
'"
.~
~
1--££=35.2
,
...
"~
------ ---~
20
N
~
~
N=25
• I
30 40
Figure 6-5. Plot of moisture content (%) vs. number of blows for the liquid limit
test results reported in Table 6-1.
ASTM also recommends this equation for detennining the liquid limit ofsoils (ASTM
designation D-431~). However, the value of wr21should ~orrespond to an Nvalue between
20 and 30. Followmg are the,values of (Nh5)o. for vanous values ofN.
20 0.973 26 1.005
21 0.979 27 1.009
22 0.985 28 1.014
23 0.990 29 1.018
24 0.995 30 1.022
25 1.000
The presence ofclay contributes to the plasticity of soil. The liquid limit of a soil will '
change depending on the amount and type of clay minerals present in it. Following are the
approximate ranges for the liquid limit of some clay minerals
Kaolinite
Illite
Montmorillonite
35-100
55-120
100-800

7
Plastic Limit Test
Introduction
The fundamental concept ofplastic limit was introduced in the introductory section of the
preceding chapter (see Fig. 6-1). Plastic limit is defined as the moisture content, in percent,
at which a cohesive soil will change from a plastic state to a semisolid state. In the
laboratory, the plastic limit is defined as the moisture content (%) at which athread ofsoil
will just crumble when rolled to a diameter of%-in. (3.18 mm). This test might be seen as
somewhat arbitrary and, to some extent, the result may depend on the person performing the
test. With practice, however, fairly consistent results may be obtained.
Equipment
2. Spatula
3. Plastic squeeze bottle with water
4. Moisture can
5. Ground glass plate
Procedure
1. Put approximately 20 grams ofa representative, air-dry soil sample, passed through
No. 40 sieve, into a porcelain evaporating dish.
2. Add water from the plastic squeeze bottle to the soil and mix thoroughly.
3. Determine the mass ofa moisture can in grams and record it on the data sheet (WI)'
4. From the moist soil prepared in Step 2, prepare several ellipsoidal-shaped soil masses
by squeezing the soil with your fingers.
5. Take one ofthe ellipsoidal-shaped soil masses (Step 4) and roll it on a ground glass
41

plate using the palm ofyour hand (Fig. 7-1). The rolling should be done at the rate
ofabout 80 strokes per minute. Note that one complete backward and one complete
forward motion ofthe palm constitute a stroke.
Figure 7-1. An ellipsoidal soil mass is being rolled into athread on
aglass plate.
6. When the thread is being rolled in Step 5 reaches Va-in. (3.18 mm) in diameter, break
it up into several small pieces and squeeze it with your fingers to form an ellipsoidal
massagam.
7. Repeat Steps 5 and 6 until the thread crumbles into several pieces when it reaches a
diameter of 'la-in. (3.18 JIl1ll).It is possible that a thread may crumble at a diameter
larger than 'la-in. (3.18 mm) during a given rolling process, whereas it did not
crumble at the same diameter during the immediately previous rolling.
8. Collect the small crumbled pieces in the moisture can put the cover on the can.
9. Take the other ellipsoidal soil masses formed in Step 4 and repeat Steps 5 through
8.
10. Determine the mass ofthe moisture can plus the wet soil (W2) in grams. Remove the
cap from the top ofthe can and place the can in the oven(with the cap at the bottom
qfthe can).
II. After about 24 hours, remove the can from the oven and determine the mass ofthe
can plus the dry soil (W3) in grams.

Calculations
Plastic limit =
mass of moisture
mass ofdry soil
w W
2 - '(100)
~-W;
(7.1)
The results may be presented in a tabular form as shown in Table 7-1. Ifthe liquid limit of
the soil is known, calculate the plasticity index, PI, as
PI=LL - PL (7.2)
Table 7-1. Plastic Limit Test
Description of soil_--'G,""ra.!i¥-y.!dc/.....
~).j'""C';l:.Y"""1"-'1t______ Sample No. _3'"-______
Location ___________________________
Tested by ______________,-- Date __________
Can No. 103
Mass ofcan, WI (g) 13.J3
Mass ofcan + moist soil, W2 (g) 23.86
Mass ofcan + dry soil, W3 (g) 22.27
PL= W, -W, xlOO 17.78
~-W;
Plasticity index, PI =LL- PL = 34 - 17.78 = 16.28
General Comments
The liquid limit and the plasticity index ofcohesive soils are important paranteters for classi-
fiction purposes. The engineering soil classification systems are described in Chapter 9. The
plasticity index is also used to determine the activity, A, of a clayey soil which is defined as
PI
A = - - - - - - - - - - - -
(% of clay - size fraction, by weight)
Following are typical values ofPI of several clay minerals.

Kaolinite
Illite
Montmorillonite
20--40
35-50
50-100

8
Shrinkage Limit Test
Introduction
The fundamental concept ofshrinkage limit was presented in Fig. 6-1. A saturated clayey
soil, when gradually dried, willlose moisture and, subsequently, there will be a reduction in
the volume ofthe soil mass. During the drying process, a condition will be reachedwhen any
further drying will result in a reduction ofmoisture content without any decrease in volume
(Fig.8-1). The moisture content ofthe soil, in percent, at which the decrease in soil volume
ceases is defined as the shrinkage limit.
v, "-T------------------i
IIV [See Eq. (8.4)]
V,
I
I
lIw I
14 ~i
I I
I [See Eq. (8.4)] : I
I I
I I I
I I I
SL LL w, Moisture.
content (%)
Figure 8-1. Definition of shrinkage limit.
45

Figure 8-2. Equipment needed for determination of shrinkage limit.
Equipment
. 1. Shrinkage limit dish [usually made ofporcelain, about 1.75 in. (44.4 m) in diameter
and 0.5 in. (12.7 mm) high]
2. A glass cup [2.25 in. (57.1S mm) in diameter and 1.25 in. (31.75 mm) high]
3. Glass plate with three prongs
4. Porcelain evaporating dish about 5.5 in. (139.7 mm) diameter
5. Spatula
7. Steel straight edge
8. Mercury
9. Watch glass
10. Balance sensitive to 0.01 g
The above required equipment is shown in Fig. 8-2.
Procedure
1. Put about 80 to 100 grams of a representative air dry soil, passed through No. 40
sieve, into an evaporating dish;
2. Add water to the soil from the plastic squeeze bottle'and mix it thoroughly into the
form ofa creamy paste. Note that the moisture content ofthe paste should be above
the liquid limit ofthe soil to ensure full saturation.
,
3. Coat the shrinkage limit dish lightly with petroleum jelly and then determine the
mass ofthe coated dish (WI) in grams.
4. Fill the dish about one-third full with the soil paste. Tap the dish on a firm surface

so that the soil flows to the edges ofthe dish and no air bubbles exist.
S. Repeat Step 4 until the dish is full.
6. Level the surface ofthe soil with the steel straight edge. Clean the sides and bottom
ofthe dish with paper towels.
7. Detennine the mass ofthe dish plus the wet soil (W2) in grams.
8. Allow the dish to air dry (about 6 hours) until the color of the soil pat becomes
lighter. Then put the dish with the soil into the oven to dry.
9. Determine the mass ofthe dish and the oven-dry soil pat (W3) in grams.
10. Remove the soil pat from the dish.
11. In order to find the volume ofthe shrinkage limit dish (Vi), fill the dish with mercury.
(Note: The dish should be placed on a watch glass.) Use the three-pronged glass plate
and level the surface ofthe mercury iIi the dish. The excess mercury will flow into
the watch glass. Determine the mass ofmercury in the dish (W4) in grams..
12. In order to determine the volume ofthe dry soil pat (VI)' fill the glass cup with mer-
cury. (The cup should be placed on a watch glass.) Using the three-pronged glass
plate, level the surface ofthe mercury in the glass cup. Remove the excess mercury
on the watch glass. Place the dry soil pat on the mercury in the glass cup. The soil pat
will float. Now, using the three-pronged glass plate, slowly push the soil pat into the
mercury until the soil pat is completely submerged (Fig. 8-3). The displaced mercury
will flow out ofthe glass cup and will be collected onthe watch glass. Determine the
mass ofthe displaced mercury on the watch glass (Ws) in grams.
glass
Figure 8-3. Determination of the volume of the soil pat (Step'12).
Calculation
1. Calculate the initial moisture content ofthe soil at molding.
Wi (%)
(8.1)
2. Calculate the change in moisture content (%) before the volume reduction ceased
(refer to Fig. 8-1).

~W (%) = (V; - VI )Pw = (»':t - Ws) (100)
, mass ofdry soil pat 13.6 (~ - w;)
(8.2)
where Pw~ density ofwater = 1 g/cm3
3. .Calculate the shrinkage limit.
SL = Wi - (~- Ws) (100)
13.6(~ -w;)
(8.3)
Note that W4 and Ws are in grams, and the specific gravity ofthe mercury is 13.6. A
sample calculation is shown in Table 8-1.
Table 8-1. Shrinkage Limit Test
Description of soil _---'"D"",,!Llrk>-Jb«n"'o"'w,u'n....
d""quvei,l!:,Y-"-sl""lt____
Location Westwind Boulevard
Tested by ______..,,-________
Mass of coated shrinkage limit dish, WI (g)
Mass ofdish + wet soil, W2 (g)
Mass ofdish + dry soil, W3 (g)
Wi (%) =(W, - W,) x 100
(W, - w;)
Mass ofmercury to fill the dish, W4 (g)
Mass ofmercury displaced by soil pat, W5 (g)
~Wi (%) = (~ - W,) X 100
(13.6)(W; - W;)
SL =Wi - (~- W,) (100)
13.6(W, -W;)
Sample No. 8
Date
I
/2.34
40.43
33.68
31.63
/98.83
/50.30
/6.72
/4.91

General Comments
The ratio ofthe liquid limit to the shrinkage limit (LLISL) of a soil gives a good idea about
the shrinkage properties ofthe soil. Ifthe ratio of LLISL is large, the soil in the field may
undergo undesirable volume change due to change in moisture. New foundations constructed
on these soils may show cracks due to shrinking and swelling of the soil that result from
seasonal moisture change.
Another parameter called shrinkage ratio (SR) may also be determined from the
shrinkage limit test. Referring to Fig. 8-1
SR = _.'l_V_/~VI,
.'lw /W,
.'lV/VI =~
(.'lVpw)/w, P'YI
where Ws = weight ofthe dry soil pat
=W3 -W
If Ws is in grams, VI is in cm3
and Pw = 1 g/cm3
. So
SR= W,
VI
(8.4)
(8.5)
The shrinkage ratio gives an indication of the volume change with change in moisture
content.

9
Engineering Classification
of Soils
Introduction
Soils are widely varied in their grain-size distribution (Chapters 4 and 5). Also,depending
on the type and quantity ofclay minerals present, the plastic properties of soils (Chapters 6,
7 and 8) may be very different. Various types ofengineering works require the identification
and classification ofsoil in the field. In the design offoundations and earth-retaining struc- .
tures, construction ofhighways, and so on, it is necessary for soils to be arranged in specific
groups and/or subgroups based on their grain-size distribution.and plasticity. The process of
placing soils into various groups and/or subgroups is called soil classification.
For engineering purposes, there are two major systems that are presently used in the
United States. They are: (i) the American Association ofState Highway and Transportation
Officials (AASHTO) Classification System and (ii) the Unified Classification System. These
two systems will be discussed in this chapter.
American Association of State Highway and
,
Transportation Officials,<AASHTO) System of
Classification
The AASHTO classification system was originally initiated by the Highway Research Board
(now called the Transportation Research Board) in 1943. This classification system has
under-gone several changes since then. This system)s presently used by federal, state, and
county highway departments in the United States. In this soil classification system, soils are
generally placed in seven major groups: A-i, A-2, A-3, A-4, A-5, A-6 andA-7. GroupA-i is
divided into two subgroups: A-i-a and A-i-b. Group A-2 is divided into four subgroups: A-2-
4, A-2-5, A-2-6 andA-2-7. Soils under group A-7 are also divided into two subgroups: A-7-5
andA-7-6. This system is also presently included in ASTM under test designation D-3284.
51

Along with the soil groups and subgroups discussed above, another factor called the
group index (Ol) is also included in this system. The importance ofgroup index can be ex-
plained as follows. Let us assume that two soils fall under the same group; however, they
may have different values of OJ. The soil that has a lower value ofgroup index is likely to
perform better as a highway subgrade material.
The procedure for classifying soil under the AASHTO system is outlined below.
Step-by-Step Procedure for AASHTO Classification
L Determine the percentage of soil passing through U.S. No. 200 sieve (0.075 mm
opening). '
1[35% or less passes No. 200 sieve, it is a coarse-grained material. Proceed to Steps
2 and 4.
If more than 35% passed No. 200 sieve, it is a fine-grained material (i.e., silty or
clayey material). For this, go to Steps 3 and 5.
Determination of Groups or Subgroups
2. For coarse-grained Soils, determine the percent passing U.S. sieve Nos. 10,40 and
200 and, additionally, the liquid limit and plasticity index. Then proceed to Table 9.1.
Start from the top line and compare the known soil properties with those given in the
table (Columns 2 through 6). Go down one line at a time until a line is found for
which all the properties ofthe desired soil matches. The soil group (or subgroup) is
determined from Column I..
3. For fme-grained soils, determine the liquid limit and the plasticity index. Then go to
Table 9.2. Start from the top line. By matching the soil properties from Columns 2,
3 and 4, determine the proper soil group (or subgroup).
Determination of Group Index
4. To determine the group index (Ol) ofcoarse-grained soils, the following rules need
to be observed.
a. OHor soils in groups (or subgroups) A-I-a, A-I-b, A-2-4, A-2-5 and A-3 is
zero.
b. For OJin soils ofgroupsA-2-6 and A-2-7, use the following equation:
OJ= 0.01 (F200 - 15)(PI - 10)
whereF200 = percent passing No. 200 sieve
PI = plasticity index
(9.1)
Ifthe 01comes out negative, round it offto zero. Ifthe 01 is positive, round
it offto the nearest whole number.

1.11' !0Ii!11IIi._/ 'I' I~r~ijliillillilijillnfJIJlniillllllllliillllllllilllUli UliRfiJtllrU!llIlUijliilll~*IIJIU_/"'" J,ll :Mt"'il,iliJffililIlJIJIIlllIItIIllWII!III'I ill ~- ,,'WI, ,_',,, ....".11.. l1li
"'J~,ji/i;:(:20:{;~~riif-h~~~~~:,~~~~~~~h'f~t1Ji¥4~?')t.i~Y;,i~'~w.';'j''''':
Table 9-1. AASHTO Classification for Coarse-Grained Soils
A-J-a 50 max. 30 max. 15 max. 6 max Stone
A-J I fragments,
A-J-b 50 max. 25 max. 6 max. gravel and sand
A-3 51 min. lOmax. Nonplastic Fine sand
I Excellent
to
A-2-4 35 max. 40 max. 10 max. good
A-2-5 I I I
35 max,
I
41 min. lOmax. Silty and
A-2 I clayey gravel
A-2-6 ! 35 max. 40 max. 11 min. and sand
I A-2-7 I I I 35 max. 41 min. 11 min.
*Based on the fraction passing No. 40 sieve

'flllechanics Laboratory Manual
Table 9-2. AASHTO Classification for Fine-Grained Soils
A-4 36 min. 40 max.
I
10 max. Silty soil Fair to poor
A-5 36 min. 41 min. 10 max. Silty soil Fair to poor
..
A-6 36 min. 40 max. 11 min. Clayey soil Fair to poor
A-7-5
I
36 min. 41 min.
11 min.
and PI :;; LL - 30 Clayey soil Fair to poor
A-7
A-7-6 j. 36 min. 41 min.
11 min.
and PI> LL - 30 Clayey soil Fair to poor
*Based on the fraction passing U.S. No. 40 sieve

(
I.
5. For obtaining the GIofcoarse-grained soils, use the following equation:
GI= (F200 - 35)[0.2 +0.005(LL - 40)] + 0.01(F2oo - l5)(PI - 10) (9.2)
Ifthe GIcomes out negative, round it offto zero. However, ifit is positive, round it
offto the nearest whole number.
Expression for Soil Classification
6. The final classification of a soil is given by first writing down the group (or
subgroup) followed by the group index in parenthesis.
General
Figure 9-1 shows the range ofPIandLL for soil groupsA-2-4, A-2-5, A-2-6, A-2-7, A-4, A-5,
A-6, A-7-5 andA-7-6.
80
70
60
20
10
0
/
L
'f'
/
A-6
A-7-6 V
A-2-6
/
V
I
V A-7-5
A-~-7
1/
.
A-4 A-5
A-2-4 A-2-5
o w w ~ ~ ~ ~ m W W 100
Liquid limit
Figure 9-1_ Liquid limit and plasticity index for nine AASHTO soil groups.

Example 9-1
The following are the characteristics of two soils. ClassifY the soils according to the .
AASHTO system.
Soil A: Percent passing No.4 sieve = 98
Percent passing No.10 sieve = 90
Percent passing No. 40 sieve = 76
Liquid limit = 38
Plastic limit = 26
Soil B: Percent passing No.4 sieve = 100
Solution
Percent passing No.10 sieve ~ 98
Liquid limit = 49
Plastic limit = 28
Soil A:
1. The soil has 34% (which is less than 35%) passing through No. 200 sieve. So this is
a coarse-grained soil.
2. For this soil, the liquid limit = 38.
From Equation (7.2), plasticity index, PI= LL - PL = 38 - 24 = 12.
From Table 9-1, by matching, the soil is found to belong to subgroup A-2-6.
3. From Equation (9.1)
.GI= 0.01 (F200 - 15)(PI - 10)
= 0.01(34 - 15)(12 - 10) = (0.01)(19)(2)
=0.38" 0
4. So, the soil can be classified as A-2-6(O).
Soil B:
1. The soil has 58% (which is more than 35%) passing through No.200.sieve. So this
is a fine-grained soil.
2. The liquid limit ofthe soil is 49.
From Equation (7.2), plasticity index, PI= LL - PL = 49 - 28 = 21.
3. From Table 9-2, the soil is either A-7-5 or A-7-6. However, for this soil
PI=21>LL- 30=49- 30=19.
So this soil isA-7-6.

4. From Equation (9-2)
GI= (F200 - 35)[0.2 + 0.005(LL - 40)] + 0.01(F2oo - 15)(PJ - 10)
= (58 - 35)[0.2 + 0.005(49 - 40)] + 0.01(58 - 15)(21 - 10)
= 5.64 +4.73 = 10.37 '" 10
5. So the soil is classified asA-7-6(JO).
Unified Classification System
This classification system was originally developed in 1942 by Arthur Casagrande for airfield
construction during World War II. This work was conducted on behalf of the U.S. Anny
Corps of Engineers. At a later date, with the cooperation of the United States Bureau of
Reclamation, the classification was modified. More recently, the American Society of
Testing and Materials (ASTM) introduced a more definite system for group name ofsoils.
In the pre-sent form, it is widely used by foundation engineers all over the world. Unlike the
AASHTO system, the Unified system uses symbols to represent the soil types and the index
properties ofthe soil. They are as follows:
G Gravel W Well,-graded (for grain-size
distribution)
S Sand
P Poorly-graded (for grain-size
M Silt distribution)
C Clay L Low to medium plasticity
0 Organic silts and clays H High plasticity
Pt Highly organic soil and peat
Soil groups are developed by combining symbols for two categories listed above, such
as GW, SM, and so forth.
Step-by-Step Procedure for Unified Classification System
1. If it is peat (i.e., primarily organic matter, dark in color, and has organic odor),
classifY it as Pt by visual observation. For all other soils, determine the percent ofsoil
passing through U.S. No. 200 sieve (F200).
2. Determine the percent retained on U.S. No, 200 sieve (R200) as

(9.3)
(nearest whole number)
3. If R200 is greater than 50%, it is a coarse-grained soil. However, if~oo is less than
or equal to 50%, it is a fine-grained soil. For the case where R200 s 50% (i.e., fine-
grained soil), go to Step 4. IfR200 > 50%, go to Step 5.
4. For fine-grained soils (i.e., R200 S 50%, determine ifthe soil is organic or inorganic
in nature.
a. If the soil is organic, the group symbol can be OH or OL. If the soil is in-
organic, the group 'symbol can be CL, ML, CH, MH, or CL-ML.
b. Determine the percent retained on U.S. No.4 sieve (R4) as
R4 = 100 - F4
i
(nearest whole number)
where F4 ='percent finer than No.4 sieve
Note that R4 is the percent of gravel fraction in the soil (OF), so
c. Determine the percent ofsand.fraction in the soil (SF), or
SF=R200 - OF
(9.4)
(9.5)
(9.6)
d. For inorganic soils, determine the liquid limit (LL) and the plasticity index
(Pl). Go to Step 4e. For organic soils, determine the liquid limit (not oven
dried), LLNOD; the liquid limit (oven dried), LIoD; and the plasticity index
(not oven dried), PINOD' Go to Step 4f.
e. With known values of R200, OF, SF, SF/OF, LL and PI, use Table 9-3 to
obtain group symbols and group names of inorganic soils.
f. With known values of LLNOD' LLoD, PI
NOD' R200 , OF, SF and SF/OF, use
Table 9-4 to obtain group symbols and group names of organic soils.
Figure 9-2 shows a plasticity chart with group symbols for fine-grained soils.
5. For coarse-grained soils:
a. IfR4 > 0.5R200> it is a gravelly soil. These soUs may have the following group
symbols:
OW OW-OM
OF OW-OC
OM OP-OM
OC OP-OC
OC-OM

70
60
50
j 40
.~
~ 30
s::
20
10
--- "MI--
CL
or
OL
~
L or
OL
CH
V
or
OR ~r,:jV
';'
<;>."",0..
y" . t-:'>$'
/ MH
or
OH
_C;;hty'
00 10 20 30 40 50 60 70 80 90 100
Liquid limit
Figure 9-2_ Plasticity chart for group symbols of fine-grained
soils.
Detennine the following:
(1) Fzoo
(2) Unifonnity coefficient, Cu = D601D1O (see Chapter 4)
(3) Coefficient of gradation, Cc = Ii'jO/(D60 x DIO)
(4) LL (ofminus No. 40 sieve)
(5) PI (ofminus No. 40 sieve)
(6) SF [based on Equations (9.3), (9.4), (9.5) and (9.6)]
Go to Table 9-5 to obtain group symbols and group names.
b. IfR4 ,;; 0.5Rzoo, it is a sandy soil. These soils may have the following group
symbols:
SW SW-SM
SP SW-SC
SM SP-SM
SC SP-SC
SM-SC

Table 9-3. Unified Classification of Fine·Grained Inorganic Soils
(Note: The group names are based on ASTM D-2487.)
LL < 50, CL <IS Lean clay
PI> 7,
15' ;,1 Lean clay with sand .
and PI
;, 0.73(LL - 20) to
29 <1 Lean clay with gravel
;,30 ;,1 <15 Sandy lean clay
;,1 ;,15 Sandy lean clay with gravel
<1 <15 Gravelly lean clay
<1 ;,15 Gravelly lean clay with sand
LL < 50, ML <15 Silt
PI<4,
15 ;,1 Silt with sand
orP]
< O.73(LL - 20) to
29 <1 Silt with gravel
;,30 ;,1 <15 Sandy silt
;,1 ;,15 Sandy silt with gravel
<1 <15 Gravelly silt
<1 ;,15 Gravelly silt with sand
LL < 50, CL-ML <15 Silty clay
4 :; PI :; 7,
15 ;,1 Silty clay with sand
and PI
:?0.73(LL - 20) to
29 <1 Silty clay with gravel
;,30 :?1 <15 Sandy silty clay
;,1 ;,15 Sandy silty clay with gravel
<1 <15 Gravelly silty clay
<1 ;,15 Gravelly silty clay with sand

/
continued
Table 9-3. continued
LL ;, 50, CH <15 Fat clay
and PI
;, 0.73(LL - 20) 15 ;,1 Fat clay with sand
to
29 <1 Fat clay with gravel
;,30 ;,1 <15 Sandy fat clay
;,1 ;,15 Sandy fat clay with gravel
~~
<1 <15 Gravelly fat clay
~1
<1 Gravelly fat clay with sand
" ;,15
)',
'<'f
LL;, 50 MH <15 ,Elastic silt
and PI
< 0.73(LL - 20) 15 ;,1 .Elastic silt with sand
to
29 <1 Elastic silt with gravel
;,30 ;,1 <15 Sandy elastic silt
;,1 ;,15 Sandy elastic silt with gravel
<1 <15 Gravelly elastic silt
<1 ;,15 Gravelly elastic silt with sand

Table 9-4. Unified Classification of Fine·Grained Organic Soils
(Note: The group names are based on ASTM D-2487.)
LLNOD < OL PJNOD ;' 4 <15
50 and
and P!NOD;' 0.73 x
15 ;,1
(LLNOD - 20) to
I1w <0.75 29
<1
ILfoW
;,30 ;,1 <15
;,1 ;,15
<1 <15
<1 ;,15
PlNOD <4 <15
and
PlNOD < 0.73 x 15 ;,1
(LLNOD - 20) to
29
<1
;,30 ;,1 <15
;,1 ;,15
<1 <15
<1 ;,15
(
Organic clay
Organic clay
with sand
Organic clay
with gravel
Sandy organic
clay
Sandy
organic clay
with gravel
Gravelly
organic clay
Gravelly
organic clay
with sand
Organic silt
Organic silt
with sand
Organic silt
with gravel
Sandy organic
silt
Sandy organic
silt with gravel
Gravelly
organic silt
Gravelly
organic silt
with sand

'
r
I
l
,.:
!f-
LLNOD ;, OH PiNOD ;' 0.73 x
50, (LLNOD - 20)
alid
LLoD <0.75
LLNOD
PiNOD < 0.73 x
(LLNOD - 20)
Table 9-4. continued
<15 Organic clay
15 Organic clay
;,1
to with sand
29 Organic clay
<1 with gravel
;,30 ;,1 <15
Sandy
organic clay
Sandy
;,1 ;,15 organic clay
with gravel
<1 <15
Gravelly
organic clay
Gravelly
<1 ;,15 organic clay
with sand
<15 - Organic silt
15 Organic silt
;,1
to with sand
29 Organic silt
<1 with gravel
;,30 Sandy
';,1 <15 organic
silt
Sandy
;,1 ;,15 organic
silt with
gravel
<1 <15
Gravelly
organic silt
Gravelly
<1 ;,15 organic silt
with sand

Table 9-5. Unified Classification of Gravelly Soils (R4 >O.5R200) (Note: The group names are based on ASTM D-2487.)
,4 I < C, < 3 GW
;,]5
<5
WSn gl1ded gravel with sand
ell <4 and/or <15 Poorly graded gravel
I> Cc > 3 GP
,15 Poorly graded .ravel with sand
PI<4 or PI12 PI>7andPI >
<15 Clayey gravel
0.73(LL - 20)
GC
,15 Clayey gravel with sand
4<PI<7 <15 Silty, clayey gravel
and GC-GM .
PI> 0.73(££ - 20) >15 Silty, clayey gravel with sand
PI<40rPI<
<IS Wen graded gravel with silt
0.73(LL - 20)
GW-GM
>15 Wen graded gravel with silt and sand
,4 I < C, < 3
PI>7andPh
<15 Wen graded gravel with clay

0.73(££ - 20)
GW-GC
5::;;F2oo :s:12
>15 Wen graded gravel with clay and sand
PI<40rPI< <15 Poorly graded gravel with silt
0.73(LL - 20)
GP-GM
ell < 4 and/or ,15 Poorly graded gravel with silt and sand
1> Cc:>3
<15 Poorly graded gravel with clay
PI> 7 and PI,
0.73(££ - 20)
GP-GC
>15 Poorly graded gravel with clay and sand

Table 9-6. Unified Classification of Sandy Soils (R4 ,;: O.5R200) (Note: The group names are based on ASTM D·2487.)
<15 Wen graded sand
>6 I < C, < 3 SW
",15 Wen graded sand with gravel
<5
ell < 6 and/or <15 Poorly graded sand
I> C,> 3 SP
>15 Poorly graded sand with gravel
PI<40rPI<
<15 ISiliy sand
0.73(LL - 20)
SM
>15 Silty sand with gravel
>12 PI> 7 and PI '"
I I <15 Clayey sand
0.73(LL - 20)
SC
I >15 Clayey sand with gravel
4<PI<7 <15 Silty, clayey sand
and SC-SM
PI> 0.73(LL - 20) . >15 Silty, clayey sand with gravel
PI < 4 or PI <
<15 W.en graded sand with silt
0.73(LL - 20)
SW-SM
>15 Wen graded sand with silt and gravel
>6 I < C, < 3
PI>7andPi>
<15 Wen graded sand with clay
0.73(LL - 20)
SW-SC
5 <F200 < 12
>15 Wen graded sand with clay and gravel
PI<40rPI< <15 Poorly graded sand with silt
0.73(LL - 20)
SP-SM
ell < 6 and/or >15 Poorly graded sand with silt and gravei
I> C,>3
Poorly graded sand with clay
PI> 7 and PI>
<15
0.73(LL - 20)
SP-SC
>15

Example 9-2
Classify Soils A and B as given in Example 9~I and obtain the group symbols and group
names. Assume Soil B to be inorganic.
Soil A: Percent passing No.4 sieve = 98
Percent passing No..40 sieve = 76
Percent passing No. 200, sieve = 34
Liquid limit = 38
Plastic limit = 26
Soil B: Percent passing No.4 sieve = 100
Solution
Percent passing No. 200 sieve;" 58
Liquid limit = 49
Plastic limit = 28
Soil A:
Step 1. F200 = 34%
Step 2. R200 = 100 - F200 = 100 - 34 = 66%
Step 3. R200 = 66% > 50%. So it is a coarse-grained soil.
Skip Step 4.
Step 5. R4 = 100 - F4 = 2%
R4 < 0.5R200 = 33%
So it is a sandy soil (Step 5b). F200 > 12%. Thus Cu and Cc values are not needed.
PI = LL - PL = 38 - 26 = 12
PI= 12 <0.73(LL - 20)=0.73(38 - 20)= 13.14
From Table 9-6, the group symbol is SM.
GF= R4 = 2% (which is < 15%)
From Table 9-6, the group name is silty sand.
Soil B:
Step 1. F200 = 58%
Step 2. R200 = 100 - F200 = 100 - 58 = 42%
Step 3. R200 = 42% < 50%. So it is a fine-grained soil.

I
Step 4. From Table 9-3, LL = 49 < 50
P/=49-28=21
P/= 21 < 0.73(LL - 20) = 0.73(49 - 20) = 21.17
So the group symbol is ML.
Again, R200 = 42% > 30%
R4 = 100 - F4 = 100 - 100 = 0%
So GF= 0% < 15%
SF=R200 - GF=42 - 0=42%
SFIGF> 1
So the group name is sandy silt.

)
10
Constant Head
Permeability Test in Sand
Introduction
The rate of flow ofwater through a soil specimen of gross cross-sectional area, A, can be
expressed as
where q = flow in unit time·
k = coefficient ofpermeability
i = hydraulic gradient
q=kiA (10.1)
For coarse sands, the value ofthe coefficient ofpermeability may vary from 1 to 0.01 cm/s
and, for fine sand, it may be in the range of0.01 to 0.001 cm/s.
Several relations between k and the void ratio, e, for sandy soils have been proposed..
They are ofthe form
e2
koc--
l+e
e3
koc--
l+e
(10.2)
(10.3)
(l0.4)
The coefficient ofpermeability ofsands can be easily determined in the laboratory by two
simple methods. They are (a) the constant head test and (b) th.e variable head test. In this
chapter, the constant head test method will be discussed.
69

70 .Soil Mechanics Laboratory Manual
Equipment
1.
2.
Constant head permeameter
Graduated cylinder (250 cc or 500 cc)
3. Balance, sensitive up to O.lg
4. Thermometer, sensitive up to 0.1°C
5. Rubber tubing
6. Stop watch
Constant Head Perrrieameter
A schematic diagram of a constant head permeameter is shown in Fig. 10--1. This can be
assembled in the laboratory at very low cost. It essentially consists ofa plastic soil specimen
cylinder, two porous stones, two rubber stoppers, one spring, one constant head chamber, a
large funnel, a stand, a scale, three clamps, and some plastic tubes. The plastic cylinder may
have an inside diameter of2.5 in. (63.5 mm). This is because 2.5 in. (63.5 mm) diameter
porous stones are usually available in most soils laboratories. The length ofthe specimen
tube may be about 12 in. (304.8 mm).
Procedure
1. Determine the mass ofthe plastic specimen tube, the porous stones, the spring, and
the two rubber stoppers (WI)'
2. Slip the bottom porous stone into the specimen tube, and then fix the bottom rubber
stopper to the specimen tube.
3. Collect oven-dry sand in a container. Use a spoon, pour the sand into the specimen
tube in small layers, and compact it by vibration and/or other compacting means.
Note: By changing the degree of compaction, a number of test specimens having
different void ratios can be prepared.
4. When the length ofthe specimen tube is about two-third the length ofthe tube, slip
the top porous stone into the tube to rest firmly on the specimen.
5. Place a spring on the top porous stone, ifnecessary.
6. Fix a rubber stopper to the top ofthe specimen tube.
Note: The spring in the assembled position will not allow any expansion ofthe speci-
men volume, and thus the void ratio, during the test.
7. Determine the mass ofthe assembly (Step 6 - W
2)•.
8. Measure the length (L) ofthe compacted specimen in the tube.
9. Assemble the permeameter near a sink, as shown in Fig. 10--1.
10. Run water into the top ofthe large funnel fixed to the stand through a plastic tube
from the water inlet. The water will flow through the specimen to the constant head
chamber. After some time, the water will flow into the sink through the outlet in the
constant head chamber.

Note: Make sure that water does not leak from the specimen tube.
Stopper
Porous stone
Plastic
cylinder
Porous stor,e-~
r;::==::::l Water supply
Constant
head
Figure 10-1. Schematic diagram of constant head
permeability test setup.
11. Adjust the supply ofwater to the funnel so that the water level in the funnel remains
constant. At the same time, allow the flow to continue for about 10 minutes in order
to saturate the specimen.
Note: Some air bubbles may appear in the plastic tube connecting the funnel to the
specimen tube.Remove the air bubbles: .
12. After a steady flow is established (that is, once the head difference h is constant), col-
lect the water flowing out ofthe constant head chamber (Q) in a graduated cylinder.
Record the collection time (t) with a stop watch.
13. Repeat Step 12 three times. Keep the collection time (t) the same and determine Q.
Then find the average value ofQ . ' '
14. Change the head difference, h, and repeat Steps II, 12 and 13 about three times.
15. Record the temperature, T, ofthe water to the nearest degree.
Note: This value is sufficiently accUrate for this type oftest.

Calculation
1. Calculate the void ratio ofthe compacted specimen as follows:
Dry density, Pd' ofthe soil specimen as
Thus
where Os = specific gravity ofsoil solids
Pw= density ofwater
D = diameter ofthe specimen
L = length ofthe specimen
2. Calculate k as
k= QL
Aht
where A = area ofspecimen = 1t D2
4
(10.5)
(10.6)
3. The value kis usually given for a test temperature ofwater at 20°C. So calculate kio0c
as
(10.7)
where 1Jroc and T]zo0c are viscosities ofwater at T'C and 20°C, respectively.
Table 10-1 gives the values of l1roc for various values of T (in °C).
l1wc '
Tables 10-2 and 10-3 give sample calculations for the permeability test.

15
16
17
18
19
20
. 21
22
Table 10-1. Variation of Ilrcill2o"c
1.135
1.106
1.077
1.051
1.025
1.000
0.976
0.953
23
24
25
26
27
28
29
30
0.931
0.910
0.889
0.869-
0.850
0.832
0.814
0.797
Table 10-2. Constant Head Permeability Test
Determination of Void Ratio of Specimen
Description of soil _-,U,,,,nU1lL!.fQ,,-,rm~$,,,,an,,,,d,--______ Sample No. ________
Location _________________~_________
Length of specimen, L _...!/..J.l...
.2~_cm Diameter of specimen, D_ ....6"".1""''5'--___ em
Tested by________________ Date_________
Volume of specimen, V= 1< D2L(cm2)
4
418.03
Specific gravity of soil solids, Gs 2.66
Mass of specimentube with fittings, WI (g) 238.4
Mass oftube with fittings and specimen, Wz(g)
.
965.3
Dry density of specimen, Pd = ~ - W;
V
(g I cm3
) 1.14
..
Void ratio of specimen, e= G,Pw_l
.
Pd 0.53
(Note: Pw= 1 g/cm3)

Table 10-3. Constant Head Permeability Test
Determination of Coefficient of Permeability
Test No. 1 2 ·3
Average flow, Q (cm3
) 305 375 395
Time ofcollection, t (s) 60 60 60
Temperature ofwater, T COC) 25 25 25
Head difference, h (cm) 60 70 80
Diameter of specimen, D (cm) 6.35 6.35 6.35
Length ofspecimen, L (cm) /3.2 /3.2 13.2
Area ofspecimen, A =11: D2 (cm2)
4
3/.67 3/.67 3/.67
k = QL (cm/s) 0.035 0.037 0.034
Aht
Averagek= 0.0:1.5 c.mls
k20•C = 'h·c
k,..c-
rJ2O'C
= 0.035(0.889) - 0.03/ cm/s

II
Falling Head
Permeability Test in Sand
Introduction
The procedure for conducting the constant head penneability tests in sand were discussed in
the preceding chapter. The falling head penneability test is another experimental procedure
to detennine the coefficient ofpenneability ofsand.
Equipment
1. Falling head penneameter
3. Thennometer
4. Stop watch
Falling Head Permeameter
A schematic diagram ofa falling head penneameter is showb. in Fig. 11-1. This consists of
a specimen tube essentially the same as that used in the constant head test. The top of the
specimen tube is connected to a burette by plastic tubing. The specimen tube and the burette
are held vertically by clamps from a stand. The bottom ofthe specimen tube is connected to
a plastic funnel by a plastic tube. The funnel is held vertically by a clamp from another stand.
A scale is also fixed vertically to this stand.
Procedure
Steps 1 through 9: ·Follow the same procedure (Le., Steps 1 through 9) as described in
Chapter 10 for the preparation ofthe specimen.
75

Water supply
L ' -
Scale
r
------- --- ------- ----- ~ ,
,
Burette
''"- --------:--------~
l
h'
, Plastic tube
--
S
"'- Glass
I ~ tube
land
......':-, ':.": ~.
f
..;'
...........
',",
L
::s~i(:.' I--Specimen
- "'~ tube
. ......
,'J ..."::..~ ..
unnel L~
~
'- [--Glass
tube
tPinch
~.
c~ck
L·~
.I- Plastic tut e
Figure 11-1. Schematicdiagram of falling head
permeability test setup.
Sland
10. Supply water using a plastic tube from the water inlet to the burette. The water will
flow from the burette to the specimen and then to the funnel. Check to see that there
is no leak. Remove all air bubbles.
II. Allow the water to flow for some time in order to saturate the specimen. When the
funnel is full, water will flow out of it into the sink.
12. Using the pinch cock, close the flow ofwater through.the specimen. The pinch cock
is located on the plastic pipe connecting the bottom ofthe specimen to the funnel.
13. Measure the head difference, hI (cm) (see Fig. II-I).
Note: Do not add any more ~a1:e'r to the burette.
14. Open the pinch cock. Water willflow through the burette to the specimen and then
out ofthe funnel. Record time (t) with a stop watch until the head difference is equal
t6 h2 (cm) (Fig. II-I). Close the flow ofwater through the specimen using the pinch
cock.

)5. Determine the volume (Vw) ofwater that is drained from burette in cm3.
16. Add more water to the burette to make another run. Repeat Steps 13, 14·and 15.
However, hi and h2 should be changed for each run.
17. Record the temperature, T, ofthe water to the nearest degree (0C).
Calculation
The coefficient ofpermeability can be expressed by the relation
.k =2.303 aL log 5...
At h2
(11.1)
where a = inside cross-sectional area ofthe burette
[For an example for derivation, see Das (1994) under "References" at the back ofthe book.]
Therefore
where A = area ofthe specimen
Asin Chapter 10
Sample calculations are shown in Tables 11-1 and 11-2.
(11.2)
(11.3)
(11.4)

78 Soil Mechanics Laboratory M;mual
Table 11-1. Falling Head Permeability Test
Description of soil_--'U""'fJ.!!.iifl.""Q:u.rm'-'-"sa"'n.<>dL.-__-,-___ Sample No. ____
Location _________________- -___~____
Length of specimen, L . /3.2 cm Diameter of specimen, 0 _-,6"".3""'5,,,-__ cm
Tested by _-'-______~______- Date ________
Volume of specimen, V =1t D2 L (cm2
)
418.03
4
Specific gravity of soil solids, Gs 2.66
Mass ofspecimen tube with fittings, WI (g) 238.4
Mass oftube with fittings arid specimen, W2 (g) 965.3
Dry density of specimen, Pd =W, ~ W; (g 1cm3
) 1.74
Void ratio ofspecimen, e =Gsp w -1
0.53
Pd
(Note: Pw=

Table 11-2. Falling Head Permeability Test
Determination ofCoefficient of Permeability
Test No. 1
Diameter of specimen, D (cm) 6.35
Length ofspecimen, L (cm) /3.2
Area ofspecimen, A (cm2
) 3/.67
Beginning head difference, hi (cm) 85.0
Ending head difference, h2 (cm) 24.0
Test duration, t (s) /5.4
Volume ofwater flow through the specimen, Vw (cm3
) 64
k 2.303VwL I hI ( / ')
= og-- cm s
(hI - h, )tA h, 0.036
.
Averagek = 0.037 cm/s
k20•C = I1T•C
= CO.QJZ)(.O.8.8'1,) 0.033 cm4
kpc - - -
112O"C
2 3
6.35 6.35
/3.2 /3.2
3/.67 3/.67
76.0 65.0
20.0 20.0
/5.3 /4.4
58 47
0.038 0.036

12
Standard Proctor
Compaction Test
Introduction
For construction ofhighways, airports, and other structures, it is often necessary to compact
soil to improve its strength. Proctor (1933) developeda laboratory compaction test procedure
to determine the maximum dry unit weight of compaction of soils which can be used for
specification offield compaction. This test is referred to as the'standard Proctor compaction
test and is based on the compaction ofthe soil fraction passing No, 4 U.S. sieve,
Equipment
1. Compaction mold
2. No.4 U.S. sieve
3. Standard Proctor hammer (5.5lb)
4. Balance sensitive up to 0.01 lb
6. Large flat pan
7. Jack
8. Steel straight edge
9. Moisture cans
10. Drying oven
Figure 12-1 shows the equipment required for the compaction test with the exception ofthe
jack, the balances, and the oven,
81

Figure 12-1. Equipment for Proctor compaction test.
Proctor Compaction Mold and Hammer
A schematic diagram ofthe Proctor compaction mold, which is 4 in. (101.6mrn)in diameter
and 4.584 in. (116.4) in height, is shown in Fig. 12-2a. There is a base plate and an extension
. that can be attached to the top and bottom ofthe mold, respectively. The inside ofthe mold
is Iho ft3 (943;9 cm3).
Figure 12-2b shows the schematic diagram ofa standard Proctor hammer. The hammer
can be lifted and dropped through a vertical distance of 12 in. (304.8 mrn).
Procedure
1. Obtain about 10 lb (4.5 kg) ofair-dry soil on which the compaction test is to be con-
ducted. Break all the soil lumps.
2. Sieve the soil on a No.4 U.S. sieve. Collect all ofthe minus-4 material in a large
pan. This should be about 6lb (2.7 kg) or more. .
3. Add enough water to the minus-4 material and mix it in thoroughly to bring the
moisture content up to about ~.
4. Determine the weight ofthe Proctor mold + base plate (not the extension), WI' (lb).
5. Now attach the extension to the top ofthe mold.
6. 'Pour the moist soil into the mold in three equal layers. Each layer should be com-
pacted uniformly by the standard Proctor hammer 25 times before the next layer of
loose soil is poured into the mold.

Extension
:1
, ,
LS
diameter
in.
<a) Mold
Drop~
12 in.
Weight
~ 5.5lb
14-2i~
(b) Hammer
Figure 12-2. Standard Proctor mold and
hammer.
Note: The layers ofloose soil that are being poured into the mold should be such that,
at the endofthe three-layer compaction, the soil should extend slightly above the top
ofthe rim ofthe compaction mold.
7. .Remove the top attachment from the mold. Be careful not to break off any of the
compacted soil inside the mold while removing the top attachment.
8.' Using a straight edge, trim the excess soil above the mold (Fig. 12-3). Now the top
ofthe compacted soil will be even with the top ofthe mold.
9. Determine the weight ofthe mold +base plate +- compacted moist soil in the mold,
Wz(lb).
10. Remove the base plate from the mold. Using a jack, extrude the compa<;ted soil
cylinder from the mold.
11. Take a moisture can and determine its mass, W3 (g).
12. From the moist soil extruded in Step 10, coliect a moisture sample in the moisture
can (Step II) and determine the mass ofthe can + moist soil, W4 (g).
13. Place the moisture can with the moist soil in the oven to dry to a constant weight.
14. Break the rest ofthe compacted soil (to No.4 size) by hand and mix it with the left-
over moist soil in the pan. Add more water and mix it to raise the moisture content
by about 2%.
..,.---

Figure 12-3. Excess soil being trimmed (Step 8).
15. Repeat Steps 6 through 12. In this process, the weight of the mold + base plate +
moist soil (W~ will first increase with the increase in moisture content and then de-
crease. Continue the test until at least two successive down readings are obtained.
16. The next day, determine the mass ofthe moisture cans + soil samples, W5 (g) (from
Step 13).
Calculation
Dry Unit Weight and Moisture Content at Compaction
The sample calculations for a standard Proctor compaction test are given in Table 12-1.·
Referring to Table 12-1,
Line 1- Weight ofmold, WI' to be determined from test (Step 4).
Line 2 - Weight ofmold +moist compacted soil, W2, to be determined from test (Step
9).
Line 3 - Weight ofmoist compacted soil = W2 - WI (Line 2 - Line I).
Line 4 - Moist unit weight
weight of compacted moist soil
Y= volume ofmold
= (30 lb / ft3) x (Line 3)
Line 6 - Mass ofmoisture can, W3, to be determined from test (Step 11).

. Line 7 - Mass ofmoisture can +moist soil, W4, to be determined from test (Step 12).
Line 8 - Mass ofmoisture can + dry soil, Ws, to be determined from test (Step 16).
Line 9 - Compaction moisture content
w (%) =fV.t - Ws x100
Ws-rt;
Line 10- Dry unit weight
'Y
'Yd = l+ W (%)
100
Line 4
1+ Line 9
100
Zero-Air-Void Unit Weight
The maximum theoretical dry unit weight of a compacted soil at a given moisture content
will occur when there is no air left in the void spaces of the compacted soil. This can be
given by
'Yd(theo'Y· m",) = 'Y=~ = w(%) 1
----'--'-+-
where Yzav = zero-air-void unit weight
Yw = unit weight ofwater
w = moisture content
Gs = specific gravity of soil solids.
100 Gs
(12.1)
. Since the values ofywand Gs will be known, several values ofw(%) can be assumed and
Yzav can be calculated. Table 12-2 shows the calculations for Yzav for the soil tested and re-
ported in Table 12-1.
Graph
Plot a graph showing Yd(Line 10, Table 12-1) versus w(%) (Line 9, Table 12-1) and deter-
mine the maximum dry unit weight ofcompaction [yd(max)l. Also dete.rmine the optimum
moisture content, wopt' which is the moisture content corresponding to Yd(max)' On the same
graph, plot Yzav versus w (%). .
Note: For a given soil, noportion ofthe experiment curve ofyd versus w(%) should plot
to the right ofthe zero-air-void curve.
Figure 12-4 shows the results ofcalculations made in Tables 12-1 and 12-2.

Table 12-1. Standard Proctor Compaction Test
Determination of Dry Unit Weight
Description of soil light brown da,v,e,vsilt Sample No.
Location
Volume
1/30 ~
Weight of Number of Number
of mold hammer 5.5 Ib blows/layer .25 of layers
Tested by Date
1. Weight ofmold, WI (lb) 10.35 10.35 10.35 10.35
2. Weight ofmold +moist soil,
14.19 14.41 14.53 14.63
W2 (Ib)
3. Weight ofmoist soil, W2- WI
3.84 4.06 4.18 4.28
(lb)
4. Moist unit weight,
= W, - W; (lb Ift3 )
Y 1.130
115.2 121.8 125.4 128.4
5. Moisture can number 202 212 222 242
6. Mass ofmoisture can, W3 (g) 54.0 53.3 53.3 54.0
7. Mass ofcan +moist soil, W4 253.0 354.0 439.0 490.0
(g)
8. Mass ofcan + dry soil, Ws (g) 237.0 326.0 401.0 441.5
9. Moisture content,
w (%) = w.. - w, x 100 8.7 10.3 10.9 12.5
W,- W3
10. Dry unit weight ofcompaction
y d (lb I ft3
) = y
106.0 110.4 //3.0 114. I
1+ w (%)
100
2
3
10.35 10.35
14.51 14.47
4.16 4.12
124.8 123.8
206 504
54.8 40.8
422.8 243.0
374.7 21/,/
15.0 18.8
108.5 104.2

table 12-2. Standard Proctor Compaction Test
Zero·Air-Void Unit Weight
Description of soil _-,L4ig;uh",-tb""r""Q"'w"-1o..l.c"'Ia,vp,e.,.y....
s"-'ilt____-'-__ Sample No. _ ...
2~.___
Location __________________________---'-
Tested by ________________ Date -'-____.,.----
a
2.68
2.68
2.68
2.68
2.68
2.68
Eq. (12.1)
120
10
/2
/4
/6
/8
20
•
Optimum
moisture
content = 12%
62.4
62.4
62.4
62.4
62.4
62.4
y-
G,=2.68
1008~-~1~0--~12~--~174--1t6;--~1~8-~2~O.--~22
Moisture content, W (%)
Figure 12-4. Plot of Vd VS. w(%) and Vzav VS. W(%) for test
results reported in Tables 12-1 and 12-2.
/3/.9
/26.5
/2/.6
117.0
112.8
/08.7

General Comments
In most ofthe specifications for earth work, it is required to achieve a compacted field dry .
unit weight of 90% to 95% ofthe maximum dry unit weight obtained in the laboratory. This
is sometimes referred to as relative compaction, R, or
R (%) = "1d(field) X 100
'Yd(max·lab)
For granular soils, it can be shown, that
R (%)' = Ro . x 100
1-D, (l-R.)
where D, = relative density ofcompaction.
.R = 'Yd(max)
o
'Yd(min)
(12.2)
(12.3)
(12.4)
Compaction ofcohesive soils will influence its structure, coefficient ofpermeability, one-
dimensional compressibility. and strength. For further discussion on this topic, refer to Das
(1994).
In this chapter, the laboratory test outlines given for compaction tests use the following:
Volume ofmold = Iho ft3
Number ofblows = 25
These values are generally used for fine-grained soils that pass through No.4 U.S. sieve.
However, ASTM and AASHTO have four different methods for the standard Proctor com-
paction test that reflect the size of the mold, the number of blows per layer, and the
maximum particle size in a soil used for testing. Summaries ofthese methods are given in
Table 12-3.
Table 12-3. Summary of Standard Proctor Compaction Test Specifications
(ASTM D-698, AASHTO T-99)
~ITI
Mold:
Volume (fi') 1/30 1/13.33 1/30 1/13.33
Height (in.) 4.58 '1.58 4.58 4.58
Diameter (in.) 4 6 4 6
Weight ofhammer (lb) 5.5 5.5 5.5 5.5
Height of drop ofhammer (in.) 12 12 12 12
Number oflayers of soil 3 3 3 3
Number ofblows per layer 25 56 25 56
Test on soil fraction passing sieve No.4 No.4 % in. % in.

13
Modified Proctor
Compaction Test
Introduction
In the preceding chapter, we have seen that water generally acts as a lubricant between solid
particles during the soil compaction process. Because of this, in the initial stages of com-
paction, the dry unit weight of compaction increases. However another factor that will
control the dry unit weight ofcompaction ofa soil at a given moisture content is the energy
ofcom-paction. For the standard Proctor compaction test, the energy ofcompaction can be
given by
(3 layers)(25 blows/layer)(5.5 lb)(l ft I blow) = 12 375 ft ·lb (593 kJ 1m3)
ljo ft3. ' ft3
The modified Proctor compaction test is a standard test procedure for compaction ofsoil
using a higher energy ofcompaction. In this test, the compaction energy is equal to
56,250 ft·!b (2694 kJ 1m3
).
ft
Equipment
The equipment required for the modified Proctor compaction test is the same as in Chapter
12 with the exception ofthe standard Proctor hammer (Item 3). The hammer used for this
test weighs 10 lb and drops through a vertical distance of 18 in. Figure 13'-1 shows the
standard and modified Proctor test hammers side by side.
The compaction mold used in this test is the same as described in Chapter 12 (i.e.,
volume = 1130 ft3.
89

Figure 13-1. Comparison of the standard and modified Proctor compaction hammer.
Note: The left-side hammer is for the modified Proctor compaction test.
Procedure
The procedure is the same as described in Chapter 12, except for Item 6. The moist soil has
to be poured into the mold in five equal layers. Each layer has to be compacted by the modi-
fied Proctor hammer with 25 blows per layer. .
CalqJlation, Graph, and Zero-Air-Void Curve
Same as in Chapter 12.

124 .------,----,-.--.---f----r----,'
~ 116
c,
,;;
.a
.~
.~ 108
g
Standard
•
10 12 14 16
Moisture content, w(%)
Figure 13-2. Comparison of standard and modified,
Proctor compaction test results for the soil
reported in Tables 12-1 and 12-2.
General Comments
18 20
1. The modified Proctor compaction test results for the same soil as reported in Tables
12-1 and 12-2 and Fig. 12-4 are shown in Fig. 13-2. A comparison ofydVs.w (%)
curves obtained from standard and modified Proctor compaction tests shows that
(a) The maximum dry unit weight ofcompaction increases with the increase in
the compacting energy, and
(b) The optimum moisture content decreases witft the increase in the energy of
compaction
2. As reported in Chapter 12, there are four different methods suggested by ASTM and
AASHTO for this test, and they are shown in Table 13-1.

Table 13-1. Summary of Modified Proctor Compaction Test Specifications
(ASTM 0-1557, MSHTOT-180)
Mold:
Volume (if) 1/30 1/13.33 1/30
Height (in.) 4.58 4.58 4.58
Diameter (in.) 4 6 4
Weight ofhammer (lb) 10 10 10
Height ofdrop ofhammer (in.) 18 18 18
Number oflayers of soil 5 5 5
Number ofblows per layer 25 56 25
Test on soil fraction sieve No.4 No.4 Y. in.
1/13.33
4.58
6
10
18
5
56
Y. in.

15
Direct Shear Test on Sand
Introduction
The shear strength, s, ofa granular soil may be expressed by the equation
where 0' = effective normal stress
<jJ = angle of friction ofsoil
s = 0' tan <jJ (15.1)
The angle offriction, <jJ, is a function ofthe relative density,ofcompaction ofsand, grain
size, shape and distribution in a given soil mass, For a givensand, an increase in the void
ratio (i.e., a decrease in the relative density of compaction) will result in a decrease ofthe
magnitude of <jJ. However, for a given void ratio, an increase in the angularity ofthe soil
particles will give a higher value ofthe soil friction angle. The general range ofthe angle of
friction of sand with relative density is shown in Fig. 15-1.
Equipment.
1. Direct shear test machine (strain controlled)
3. Large porcelain evaporating dish
4. Tamper (for compacting sand in the direct shear box)"
5. Spoon
Figure 15-2 shows a direct shear test machine. It consists primarily of a direct shear box,
which is split into two halves (top and bottom) and which holds the soil specimen; a proving
ring to measure the horizontal load applied to the specimen; two dial gauges (one horizontal
and one vertical) to measure the deformation ofthe soil during the test; and a yoke by which
a vertical load can be applied to the soil specimen. A horizontal load to the top halfofthe
shear box is applied by a motor and gear arrangement. In a strain-controlled unit, the rate of
movement ofthe top half ofthe shear box can be controlled.
99

200~--~2~O----4~O~--~60~--~80~--~IOO
Relative density, D, (%)
Figure 15-1. General range of the variation of
angle of friction of sand with relative
density of compaction.
Figure 15-2 shows a direct shear test machine. It consists primarily ofa direct shear box,
which is split into two halves (top and bottom) and which holds the soil specimen; a proving
ring to measure the horizontal load applied to a specimen; two dial gauges (one horizontal
and one vertical) to measure the deformation ofthe soil during the test; and a yoke by which
a vertical load can be applied to the soil specimen. A horizontal load to the top halfofthe
shear box is applied by a motor an~ gear arrangement. In a strain-controlled unit, the rate of
movement on the top halfofthe shear box can be controlled.
Figure 15-3 shows the schematic diagram ofthe shear box. The shear box is split into
two halves-top and bottom. The top and bottom halves of the shear box can be held
together by two vertical pins. There is a loading head which can be slipped from the top of
the shear box to rest on the soil specimen inside the box. There are also three vertical screws
and two horizontal screws on the top halfofthe shear box.
Procedure
1. Remove the shear box assembly. Back off the thrt;e vertical and two horizontal
screws. Remove the loading head. Insert the two vertical pins to keep the two halves
ofthe shear box together.
2. Weigh some dry sand in a large porcelain dish, WI' Fill the shear box with sand in
small layers. A tamper may be used to compact the sand layers. The top of the
compacted specimen should be about Y. in. (6.4 mm) below the top ofthe shear box.
Level the surface ofthe sand specimen.

Figure 15-2. A direct shear test machine.
SL'"I :,If. '11
L( i'5{, t) .j'tf
3. Determine the dimensions ofthe soil specimen (i.e., length L, width B, and height H
ofthe specimen).
4. Slip the loading head down from the top ofthe shear box to rest on the soil specimen.
5. Put the shear box assembly in place in the direct shear machine.
6. Apply the desired nonnalload<.N, on the specimen. This can be done by hanging
dead weights to the vertical load yoke. The top crossbars will rest on the loading head
ofthe specimen which, in tum, rests onthe soil specimen.'
Note: In the equipment shown in Fig. 15-2, the weights ofthe hanger, the loading
head, and the top half of the shear box can be tared. In some other equipment, if
taring is not possible, the nonnal load should be calculated as' N = load hanger +
weight ofYQke +weight ofloading head + weight oftop half ofthe shear box.
7. Remove the two vertical pines (which were inserted in Step 1to keep the two halves
ofthe shear box together).
8. Advance the three vertical screws that are located on the side walls ofthe top halfof
the shear box. This is done to separate the two halves ofthe box. The space between

Normal load = N h
Section
a
5
IC ~=f::t:J4--jshear
.1,- ,force = S
Plan
LEGEND
a-Top halfofthe shear box
b-Bottom halfofthe shear box
c-Vertical pins
d-Loading head
e-Vertical screw
f-Horizontal screw
g-Horizontal dial gauge
'h-Vertical dial gauge
Figure 15-3. Schematic diagram of adirect shear test box.
the two halves ofthe box should be slightly larger than the largest grain size ofthe
soil specimen (by visual observation).
9. Set the loading head by tightening the two horizontal screws located at the top half
ofthe shear box. Now back offthe three vertical screws. After doing this, there will
be no connection between the two halves ofthe shear box except the soil.
10. Attach the horizontal and vertical dial gauges (0.001 in.!small div) to the shear box
to measure the displacement during the test.
11. Apply horizontal load, S, to the top halfofthe shear box. The rate ofshear displace-
ment should be between 0.1 to 0.02 in.!min (2.54 to 0.51 mmlmin). For every tenth
small division displacement in the horizontal dial gauge, record the readings ofthe
vertical dial gauge and the proving ring gauge (which measures horizontal load, 8).
Continue this until after
(a) the proving ring dial gauge reading reaches a maximum and then falls, or
(b) the proving ring dial gauge reading reaches a maximum and then remains
constant.

Table 15-1. Direct Shear Test on Sand
Void Ratio Calculation
Description of soil _--'U""n'..!!.ifi"'o"-1.rTn.J..L,2smanjJ.d'--______ Sample No. _~2"--_
Location Acgonaut Circle
Tested by Date ________
1. Specimen length, L (in.)
2. Specimen width, B (in:)
3. Specimen height, H (in.)
4. Mass ofporcelain dish + dry sand (before use), WI (g)
5. Mass ofporcelain dish + dry sand (after use), W2 (g)
6. Dry unit weight ofspecime.(.~:~lb I ft3) = W; - ~ (;) x 3.808
:..~ LBH (m. )
7. Specific gravity ofsoil solids, Gs
8. Void ratio, e = G,Y" -1
Yd
Note: Yw = 62.4lb/ft3; Yd is in Ib/ft3
2
2
1.31
540.3
397.2
104.0
2.66
0.596

Table 15-2. Direct Shear Test on Sand
Stress and Displacement Calculation
Description of soil_-",U,:u.nifi.",,·
o"-,rm~sa""n",,,d______ Sample No. 2
Location _---'A""cg..;;o6!Lv1f!a""'utc.;G""in""r;A""e___'--_--,-_______
Normal load, N __"",5"",6___ lb Void ratio, e--:0'''''.5''''5'''''6'---____
Tested by ______________ Date_·_______~
14 0 0 0 0.31 0 0
14 0.01 +0.001 45 0.31 13.95 3.49
14 0.02 . +0.002 76 0.31 23.56 5.89
14 0.03 +0.004 95 0.31 29.76 7.44
14 0.04 +0.006 112 0.31 34.72 8.68
14 ·0.05 +0.008 124 0.31 38.44 9.61
14 0.06 +0.009 129 0.31 39.99 10.00
14 0.07 +0.010 125 0.31 38.75 9.69
14 0.08 +0.010 119 0.31 36.89 9.22
14 0.09 +0.009 114 0.31 35.34 8.84
14 0.10 +0.008 109 0.31 33.79 8.45
14 0.11 +0.008 108 0;)1 33.48 8.37
14 0.12 +0.008 105 0.31 32.55 8.14
* Plus (+) sign means expansion

10
s = 10 Ib/in.2
+---------
0'= 141b/in.'
3,0 (/
;2" s~o
1, Vi 0
~
g 0
i'l 0.010
"
~ 0.008
I·So
~
:a0.004
~ (b)
~ 00 2 4 6 8 10 12
Horizontal displacement x 102
(in.)
Figure 15-4. Plot of shear stress and vertical
displacement vs. horizontal
displacement for the direct shear
test reported in Tables 15-1 and
15-2.
3··5-3
) ( ' c
,7 ' c) .:/
j 1-s
General Comments . o· "" L/
Typical values ofthe drained angle offriction, <1>, for sands aregivefi r,e!ow:
Loose
Medium
Dense
28-32
30-35
34-38
Loose
Medium
Dense
30-36
34-40
40-45
L/.O'7
c:::>
:..; 'loy
II· (:C, (,
:s L(
;; .
" ·V
~ B"C)
G·
e..ek
O. lf2

25r--.---,---.---,--~---,
20
<p=35.'.W
°O~~-UL-~10~~--~20~~--~30
0' (lb/in.')
Figure 15-5. Plot of s vs. 0' for the sand
reported in Tables 15-1 and 15-2.
Note: The results for tests with 0.' =7Ib/in.2 and 28
Ib/in.2
are not shown in Table 15-2.

16
Unconfined Compression Test
Introduction
Shear strength ofa soil can be given by the Mohr-Coulomb failure criteria as
where s = shear strength
c = cohesion
o = normal stress
<p = angle of friction.
s=c+o+tan<p
For undrained tests ofsaturated clayey soils (<p = 0)
where Cu = undrained cohesion (or undrained shear strength).
(16.1)
(16.2) .
The unconfined compression test is a quick method ofdetermining the value of Cu for a
clayey soil. The unconfined strength is given by the relation [for further discussion see any
soil mechanics text, e.g., Das (1994)]
(16.3)
where qu = unconfined compression strength.
The unconfined compressiou strength is determined by applying an axial stress to a cylin-
drical soil specimen with no confining pressure and observing the axial strains corresponding
to various.stress levels. The stress at which failure in the soil specimen occurs is referred to
as the unconfined compression strength (Figure 16-1). For saturated clay specimens, the
unconfined compression strength decreases with the increase in moisture content. For
109

11 0 Soil Mechanics Laboratory Manual
unsaturated soils, with the dry unit weight remaining constant, the unconfined compression
strength decreases with the increase in the degree of saturation.
q q at failure =q,
Figure 16-1. Unconfined compression strength-definition
Equipment
1. Unconfined compression testing device
2. Specimen trimmer and accessories (ifundisturbed field specimen is used)
3. Harvard miniature compaction device and accessories (if a specimen is to be molded
for classroom work)
4. Scale
6. Oven
Unconfined Compression Test Machine
An unconfined compression test machine in which strain-controiled tests can be performed
is shown in Fig. 16-2. The machine essentially consists ofa top and a bottom loading plate.
The bottom ofa proving ring is attached to the top loading plate. The top ofthe proving ring
is attached to a cross-bar which, in tum, is fixed to two metal posts. The bottom loading plate
can be moved up or down.
Procedure
1. Obtain a soil specimen for the test. If it is an undisturbed specimen, it has to be
trimmed to the proper size by using the specimen trimmer. For classroom laboratory
work, specimens at various moisture contents can be prepared using a Harvard mini-
a~e compaction device.
The cylindrical soil specimen should have a height-to-diameter (LID) ratio of be-
tween 2 and 3. In many instances, specimens with diameters of 1.4 in. (35.56 mm)
and heights of 3.5 in. (88.9 mm) are used.
,
I

Figure 16-2. An unconfined compression
testing machine.
2. Measure the diameter (D) and length (L) ofthe specimen and detennine the mass of
the specimen.
3. Place the specimen centrally between the two loading plates ofthe unconfined com-
pression testing machine. Move the top loading plate very carefully just to touch the
top ofthe specimen. Set the proving ring dial gauge t.o zero.
A dial gauge [each small division ofthe gauge should be equal to 0.001 in. (0.0254
mm) of vertical travel] should be attached to the unconfined compression testing
machine to record the vertical upward movement (i.e., compression ofthe specimen
during testing) ofthe bottom loading plate. Set this dial gauge to zero.
4. Turn the machine on. Record loads (i.e., proving ring dial gauge readings) and the
corresponding specimen deformations. Durin~ the load application, the rate of verti-
cal strain should be adjusted to Yz% to 2% per minute. At the initial stage ofthe test,
readings are usually taken every 0.01 in. (0.254 mm) ofspecimen deformation. How-
ever, .this can be varied to every 0.02 in. (0.508 mm) of specimen deformation at a
later stage ofthe test when the load-deformation curve begins to flatten out.
5. Continue taking readings until
a. Load reaches a peak and then decreases; or

Figure 16-3. A soil specimen after failure
b. Load reaches a maximum value and remains approximately constant
thereafter (take about 5 readings after it reaches the peak value); or
c. Deformation of the specimen is past 20% strain before reaching the peak.
This may happen in the case ofsoft clays.
Figure 16-3 shows a soil specimen after failure.
6. Unload the specimen by lowering the bottom loading plate.
7. Remove the specimen from between the two loading plates.
8. Draw a free-hand sketch ofthe specimen after failure. Show the nature ofthe failure.
9. Put the specimen in a porcelain evaporating dish and determine the moisture content
(after drying it in an oven to a constant weight).
Calculation
For each set ofreadings (refer to Table 16-1):
I. Calculate the vertical strain (Column 2)
M
E=-
L
where tJ.L = total vertical deformation ofthe specimen
L = original length of specimen.
2. 'Calculate the vertical load on the specimen (Column 4).
(16.4)
Load = (proving ring dial reading, i.e. Column 3) x (calibration factor) (16.5)

Table 16-1. Unconfined Compression Test
Description of soil Lightbrown clav Specimen No. _~3,--,-____
Location Trin/v Boulevard
Moist weight Moisture Length of Diameter of
of specimen 149,8 g content~% specimen,L_3_in. specimen 1.43 in.
Proving ring calibration factor: 1 div. = 0.264 IbArea, Ao = !!.02 = 1.605 in2
4 -~"""----
Tested by ______________ Date _____-'-__
0 0 0 0 1.605 0
0.01 0.0033 12 3.168 1.6// 1.966
0.02 0.0067 38 10.032 1.617 6.205
0.03 0.01 52 13.728 1.622 8.462
0.04 0.0/3 58 15.312 1.628 9.407
0.06 0.02 67 17.688 1.639 10.793
0.08 0.027 74 19.536 1.650 11.840
0.10 0.033 78 20.592 1.661 12.394
0.12 0.04 81 21.384 1.673 12.782
0.14 0.047 83 21.912 1.685 /3.007
0.16 0.053 85 22.440 1.697 13.227
0.18 0.06 86 22.704 1.709 13.288
0.20 0.067 86 22.7'04 1.721 13.194
0.24 0.08 84 22. 176 1.746 12.703
0.28 0.093 83 21.912 1.771 12.370
0.32 0.107 82 21.912 1.798 12.041
0.36 0.12 81 21.384 1.825 11.717

3. Calculate the corrected area ofthe specimen (Column S)
A =~
c 1-£
where Ao = initial area ofcross - section ofthe specimen =1t D2
4
4. Calculate the stress, 0, on the specimen (Column 6)
Load Column 4
<r=--=----
Ac ColumnS
Graph
(16.6)
(16.7)
Plot the graph ofstress, 0 (Column 6), vs. axial strain, E, inpercent (Column 2 x 100). Deter~
mine the peak stress from this graph. This is the unconfined compression strength, qu' ofthe
specimen. Note,' If20% strain occurs before the peak stress, then the stress corresponding to
20% strain should be taken as quo
A sample calculation and graph are shown in Table 16-1 and Fig. 16'-4.
16r---r--.--.--~-.--,
4
2
°OL--~2-~4~-6L--~8-~IO~~12·
Axial strain, E (%)
Figure 16-4. Plotofavs. e (%) for the test
results shown in Table 16--1.

(
Soil Mechanics Laboratory Manual 11 5
General Comments
I. In the detennination ofunconfined compression strength, it is better to conduct tests
on two to three identical specimens. The average value of qu is the representative
value.
2. Based on the value ofqu' the consistency of a cohesive soil is as follows,:
Very soft
Soft
Medium
Stiff
stiff
0-500
500-1000
1000-2000
2000-4000
4000-8000
3. For many naturally deposited clayey soils, the unconfined compression strength is
greatly reduced when the soil is tested after remolding without any change in
moisture content. This is referred to as sensitivity and can be defined as
s = qu(undisturbed)
I
qu(remolded)
(16.8)
The sensitivity ofmost clays ranges from 1to 8. Based on the magnitude ofSt, clays
can be described as follows:
1-2
2-4
4-8
8-16
16--32
32-64
>64
Slightly sensitive
Medium sensitivity
Very sensitive
Slightly quick
Medium quick
Very quick
Extra quick

17
Consolidation Test
Introduction
Consolidation is the process oftime-dependent settlement ofsaturated clayey soil when sub-
jected to au increased loading. In this chapter, the procedure ofa one-dimensional laboratory
consolidation test will be described, aud the methods ofcalculation to obtain the void ratio-
pressure curve (e vs.logp), the preconsolidation pressure (Pc), aud the coefficient ofconsoli-
dation (cv) will be outlined.
Equipment
1. Consolidation test unit
2. Specimen trimming device
3. Wire saw
4. Balauce sensitive to 0.01 g
. 5. Stopwatch
6. Moisture cau
7. Oven
Consolidation Test Unit
The consolidation test unit consists ofa consolidometeraud a loading device. The consolido-
meter cau be either (1) a floating ring consolidometer (Fig. 17-1a) or (ii) a fixed ring con-
solidometer (Fig. 17-lb). The floating ring consolidometer usually consists ofa brass ring
in which the soil specimen is placed. One porous stone is placed at the top ofthe specimen
aud auother porous tone at the bottom. The soil speCimen in the ring with the two porous
stones is placed on a base plate. A plastic ring surrounding the specimen fits into a groove
on the base plate. Load is applied through a loading head that is placed on the top porous
stone. In the floating ring consolidometer, compression ofthe soil specimen occurs from the
117

d
a SPecimen
c
(a)
g
(b)
Figure 17-1. Schematic diagram of (a) floating ring consolidometer;
(b) fixed ring consolidometer.
LEGEND
a-Brass ring
b-Porous stone
c-Base plate
d--Plastic ring
e-Loading head
f-Metal ring
g-Stand pipe
h-Dial gauge
top and bottom towards the center. The fixed ring consolidometer essentially consists ofthe
same components, i.e., a hollow base plate, two porous stones, a brass ring to hold the soil
specimen, and a metal ring that can be fixed tightly to the top ofthe base plate. The ring
surrounds the soil specimen. A stand pipe is attached to the side ofthe base plate. This can
be used for permeability determination of soil. In the fixed ring consolidometer, the
compression ofthe specimen occurs from the top towards the bottom.
The specifications for the loading devices ofthe consolidation test unit vary depending
upon the manufacturer. Figure 17-2 shows one type ofloading device.
During the consolidation test, when load is applied to the soil specimen, the nature of
variation ofside friction between the surrounding brass ring and the specimen are different
for the fixed ring and the floating ring consolidometer, and this is shown in Fig. 17-3. In
most cases, a side friction of 10% ofthe applied load is a reasonable estimate.
Procedure
I. Prepare a soil specimen for the test. The specimen is prepared by trimming an undis-
turbed natural sample obtained in shelby tubes. The shelby tube sample should be
about V. in. to Y2 in. (6.35 mm to 12.7 mm) larger in diameter than the specimen dia-
meter to be prepared for the test.

Soil Mechanics Laboratory Manual 11 9
Figure 17-2. Consolidation load assembly. In this
assembly, two specimens can be
simultaneously tested. Lever arm ratio
for loading is 1:10.
Note: For classroom instruction purposes, a specimen coo be molded in the
laboratory.
2. Collect some excess soil that has been trimmed in a moisture can for moisture
content determination.
3. .Collect some ofthe excess soil trimmed in Step I for determination ofthe specific
gravity of soil solids, Gs'
4. Determine the mass ofthe consolidation ring (WI) in grams.

5. Place the soil specimen in the consolidation ring. Use the wire saw to trim the speci-
men flush with the top and bottom ofthe consolidation ring. Record the size ofthe
specimen, i.e., height [H'(i)] and diameter (D).
Specimen
top
'-'--~~---''---- 1
Specimen
bottom
(a)
Specimen
top
I'" friction/unit cOntact area
"------1
Specimen
bottom
(b)
Figure 17-3. Nature of variation of soil-ring friction per unit contact areas in
(a) fixed ring consolidometer; (b) floating ring consolidometer.
6. Determine the mass ofthe consolidation ring and the specimen (W2) in grams.
7. Saturated the lower porous stone on the base ofthe consolidometer.
8. Place the soil specimen in the ring over the lower porous stone.
9. Place the upper porous stone on the specimen in the ring.
10. Attach the top ring to the base ofthe consolidometer.
11. Add water to the consolidometer to submerge the soil and keep it saturated. In the
case ofthe fixed ring consolidometer, the outsidering (which is attached to the top
of the base) and the stand pipe connection attached to the base should be kept full
with water. This needs to be done for the entire period ofthe test.
12. Place the consolidometer in the loading device.
13. Attach the vertical deflection dial gauge to measure the compression ofsoil. It should
be fixed in such as way that the dial is at the beginning of its release run. The dial
gauge should be calibrated to read as 1 small division = 0.0001. (0.00254 mm).
14. Apply load to the specimen such that the magnitude ofpressure, p, on the specimen
is II, ton/W (45.88 kN/m~. Take the vertical deflection dial gauge readings at the
following times, t, counted from the time ofload application-O min., 0.25 min. 1
.min., 2.25 min., 4 min., 6.25 min., 9 min., 12.25 min:, 20.25 min., 25 min., 36 min.,
60 min., 120 min., 240 min., 480 min., and 1440 min. (24 hr.).
15. The next day, add more load to the specimen such that the total magnitude ofpres-
'sure on the specimen becomes 1 tOn/ft2 (95.76 kN/m2). Take the vertical·dial gauge
reading at similar time intervals as stated in Step 14. Note: Here we have I1p/ p = 1
(where tlp = increasein pressure and p = the pressure before the increase).

16. Repeat Step 15 for soil pressure magnitudes of2 tonlft2 (299.52 kN/m2),
4 tonlrt2 (383.04 kN/m2) and 8 tonlft2 (766.08 kN/m2). Note: !>.pIp = 1.
17. At the end ofthe test, remove the soil specimen and determine its moisture content.
0.06 r--,.---,--,----.,,--,---,
A
~ 0.08
g
on
.S
iii 0.09
e
~ 0.10
0.11
C ----------------- -
B D
O,12~-+-~;__-_;_-~--+-_:_!
o 2- 4 6 8 10 12
{time,(min°,')
Figure 17-4. Plot of dial reading vs. jtime for the test results given in Table
17-1. Determination of t90 by square-root-of-time method.
Calculation and Graph
The calculation procedure for the test can be explained with reference to Tables 17-1 and
17-2 and Figs. 17-4, 17-5 and 17..fJ, which show the laboratory test results for a light brown
clay.
1.
2.
3.
Collect all ofthe time vs. vertical dial readings data. Table 17-1 shows the results of
a pressure increase from p = 2 tonlft2 toP + I:!.p = 4 toDirt2.
Determine the time for 90% primary consolidation, t90, from each set oftime vs. ver-
tical dial readings. An example ofthis is shown in Fig. 17-4, which is a plot ofthe
results ofvertical dial reading vs. jtime given in Table 17-1. Draw a tangent AB
to the initial consolidation curve. Measure the lengthBC. The abscissa ofthe point
of intersection ofthe line AD with the consolidation curve will give {t;;, .In Fig.
17-4, {t;;, = 4.75 min.O.5, so t90 = (4.75i =22,56 min. This technique is referred
to as the square-root-of-time fitting method (Taylor, 1942).
Determine the time for 50% primary consolidation, tso,from each set oftime vs. ver-
tical dial readings. The procedure for this is shown in Fig. 17-5, which is a semilog
plot (vertical dial reading in natural scale and time in log scale) for the set ofreadings
shown in Table 17-1. Project the straight line portion ofthe primary consolidation

Table 17-1. Consolidation Test
Time VS. Vertical Dial Reading
Description ofsoil_---'LbI,ig.;:Lh!1.t~bn""o"'w.<L'I7u.c'"'/Ci,"'_v------_____
Location _-""SUblLWL1JmC!.ill.lt.'=D""n""·ve"------------_____
Tested by _______________ Date _________
Pressure on specimen._._4_ Ib/ff Pressure on specimen __ Ib/ff
0 0 0.0638
0.25 0.5 0.0654
1.0 1.0 . 0.0691
2.25 1.5 0.0739.
4.0 2.0 0.0795
6.25 2.5 .0.0833
9.0 3.0 0.0868
12.25 3.5 0.0898
16.0 4.0 0.0922
20.25 4.5 0.0941
25 5.0 0.0954
36 6.0 0.0979
60 7.75 0.1004
120 10.95 0.1019
240 15.49 0.1029
180 21.91 0.1048
1440 37.95 0.1059

~J:;p:$) _A,A¥M&iIJ;;1iMJk
Table 17-1. Consolidation Test
Void Ratio-Pressure and Coefficient of Consolidation Calculation
Description of soil Lightbrown clav Location __________________________
Specimen diameter 2.5 in. Initial specimen height, Ht(~ / in. Height of solids, Hs /.356 cm = ·0.539 in.
Moisture Content: Beginning of test 30.8 % End of test 32. / % Weight of dry soil specimen / /6.14 g Gs-"2
...£,.12"-____
Tested by Date _______________- - - - - - -
0
I 0.200
I 1.000 0.46/0 0.855
0.0083 0.9959 302 68.7 0.696 0.7//
!1
I 0.0283 I 0.99/7 0.4527 0.840
I
0.0073 0.988/ 308 560 0.672 0.859
/ I 0.0356 0.9844 0.4454 0.826
I
0.0282 0.9703 492 /44 0.406
I 0.322
2 I 0.0638 0.9562 0.4/72 0.774
0.042/ 0.9352 / /02
I 294
I 0. /68
I 0./47
.4
I O. /059 0.9/4/ 0.375/ 0.696
I I
0.0455
I 0.89/4
I /354
I 240
I 0./24 r 0./63
8 I 0./5/4 I 0.8686 0.3296 0.612
I I I I

0,05 r-.,--.---r----,-----.--~-.__,
~~-------------c
, x
-------------
x
t .1 ----r
, '
0.07
~
.S
{0.08
.a 0.09
is
_....:,____L;..:~!.L__
dso I
I
- ,
,
,
0.10
0.11
,I
, ,
-.......------------+------~
d100 , A
,
,
,
IIS{)
t,
0,12 ';-;~_;_;:___!---'-_7;;---._!c;;_------;c=_;;', ..
0.1 0.2 0.5 1 10 100 1000 2000
Time (min) -log scale
Figure 17-5. Lo.garithm of time curve fitting method for the laboratory
results given in Table 17-1.
downward and the straight line portion ofthe secondary consolidation backward. The
point ofintersection ofthese two lines is A. The vertical dial reading corresponding
to A is dlOO (dial reading at 100% primary consolidation). Select times t and t2 = 4t.
(Note: t and t2 should be within the top curved portion ofthe consolidation plot.)
Determine the difference in dial readings, X, between times t and t2• Plot line BC,
which is vertically X distance above the point on the consolidation curve correspon-
ding to time t. The vertical dial gauge corresponding to line BC ill d , i.e., the
reading for 0% consolidation. Determine the dial gauge reading corresponding to
50% primary consolidation as
d _ do +d,oo
50 - 2 (17.1)
The time corresponding to d50 on the consolidation curve is t50' This is the logarithm-
of-time curve fitting method (Casagrande and FadUm, 1940). In Figure 17-5, t50 =
14.9 min.
4. Complete the experimental data in Columns 1, 2, 8 and 9 of Table 17-2. Columns
< I and 2 are obtained from time-dial reading tables (such as Table 17-1), and
Columns 8 and 9 are obtained from Steps 2 and 3, respectively.
5. Determine the height ofsolids (Hs) ofthe specimen in the mold as (see top ofTable
17-2)
-.-.&... I

Soil Mechanics Laboratory Manual
where Ws = dry mass ofsoil specimen
D '= diameter ofthe specimen
Gs = specific gravity ofsoil solids
Pw = density ofwater.
125
(17.2)
6. In Table 17-2, determine the change in height, /:;.H, of the specimen due to load
increments fromp to p + /:;.p (Column 3). For example,
p = y, tonlrt2, final dial reading = 0.0283 in.
p + /:;.p = J tonlft2, final dial reading = 0.0356 in.
Thus
/:;.H = 0.0356 - 0.0283 = 0.0073 in.
7. Determine the fmal specimen height, Ht(f), at the end ofconsolidation due to a given
load (Column 4 in Table 17-2). For example, in Table 17-2 ~(f) at p = y, tonlft2is
0.9917. /:;.H from p = y, tonlrt2 and 1 tonlrt2 is 0.0073. So Ht(f) atp = 1 tonlrt2
is 0.9917 - 0.0073 = 0.9844 in. .
8. Determine the height ofvoids, Hv, in the specimen atthe end ofconsolidation due
to a given loading, p, as (see Column 5 in Table 17-:-2)
(17.3)
9. Determine the final void ratio at the end ofconsolidation for each loading,p, as (see
Column 6, Table 17-2)
Hv ColumnS
e=-=----
H, H,
(17.4)
10. Determine the average specimen height, ~(av)' during consolidation for each incre-
mental loading (Column 7, Table 17-2). For example, in Table 17-2, the value of
~(av) betweenp = y, tonlft2 and p = 1 tonlft2 is ,
H'(f) atp =! ton / jt'+ H'(f) atp =1ton / jt'
2
0.9917+0.9844
09881 in.
2
11. Calculate the coefficient ofconsolidation, Cv (Column 10, Table 17-2), from
190 (Column 8) as
(17.5)

where
Thus
Tv = time factor t90 = 0.848
H =maximum length of drainage path =
(since the specimen is drained at
top and bottom)
H,(.V)
2
12. Calculate the coefficient ofconsolidation,cv (Column 11, Table 17-2), from
t50 (Column 9) as
T - 0197 - cJso _ cJso
,(50%) -. - H2 - [ ]2
H,(.v)
2
(17.6)
(17.7)
For example, fromP = Y, ton/if toP = 1 tOn/ft2, ~(av) = 0.9881 in.; t50 = 56.0 s. So
c = 0.197(0.9881)2 0.859 X 10-3 in.2/S
, 4(56)
13. Plot a semilogarithmic graph ofpressure vs. final void ratio (Column 1 vs. Column
6, Table 17-2). Pressure,p, is plotted on the log scale and the final void ratio on the
linear scale. As an example, the results ofTable 17-2 are plotted in Fig. 17-6.
Note: The plot has a curved upper portion and, after that, e vs. log p has a linear
relationship.
14. Calculate the compression index, Ce. This is the slope ofthe linear portion ofthe e
vs. logp plot (Step 13). In Fig. 17-6
C = el -e2 = 0.696-0.612 0.279
, 8
logP2 log-
PI 4
15. On the semilogarithmic graph (Step 13), using the same horizontal scale (the scale
for p), plot the values of Cv (Column 10 and II, Table 17-2). As an example, the

values determined in Table 17-2 are plotted in Fig.17-6.
Note: Cv is plotted on the linear scale corresponding to the average value ofp, i.e.,
..
.g-
el
:ll
0.85
0.80
~ 070
01'
&!
0.60
- - - - - B
I '
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
fPc
I
I
D
c
1.2 r-~----r----'--------'r-------'
• From,."
• Fromt",
~
j 0.8l-----..
g
~ 0.4
x
O~--~~~~~~--~
0.5 I 2 5 10
Pressure, p (toniit')
Figure 17-6. Plot of void ratio and the coefficient of consolidation against pressure for the soil
reported in Table 17-2.
16. Determine the preconsolidation pressure, Pc' The procedure can be explained with
the aid ofthe e-logp graph shown in Fig. 17-6 (Casagrande, 1936). First, determine
point A, which is the point on the e-log p plot that has the smallest radius ofcurvaC
ture. Draw a horizontal line AB. Draw a line AP which is the bisector of angle BAC.
Project the straight line portion ofthe e-log p plot backwards to meet line AD at E.
Thepressure corresponding to point E is the preconsolidation pressure. In Fig. 17-6,
2 .
Pc = 1.6 ton/ft .

General Comments
The magnitude ofthe compression index, Cc, varies from soil to soil. Many correlations for
Cc have been proposed in the past for varioustypes of soils. A summary ofthese correlations
is given by Rendon-Herrero (1980). Following is a list of some ofthese correlations.
Cc = 0.007(LL - 7)
Cc = 0.009(LL - 10)
Cc = 1.1S(eo - 0.27)
Cc = 0.0046(LL - 9)
Cc = 0.208eo + 0.0083
Note: LL = liquid limit
eo = in situ void ratio
Remolded clay
Undisturbed clays
All clays
Brazilian clays
Chicago clays

18
Triaxial Tests in Clay
Introduction
In Chapters 15 and 16, some aspects of the shear strength for soil were discussed. The
triaxial compression test is a more sophisticated test procedure for determining the shear
strength of soil. In general, with triaxial equipment, three types of common tests can be
conducted, and they are listed below. Both the unconsolidated-undrained test and the
consolidated-undrained test will be described in this ch~lptt~r.
Unconsolidated-undrained (U-U)
Consolidated-drained (C-D)
Consolidated-undrained (C-U)
Cu = undrained cohesion
c = cohesion
 = drained angle offriction
A = pore water pressure parameter
cu( = 0)
c, 
c, <1>, A
Note: s =c + 0' tab (c =cohesion, 0' =effective normal stress).
For undrained condition, = 0; s = Cu [Eq. (16.2)]
Equipment
1. Triaxial cell
2. Strain-controlled compression machine
3. Specimen trimmer
4. Wire saw
5. Vacuum source
6. Oven 129

Drainage
-
Soil
specimen
Top
platen
Potous
slone
Rubber
Figure 18-1, Schematic diagram of triaxial cell.
7. Calipers
8. Evaporating dish
9. Rubber membrane
10. Membrane stretcher
Rubber
gasket
Lucile
cylinder
Rubber
gaskel
Chamber
fluid
Saturation
aud drainage
Triaxial Cell and Loading Arrangement .
Figure 18-1 shows the schematic diagram of a triaxial celt. It consists mainly ofa bottom
base plate, a Lucite cylinder and a top cover plate. A bottom platen is attached to the base
plate. A porous stone is placed over the bottom platen, over which the soil specimen is
placed. A porous stone and a platen are placed on top of the specimen. The specimen is
enclosed inside a thin rubber membrane. Inletand outlet tubes for specimen saturation and
drainage are provided through the base plate. Appropriate valves to these tubes are attached
to shut offthe openings when desired. There is an opening in the base plate through which

water (or glycerine) can be allowed to flow to fill the cylindrical chamber. A hydrostatic
chamber pressure, 03, can be applied to the specimen through the chamber fluid. Ah added
axial stress, D.o, applied to the top ofthe specimen can be provided using a piston.
During the test, the triaxial cell is placed on the platfonn ofa strain-controlled compres-
sion machine. The top ofthe piston ofthe triaxial chamber is attached to a proving ring. The
proving ring is attached to a crossbar that is fixed to two metal posts. The platfonn ofthe
compression machine can be raised (or lowered) at desired rates, thereby raising (or
lowering) the triaxial cell. During compression, the load on the specimen can be obtained
from the proving ring readings and the corresponding specimen defonnation from a dial
gauge [1 small div. = 0.001 in. (0.0254 mm)].
The connections to the soil specimen can be attached to a burette or a pore-water pressure
measuring device to measure, respectively, the volume change ofthe specimen or the excess
pore water pressure during the test.
Triaxial equipment is costly, depending on the accessories attached to it. For that reason,
general procedures for tests will be outlined here. For detailed location of various
components ofthe assembly, students will need the help oftheir instructor.
Triaxial Specimen
Triaxial specimens most commonly used are about 2.8 in. in diameter x 6.5 in. in length
(71.1 mm diameter x 165.1 mm length) or 1.4 in. in diameter x 3.5 in. in length (35.6 mm
diameter x 88.9 length). In any case, the length-to-diameter ratio (LID) should be between
2 and 3. For tests on undisturbed natural soil samples collected in shelby tubes, a specimen
trimmer may need to be used to prepare a specimen ofdesired dimensions. Depending on the
triaxial cell at hand, for classroom use, remolded specimens can be prepared with Harvard
miniature compaction equipment.
After the specimen is prepared, obtain its length (Lo) and diameter (~). The length
should be measured four times about 90 degrees apart. The average of these four values
should be equal to Lo. To obtain the diameter, take four measurements at the top, four at the
middle and four at the bottom ofthe specimen. The average ofthese twelve measurements
is Do.
Placement of Specimen in the Triaxial Cell
I. Boil the two porous stones to be used with the specimen.
2. De-air the lines connecting the base ofthe triaxial cell.
3. Attach the bottom platen to the base ofthe cell.
4. Place the bottom porous stone (moist) over the bottom platen..
5. Take a thin rubber membrane ofappropriate size to fit the specimen snugly. Take a
membrane stretcher, which is a brass tube with an inside diameter ofabout V. in. ("
6 mm) larger than the specimen diameter (Figure 18-2). The membrane stretcher can
be connected to a vacuum source. Fit the membrane to the inside ofthe membrane
stretcher and lap the ends of the membrane over the stretcher. Then apply the
vacuum. This will make the membrane fonn a smooth cover inside the stretcher.

Brass,
tube
Top
platen
,. ~.. .
..... __ Vacuum
~ source
Rubber
membrane'-.....j
.. : ...... ::
,,,,,:' ; .. ~.-
Bottom
platen
Figure 18-2. Membrane stretcher.
6. Slip the soil specimen to the inside ofthe stretcher with the membrane (Step 5). The
inside ofthe membrane may be moistened for ease in slipping the specimen in. Now
release the vacuum and unroll the membrane from the ends ofthe stretcher.
7. Place the specimen (Step 6) on the bottom porous stone (which is placed on the
bottom platen ofthe triaxial cell) and stretch the.bottom end ofthe membrane around
the porous stone and bottom platen. At this time, place the top porous stone (moist)
and the top platen on the specimen, and stretch the top ofthe membrane over it. For
air-tight seals, it is always a good idea to apply some silicone grease around the top
and bottom platens before the membrane is stretched over them.
8. Using some rubber bands, tightly fasten the membrane around the top and bottom
platens.
9. Connect the drainage line leading from the top platen to the base ofthe triaxial cell.
10. Place the Lucite cylinder and the top ofthe triaxial cell on the base plate to complete
the assembly.
Note:
1.
2.
In the triaxial cell, the specimen can be saturated by connecting the drainage
line leading to the bottom ofthe specimen to a saturation reservoir. During
this process, the drainage line leading from the top ofthe specimen is kept
open to the atmosphere. The saturation ofclay specimens takes a fairly long
time.
For the unconsolidated-undrained test, if the specimen saturation is not re-
quired, nonporous plates can be used instead ofporous stones at the top and
bottom ofthe specimen.

Unconsolidated-Undrained Test
Procedure
1. Place the triaxial cell (with the specimen inside it) on the platfonn of the
compression machine.
2. Make proper adjustments so that the piston ofthe triaxial cell just rests on the top
platen ofthe specimen
3. Fill the chamber ofthe triaxial cell with water. Apply a hydrostatic pressure, 03'. to
the specimen through the chamber fluid. Note: All drainage to and from the specimen
should be closed now so that drainage from the specimen does not occur.
4. Check for proper contact between the piston and the top platen onthe specimen. Zero
the dial gauge ofthe proving ring and the gauge used for measurement ofthe vertical
compression ofthe specimen. Set the compression machine for a strain rate ofabout
0.5% per minute, and tum the switch on.
5. Take initial proving ring dial readings for vertical compression intervals of0.01 in.
(0.254 n1m). This interval can be increase to 0.02 in. (0.508 mm) or more later when
the rate ofincrease ofload on the specimen decreases. The proving ring readings will
increase to a peak value and then may decrease or remain approximately constant.
Take about four to five readings after the peak point.
6. After completion ofthe test, reverse the compression machine, lower the triaxial cell,
and then tum offthe machine. Release the chamber pressure and drain the water in
the triaxial cell. Then remove the specimen and deternline its moisture content.
Calculation
The calculation procedure can be explained by referring to Tables 18-1 and 18-2, which
present the results of an unconsolidated-undrained triaxial test on a dark brown silty clay
specimen. Referring to Table 18-1
1. Calculate the final moisture content ofthe specimen, w, as (Line 3)
w (%) =moist mass of specimen, W; - d?, mass of specimen, W2 (100)
dry mass of speCImen, W
2
= Line I - Line 2 (100) (18.1)
Line 2
2. Calculate the initial area ofthe specimen as (Line 6)
A - rtn2 - rt(L. 5)2
"0-- 0 - - me
4 4
(18.2)
3. Now, refer to Table 18-2, calculate the vertical strain as (Column 2)

tlL Column 1
e =- =-------
Lo Line 4, Table 18-1
where AL = total deformation ofthe specimen at any time.
Table 18-1. Unconsolidated-Undrained Triaxial Test
Preliminary Data
(18.3)
Description of SOil _ _.bD.",'i1lUrk",b",l1""o""WI"",n,",,5,",i/ty;LkcJ.,,,~l...V____ Specimen No. _.b8,--_~__
Location ___________________________
Tested by Date ________
1. Moist mass of specimen (end oftest), WI 18S.68g
2. Dry mass of specimen, Wz /S/.80g
. W,-W
3. Moisture content (end oftest), w (%) = 1 2 X 100 22.3%
W;
4. Initial average length ofspecimen, Lo 3.S2 in.
5. Initial average diameter of specimen, Do 1.41 in.
6. Initial area, Ao = ~D 2 / 56 . 2
4 . tn.
7. Specific gravity ofsoil solids, Gs 2.73
8. Final degree ofsaturation 98.2%
9. Cell confining pressure, 03 ISIbfln.2
10. Proving ring calibration factor 0.37Ib/div.

0
0.01
0.02
0.03
0.04
0.05
0.06
0.10
0.14
0.18
0.22
0.26
0.30
0.35
0.40
0.45
0.50
Table 18-2. Unconsolidated-Undrained Triaxial Test
Axial Stress-Strain Calculation
0 0 0 1.560
0.0028 3.5 1.295 1.564
0.0057 .7.5 2.775 1.569
0.0085 // 4.07 1.573
0.0114 14 5.18 1.578
0.0142 18 6.66 1.582
0.0171 21 7.77 1.587
0.0284 31 11.47 1.606
0.0398 38 14.06 1.625
0.051 I 44 16.28 1.644
0.0625 48 17.76 1.664
0.0739 52 19.24 1.684
0.0852 53 19.61 1.705
0.0994 52 19.24 1.735
0.//36 50 18.5 1.760
0.1278 49 18.13 1.789
0.1420 49 18.13 1.818
0
0.828
1.769
2.587
3.28
4.210
4.896
7.142
8.652
9.903
10.673
11.425
//.501
//.109
10.5//
10.134
9.970

4. Calculate the piston load on the specimen (Column 4) as
P = (proving ring dial reading) x (calibration factor)
= (Column 3) x (Line 10, Table 18 -1)
5. Calculate the corrected area, A, ofthe specimen as (Column 5)
A =~ =Line 6, Table 18-1
. 1- E 1 - Column 2
6. Calculate the deviatory stress (or piston stress), AU, as (Column 6)
Acr =P =Column 4
A ColumnS
Graph
(18.4)
(18.5)
(18.6)
1. Draw a graph ofthe axial strain (%) vs. deviatory stress (AU). As an example, the
results of Table 18-2 are plotted in. Fig. 18-3. From this graph, obtain the value of
Au at failure (AU =AUf).
2. The minor principal stress (total) on the specimen at failure is 03 (i.e., the chamber
confining pressure). Calculate the major principal stress (total) at failure as
UI = 03 + AUf
12 _+,------------- _
l>.0/~ 11.6Ib/in.'
8
0 3 = lS1h/in.2
0, ~ 15 + 1I.6Ib/in.'
4 8 12 16
Axial strain, e (%)
Figure 18-3. Plot of l1a against axial strain for the test
reported in Table 18-2.

t<'
.EI
~15
~
~
~
il lO
.d
'"
5
00 10
at
20 30
Normal stress (lh/in.')
Figure 18-4. Total stress Mohr's circle at failure for test of Table 18-2
and Fig. 18-3.
3. Draw a Mohr's circle with °I and 03 as the major and minor principal stresses. The
radius of the Mohr's' circle is equal to cu' The results of the test reported in Table
18-2 and Fig. 18-3 are plotted in Fig.18-4.
.General Comments
1. For saturated clayey soils, the unconfined compression test (Chapter 16) is a special
case ofthe U-Utest discussed previously. For the unconfined compression test, 03
= O. However, the quality ofresults obtained from U-Utests is superior.
2. Figure 18-5 shows the nature ofthe Mohr's envelope obtained from U-Utests with
varying degrees ofsaturation. For saturatedspecimens, the value ofAOp and thus cU
'
is constant irrespective of the chamber confining pressure, 03' So the Mohr's
envelope is a horizontal line ( = 0). For soil specimens with degrees ofsaturation
less than 100%, the Mohr's envelope is curved and falls above the = 0 line.
Consolidated-Undrained Test
Procedure
1. Place the triaxial cell with the saturated specimen on the compression machine
platform and make adjustments so that the piston ofthe cell makes contact with the
top platen ofthe specinien.
2. Fill the chamber ofthe triaxial cell with water, and apply the hydrostatic pressure, 03'
to the specimen through the fluid.

Total stress
failure envelope
0 3
8 = degree ofsaturation
81 <82 <83
81
82
0 1 Nonna! stress
Figure 18-5. Nature of variation of total stress failure envelopes with the degree
of saturation of soil specimen (for undrained test).
3. The application ofthe chamber pressure, 03' will cause an increase in the pore water
pressure in the specimen. For consolidation connect the drainage lines from the
specimen to a calibrated burette and leave the lines open. When the water level in the
burette becomes constant, it will indicate that the consolidation is complete. For a
saturated specimen, the volume change due to consolidation is equal to the volume
ofwater drained from the burette. Record the volume ofthe drainage (AV).
4. Now connect the drainage lines to the pore-pressure measuring device.
5. Check the contact between the piston and the top platen. Zero the proving ring dial
gauge and the dial gauge, which measures the axial deformation ofthe specimen.
6. Set the compression machine for a strain rate ofabout 0.5% per minute, and turn the
switch on. When the axial load on the specimen is increased, the pore water pressure
in the specimen will also increase. Record the proving ring dial gauge reading and
the corresponding excess pore water pressure (Au) in the specimen for every 0.01 in.
(0.254 mm) or less ofaxial deformation. The proving ring dial gauge reading will in-
crease to a maximum and then decrease or remain approximately constant. Take at
least four to five readings after the proving ring dial gauge reaches the maximum
value.
7. At the completion ofthe test, reverse the compression machine and lower the triaxial
cell. Shut offthe machine. Release the chamber pres·sure, 03' and drain the water out
ofthe triaxial cell.
8. Remove the tested specimen from the cell and determine its moisture content.
9. .Repeat the test on one or two more similar specimens. Each specimen should be
tested at a different value of 03.

I
I
Calculation and ~raph
The procedure for making the required calculations and plotting graphs can be explained by
referring to Tables IS~3 and IS--4 and Figs. IS-6 and IS-7. First, referring to Table IS-3,
1. Calculate the initial area ofthe specimen as (Line 5)
1t21t· 2
Ao =-Do =- (Lllle 4)
4 4
2. Calculate the initial volume ofthe specimen as (Line 6)
Vo =AoLo =(Line 5) x (Line 3)
3. Calculate the volume ofthe specimen after consolidation as (Line 9)
Ve =Vo - L'1V =(Line 6) - (Line S)
where Ve = final volume ofthe specimen.
4. Calculate the length, Le (Line 10), and cross-sectional area, Ae (Line 11)
ofthe specimen after consolidation as
( )
1/3 1/3
Le = Lo Ve = (Line 3)(L~ne 9)
Vo Lllle 6
and
( )
2/3 213
Ae =Ao Ve =(Line 5)(L~e 9)
Va Lllle 6
Now refer to Table IS--4.
5. Calculate the axial strain as (Column 2)
M Column 1
E=-
Le Line 10, TablelS~3
where L'1L = axial deformation
6. Calculate the piston load, P (Column 4)
(1S.S)
(IS.9)
(IS.10)
(IS.11)
(IS.12)
(1S.13)
P = (proving ring dial reading, i.e. Column 3) x (calibration factor) (IS.14)

Table 18-3. Consolidated-Undrained Triaxial Test
Preliminary Data
Description of soil_-,-R""e!.!.m",o",{cJ.""e~d,-<g,,,"ru,,,n,,,d,,,-1~,,,e~___ Specimen No. _-,,2~______
Location _____________________________
Tested by _________________
Date_--------
1. Moisfunit weight ofspecimen (beginning
oftest)
2. Moisture content (beginning oftest)
3. Initial length ofspecimen,Lo
4. Initial diameter ofspecimen, Do
5. Initial area ofthe specimen, Ao = E..D :
4
6. Initial volume ofthe specimen, Vo = Ao Lo
7. Cell consolidation pressure, 03
8. Net drainage from the specimen during
consolidation, !:J.V
9. Volume ofspecimen after consolidation,
Vo-!:J.V=Vc
10. Length ofthe specimen after consolidation,
L=L (Vc
)"3
c 0 V
o
11. Area ofthe specimen after consolidation,
( J
2/3
A =A v;,
c 0 V.
o
35.35%
7.62 em
3.57em
IO.Oerrt
76.2 err?
392kN/rrt
11.6 err?
76.2 - 11.6 = 64.6 err?
7.62 ( 64.6) 1/3= 7.212 em
76.2
10(' 64.6) 2/3 = 8.96 em3
76.2

Table 18-4. Consolidated-Undrained Triaxial Test
Proving ring calibration factor 1.0713 Nldiv. (the results have been edited)
, "" "
't('~"Wl~i'!'" " ,'I ' ,"
r.
,
I'
,',,', ,",
" " ','" "., "', ,i ,""', ',' "
"" "~,1,"'tlk " p , '", ",', ,,'•• ,
, >{,.~;.X' < "Ii ,..t&?".•~,~'.J ."
,
A~til·k, '
....
.'." .'", ·'/~i£2;« :.",,," ..... . , 11.'0-'"-
";"',(~[-.'
' ."'. '. ,griJ5
} !~"~'''J '"
I {~t' .. ,It, '.,.''.,','.• .,
•. ~;tt ii'(~J. ',(~j> 1'~7) {sr
. '.,' '.. ";//'" .,.' .." .', . ; ............'
0 0 0 0 8.96 0 0 0
0.015 0.0021 15 16.07 8.98 17.90 2.94 0./64
0.038 0.0053 109 116.77 9.01 129.60 49.50 0.378
0.061 0.0085 135 144.63 9.04 159.99 74.56 0.466
0.076 0.0105 147 157.48 9.06 173.82 89.27 0.514
0.114 0.0158 172 184.26 9.11 202.26 111.83 0.553
0.152 0.0211 192 205.69 9.15 224.80 135.38 0.602
0.183 0.0254 205 219.62 9./9 238.98 148.13 0.620
0.229 0.0318 225 241.04 9.25 260.58 160.88 0.618
0.274 0.0380 236 252.83 9.31 271.57 167.75 0.618
0.315 0.0437 247 264.61 9.37 282.40 175.60 0.622
0.427 0.0592 265 .283.89 9.52 298.20 176.58 0.592
0.457 0.0634 270 289.25 9.57 302.25 176.58 0.584
0.503 0.0697 278 297.82 9.63 309.26 ,176.58 0.570
0.549 0.0761 284 304.25 9.70. 313.66 176.58 0.563
0.594 0.0824 287 307.46 9.76 315.02 176.58 0.561
0.653 0.905 288 308.53 9.85 313.23 176.57 0.564
0.726 0.1007 286 306.39 9.96· 307.62 160.88 0.523
0.853 0.183 275 294.61 10./6 289.97 163.82 0.565

7. Calculate the corrected area, A, as (Column 5)
A = ~= Line I I, Table 18-3
I -€ I - Column 2
8. Determine the deviatory stress, .6.0' (Column 6)
.6.0' =P =Column 4
A· Column5
9. Determine the pore water pressure parameter, A (Column 8)
10. Plot graphs for
(a) ..6.O' vs. E(%)
(b) .6.u vs. E (%)
(c) A vs. E (%)
A = .6.u = Column 7
.6.0' Column 6
(18.1 5)
(18.16)
(18.17)
As an example, the results ofthe calculation shown in Table 18-4 are plotted in Fig.
18-6.
0.7 280 3 5 0 r - - - - - - - - - - - - - - ,
!J.o,= 316 leN/m'
................",..:!:- -- ---
0.6 240 300
0
0.4 1i'160 1i'200
~
~ ~
~ t:>
<l <l
0.2 80 100
o o O~-~-~--~--~L-~~~
o 2 4 6 8 10 12
Axial strain. € (%)
Figure 18-6. Plot of.6.0, i::J.u and A against axial strain for the
consolidated drained test reported in Table 18-4.

6oor-------.-------,--------.------~
t<'
J§ 400
g
i[;;
.1l 200
en
°0~--~~2~OO~----~4~0~0----L-~60~0~----~800
Effective nonnal stress, 0' (kN/m2)
Figure 18-7. Effective stress Mohr's circle for remolded
grundite reported in Table 18-4.
11. From the 110 vs. E (%) graph, determine the maximum Value of 110 = 110f and the
corresponding values ofl1u =l1uf and A =At .
In Fig. 18--6, 110f =316 kN/m2
at E =8.2% and, at the same strain level, l1uf= 177
kN/m2 and A = 0.56. .
12. Calculate the effective major and minor principal stresses at failure.
Effective minor principal stress at failure
Effective major principal stress at failure
For the test on the remolded grundite reported in Tables 18-3 and 18-4
0;=392- 177=215kN/m2
oj"'; (392 + 316) - 177 =,531 kN/m2
(18.18)
(18.19)
13. Collect 0; and 0; for all the specimens tested and plot Mohr's circles. Plot a failure
envelope that touches the Mohr's circles. The equation for the failure envelope can
be given by

s = c + 0' tan 
Detennine the values of c and from the failure envelopes.
Figure 18-7 shows the Mohr's circles for two tests on the remolded grundite reported
in Table 18-4; (Note: The result for the Mohr's circle No.2 is not given in Table
18-4.) For the failure envelope, c = 0 and = 25°. So
S = 0' tan 25°
General Comments
1. For nonnally consolidatedsoils, c= 0; however, for overconsolidated soils, c> O.
2. Atypical range ofvalues of A at failure for clayey soils is given below:
Clays with high sensitivity 0.75 to 1.5
Nonnally consolidated clays 0.5 to 1.0
Overconsolidated clays -0.5 to 0
0.5 to 0.75

145
REFERENCES
1. American Society for Testing and Materials, 1995 Annual Book 0/ASTMStandards
-Vol. 04.08, Philadelphia, PA, 1995.
2. Atterberg, A., "Uber die Physikalishce Budenuntersuchung, and iiber die Plastizitat
der Tone," Internationale Mitteilungenfor Bodenkunde, Vol. 1, 1911.
3, Casagrande, A., "Determination ofPreconsolidation Load and Its Practical Signifi-
cance," Proceedings, First International Conference on Soil Mechanics and Founda-
tion Engineering, Vo!.3, 1963, pp. 60-64.
4. Casagrande, A. and Fadum, R.E., ''Notes on Soil Testing for Engineering Purposes,"
Engineering Publication No.8, Harvard University Graduate School, 1940.
5. Das, B.M., Principles o/Geotechnical Engineering, 3rd Edition, PWS Publishing
Company, Boston, 1994.
6. Proctor, R.R., "Design and Constsruction ofRolled Earth Dams," EngineeringNews-
Reconrd, August31, September 7, September 21, and September 28,1933.
7. Rendon-Herrero, 0., "University Compression Index Equation," Journal o/the Geo-
technical Engineering Division, American Society ofCivil Engineers, Vol. 106, No.
OTtl, 1980, pp.1179-1200.
8. Taylor, D.W., "Research on the Consolidation ofClays," Serial No. 82, Department
of Civil and Sanitary Engineering, Massachusetts Institute ofTechnology, 1942.
9. Waterways Experiment Station, "Simplification ofthe"Liquid Limit Test Procedure,"
Technical Memorandum No. 3-286, 1949.

ApPENDIX A
Weight-Volume
Relationships
147

149
For the weight-volume relationships given below, the following notions were used.
e = void ratio
Gs = specific gravity of soil solids
n = porosity
S = degree of saturation
V = total volume of soil
Vs = volume of solids in a soil mass
Vv = volume ofvoids in a soil mass
Vw = volume ofwater in a soil mass
W = total weight ofa soil mass
Ws = dry weight ofa soil mass
Ww = weight ofwater in a soil mass
w = moisture content
y = moist unit weight
yd = dry unit weight
Ysat = saturated unit weight
Yw = unit weight ofwater
e = v" =~ = Gs Yw -I
V, I-n Yd
n = v" =_e_=l_~
V l+e G,Yw
S = Vw = wG,
V, e
Ww Se
w=-=-
W, Gs
W
y=-
v
GsYw(1+w)
Y= l+e
Y= Gs Yw(l-n)(l+w)
Volume Relationships
Weight Relationships

150
W
"fa =_s
V
Gs"f w
"fa = l+e
"fa = (l-n}Gs"fw
(Gs +e)y"
"fsat = l+e
(Gs + wGJ"f"
"fsat l+wGs
Gs(l + w)y "
l+wGs
"fsat = [Gs - n(Gs -l)]"f"

ApPENDIX B
Data Sheets for
Laboratory' Experiments
151

Determination of Water Content
Description ofsoil ________________ Sample No.____
Location ____--'-______________- - - - - - _ - , -
Tested by ______________ Date _________
Can No.
Mass ofcan, WI (g)
Mass ofcan + wet soil, W2 (g)
Mass of can + dry soil, W3 (g)
Mass ofmoisture, W2 - W3 (g)
Mass ofdry soil, W3 - WI (g)
W2 - W3
Moisture content, W (%) = x 100
W3 -WI
Average moisture content, w____ %
153

!
I
Specific Gravity of Soil Solids
Description ofsoil,~_~____________ Specimen No.~__
.Volume of flask at 20'C __ ml temperature of test __~_'C A,_=-:-:-::-=:-
(Table 3-2)
Location,______________'--_~_________
Tested by ______________
Volumetric flask No.
Mass offlask + water filled to mark, WI (g)
Mass offlask + soil +water filled to mark,
W2 (g)
Mass of dry soil, Ws (g)
Mass ofequal volume ofwater as the soil
solids, Ww (g) = (WI + Ws) - Wz
Date.'--~_~____
Average Gs _ _ _- - - - - - - -
155

Sieve Analysis
Description of soil ________________ Sample No. ____
Mass of oven dry sample, W g
Location ___________________________
Tested by _________________ Date._________
boo 1.10
Pan
9--(') 0
____ =W,
W - W,
Mass loss during sieve analysis =. x 100 =____ % (OK iflessthan 2%)
W
157

Shrinkage Limit Test
Description of soil __________~------ Sample No. --'..'__
Location __________________________
Tested by ________________
Mass ofcoated shrinkage limit dish, WI (g)
Mass of dish + wet soil, W2 (g)
Mass ofdish + dry soil, W3 (g)
Mass ofmercury to fill the dish, W4 (g)
Mass ofmercury displaced by soil pat, Ws (g)
~w;(%)= (~-W,) xlOO
(13.6)(W, - IT';)
SL=w- (~-W,) xlOO
, (13.6)(W, - IT';)
Date ________
165

Constant Head Permeability Test
Description ofsoil _______________ Sample No. _____
Location ___________________________
Length of specimen, L _______c,m Diameter of specimen, D _____,cm
Tested by ____________ Date,_____- - - - - -
Volume of specimen, V= 1t D2L(cm2)
4
Specific gravity ofsoil solids, G,
Mass ofspecimen tube with fittings, WI (g)
Mass oftube with fittings and specimen, W2 (g)
Dry density of specimen, Pd =W
2- If; (g / cm3
)
V
V'd . f ' G,pw 1
OJ ratIO 0 specImen, e =,---
Pd
(Note: Pw ~ 1 glcm3
)
167

Constant Head Permeability Test
Test No. 1
Average flow, Q (cm3
)
.
Time of collection, t (s)
Temperature ofwater, T (Oe)
Head difference, h (cm)
Diameter of specimen, D (cm)
Length ofspecimen, L (cm)
Area of specimen, A =1t D2 (cm2
)
4
k=QL (cm/s)
Aht
Average k=
k20"C = flr"c = = emfs
kr"C--
fl2."c
2 3
.
emls
169

I
I
.
Falling Head Permeability Test
Description ofsoil ______________ Sample No. ______
Location _______________________- - - -
Length of specimen, L _______,cm Diameter of specimen, 0 ___-_cm
Tested by _~_______'__~______ Date ________
Volume of specimen, V = n D'L (cm')
4
Specific gravity ofsoil solids, Gs
Mass ofspecimen tube with fittings; WI (g)
Mass oftube with fittings and specimen, Wz (g)
Dry density of specimen, Pd = W, - W; (g / em3
)
V
Void ratio of specimen, e = G,p w -1
Pd
(JVote: Pw = 1 glcm3
)
171

Falling Head Permeability Test
Test No. 1
Diameter of specimen, D (em)
Length of specimen, L (cm)
Area of specimen, A (cm2
)
Beginning head difference, hI (em)
Ending head difference, h2 (cm)
Test duration, t (s)
Volume ofwater flow through the specimen, Vw (cm3
)
k 2.303Vw L I hI ( / 2)
= og- em s
(hl -h2 )tA h,
Average k = cm/s
.
k,o·c = IlT"C - = em/s
kT"C--
- 112o•c
2 3
173

•
Modified Proctor Compaction Test
Zero-Air-Void Unit Weight
Description of soil Sample No. ___
Location _________________________
Tested by Date ___--,____
aEq.(12.1)
181

Modified Proctor Compaction Test
Determination of Dry Unit Weight
Description of soil Sample No. __-'-__
Location __________________________
Volume Weight of Number of Number
of mold ____ ft3 hammer ___ Ib blows/ layer ___ of layers ___
Tested by _______________
1. Weight ofmold, WI (lb)
2. Weight ofmold +moist soil, W2
(lb)
3. Weight ofmoist soil, W2- WI (lb)
4. Moist unit weight,
Y= W, -If; (lb/ft3)
1/30
5. Moisture can number
6. Mass ofmoisture can, W3 (g)
7. Mass ofcan +moist soil, W4 (g)
8. Mass ofcan + dry soil, W5 (g)
9. Moisture content,
w (%) = ~ -Ws xlOO
Ws-w,
10. Dry unit weight ofcompaction
Yd (lb/ft3) :(%)
+--
100
Date ________
179

I
1
I
I
f
f
I
I
Void Shear Calculation
Description ofsoil _______________ Sample No. ___
Location _______________-,--__---,-_______
Tested by ___________- - - - Date ___~----
1. Specimen length, L (in.)
2. Specimen width, B (in.)
3. Specimen height, H (in.)
4. Mass ofporcelain dish + dry sand (before use), WI (g)
5. Mass ofporcelain dish + dry sand (after use), W2 (g)
1--------------------------1-----'1 Ip'<C' ,
6. Dry unit weight ofspecimen, 'Yd (lb / ft3) = W; - ~ g) x 3.808
LBH(m. )
7. Specific gravity ofsoil solids, Gs
8. Void ratio, e =G,'Yw -1
'Yd
Note: yw = 62.4 Ib/ft3; Yd is in IblW
i
bv!
'''',
<f ''(;6<"(
185
/)

- ,)
, I
Description of soil_~_.,.-________--:-_ Sample No. _____
Location _____~_____.,_...--------------
Normal load, N __'"'t5""6_',,,,~,_·._)__---,.Ib Void ratio, e __________
Tested by~_____~________ Date _________
() t?
() '2 f
i:~ .•
r)- i
10 (
I, )~(
)
,
(';
,
I~, 0
a, ,',
p')
, .r
* Plus (+) sign means expansion • <7 J
()
t " "
,)
11 ~
r ('l ,~~
I Co "
!f-,
t '1 J 187

,
I
()
. (,I
~irect Shear Test on Sand
Description of soil ______________ Sample No. __--'-__
Location __________-,--_______________
Normal load, N __....cl---,b:....,,_f_'_t.C,--,"'--,'__ lb Void ratio, e ___________
Tested by _______________ Date _________
o
D' r ·r
I r, 0
"·0 ">,()
• Plus (+) sign means expansion ~'O
Cl''
~. z. ' r
•. (,
. '6 ,'l
?
189

Description ofsoil _____________~ Sample No. _____
Location ____________~_____________
Normal load, N __-,I_"c-I,_1_._~__ Ib Void ratio, e ___________
Tested by ____________~__ Date _________
II .C>
'2.' 0
~ ·r
• Plus (+) sign means expansion
191

Consolidation Test
Time VS. Vertical Dial Reading
Description ofsoil _______..,-_________________
Location ___- - - - - - - - - - - - - - - - - - - - - - - _
Tested by ______,--________ Date __________
Pressure on specimen __ Ib/ft2 Pressure on specimen __ Ib/ft2
195

Consolidation Test
Time VS. Vertical Dial Reading·
Description ofsoil _________________________
Location ___________________________
Tested by _______________ Date __________
Pressure on specimen __ Ib/tt' Pressure on specimen __ Ib/fe
197

Consolidation Test
Time vs. Vertical Dial Reading
Description ofsoil ______________________-'--__
Location ___________________________
Tested by _______________ Date __________
Pressure on specimen __ Ib/ft2 Pressure on specimen __ Ib/tt"
199

Consolidation Test
Void Ratio·Pressure and Coefficient of Consolidation Calculation
Description of soil ___________ Location ____________
Specimen diameter __ in. Initial specimen height, Ht(i) __ in. Height of solids, Hs _ cm = __ in.
Moislure Content: Beginning of lesl ___ % End of lest ____ %
Weight of dry soil specimen _____ g G
s
_ _ __
Tesled by _____________ Dale _______________
201

Unconsolidated-Undrained Triaxial Test
Preliminary Data
Description of soil _______________ Specimen No. ______
Location _____~_______________________
Tested by ________________ Date _________
I. Moist mass of specimen (end oftest), WI
2. Dry mass of specimen, W2
W,-W
3. Moisture content (end oftest), w (%) = I 2 X 100
~
4. Initial average length ofspecimen, Lo
5. Initial average diameter of specimen, Do
6. Initial area, Ao = ~D 2
4
7. Specific gravity of soil solids, Gs
8. Final degree of saturation
9. Cell confining pressure, 03
10. Proving ring calibration factor
203

Unconsolidated-Undrained Triaxial Test
205

Consolidated-Undrained Triaxial Test
Preliminary Data
Description of soil _______________ Specimen No. ______
Location _____________________________
Tested by -'-_______~_________
1. Moist unit weight ofspecimen (beginning
oftest)
3. Initial length of specimen, Lo
4. Initial diameter of specimen, Do
5. Initialarea ofthe specimen, A =!!..D 2
o 4 0
6. Initial volume ofthe specimen, Vo = Ao Lo
consolidation, I:lV
9. Volume of specimen after consolidation,
Vo - I:lV= Vc
L=L (Vc )1I3
c ' 0 V
o
11, Area ofthe specimen after consolidation,
Date ________
207

Proving ring calibration factor _________
209

Preliminary Data
Description of soil ______________ Specimen No. ____~-_
Location _____________________-,-----'-______
Tested by _________________
1. Moist unit weight ofspecimen (beginning
oftes!)
3. Initial length ofspecimen, Lo
4. Initial diameter ofspecimen, Do
5. Initial area ofthe specimen, A = ~D2
o 4 0
consolidation, I1V
9. Volume of specimen after consolidation,
Vo- I1V= Vc
L=L (Vc)"3
c 0 V
o
11. Area ofthe specimen after consolidation,
( J
213
A =A Vc
c 0 V.
o
Date _______
211

Proving ring calibration factor _________
213

ApPENDIX C .
Data Sheets for
. Preparation of
Laboratory Reports
215

',,,
~{'.h. .
N
OW in its sixth edition, Soil Mechanics Laboratory Manual is designed for the junior-
. level soil mechanics/geotechnical engineering laboratory course in civil engineering
programs. It includes eighteen laboratory procedures that cover the essential proper-
ties of soils and their behavior under stress and strain, as well as explanations, procedures,
sample calculations, and completed and blank data sheets. Written by Braja M. Das, respected
author ofmarket-leading texts in geotechnical and foundation engineering, this unique man-
ual provides a detailed discussion ofthe AASHTO Classification System and the Unified Soil
Classification System updated to conform to recent ASTM specifications.
To improve ease and accessibility of use, this new edition includes not only the stand-alone
version of the Soil Mechanics Laboratory Test software but also ready-made Microsoft
Excel® templates designed to perform the same calculations. With the convenience of point
and click data entry, these interactive programs can be used to collect, organize, and evaluate
data for each of the book's eighteen labs. The resulting tables can be printed with their cor-
responding graphs, creating easily generated reports that display and analyze data obtained
from the manual's laboratory tests.

Das b. m._,soil_mechanics_laboratory_manual,_6th_ed,_2002

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