This presentation includes basic definitions related to soil mechanics and Weight- Volume and Functional relationships between basic properties of soil, test carries out to find index properties of soil, Relative Density

1. Arbaz Mubarak Kazi,
B.E, M.E (Civil Engineering)
Email: arbaazkazi91@gmail.com
https://gtearchives.wordpress.com
www.linkedin.com/in/arbaz-kazi-20747570
SOIL - BASIC
DEFINITIONS &
RELATIONSHIPS
“Everyday is an
Adventure
When you are
Civil Engineer”

2. BASIC DEFINITIONS AND RELATIONSHIPS
Soil has two principle components: solid
particles and voids. Voids are the empty
spaces in between the solid particles that may
be filled with air or liquid or both. These
components make solid a complex matter and
difficult to study about. Therefore, with a
view to simplify the study, these particles are
segregated and shown in different layers (like
a block diagram). The diagram which shows
solid, water and air of soil separately is
known as 3-phase diagram (figure shown)
Three Phase Diagram:

3. Here,
W = Total Weight = Weight of solid particles + Weight of water
(Weight of air can be neglected because of its low density)
V = Total Volume = Volume of solid particles + Volume of water +
Volume of air
Ws = Weight of solid particles
Wa = Weight of air
Vs = Volume of solid particles
Vw = Volume of water
Vv = Volume of voids = Total volume (V) - Volume of solid
particles (Vs)

4. TWO PHASE DIAGRAM FOR
FULLY SAURATED SOIL
• In this case two phases, solid, water is
present.
• Air is absent. Voids are filled with
water only.

5. • Moisture Content: It is defined as the ratio of mass of water to mass of
solids. It is denoted by (w) and expressed in percentage.
𝑤 = 𝑀𝑤/𝑀𝑠 x 100
• Void ratio: It is defined as the ratio of the volume of voids to the volume
of solids. It is denoted by (e).
For coarse grained soil, void ratio is larger and for fine grained soil it is
vice-versa
𝑒 = 𝑉𝑣/𝑉𝑠
• Porosity: It is defined as the ratio of the volume of voids to the total
volume. It is denoted by (n).
n = Vv/V
FUNDAMENTAL DEFINITION:

6. Relationship 1: Between Void ratio and Porosity
We Know, V = Vs + Vv
𝑛 =
𝑉
𝑣
𝑉
=
𝑉
𝑣
𝑉
𝑠 + 𝑉
𝑣
=
𝑉
𝑣/𝑉
𝑠
𝑉
𝑠
𝑉
𝑠
+
𝑉
𝑣
𝑉
𝑠
=
𝑒
1 + 𝑒
𝑒 =
𝑉
𝑣
𝑉
𝑠
=
𝑉
𝑣
𝑉 − 𝑉
𝑣
=
𝑉
𝑣/𝑉
𝑉
𝑉
−
𝑉
𝑣
𝑉
=
𝑛
1 − 𝑛

7. • Degree of saturation: It is the ratio of the volume of water to the volume
of voids and is generally expressed as a percentage and denoted by (S).
S= 𝑉𝑤/𝑉𝑣
In case of fully saturated soil, voids are completely filled with water.
There is no air. Vw = Vv, Hence S = 1.
In case of fully dry soil, voids are completely filled with air. There is no
water i.e. Vw = 0, Hence S = 0.
• Air Content: It is defined as volume of air to volume of voids. It is
denoted by (ac)
ac= 𝑉𝑎/𝑉𝑣

8. • Percentage air content: It is defined as volume of air to total volume. It
is denoted by (na). It is expressed as percentage.
Relationship 2: Between Percentage Air content, Air content
& Porosity
na= 𝑉𝑎/𝑉= 𝑉𝑎/𝑉𝑣 * 𝑉𝑣/𝑉= n*ac
• Density: It is the ratio of the total mass to the total volume of the soil. It
is denoted by (ρ) and is also referred as bulk density (ρb) or mass density.
ρ or ρb = M/V

9. • Unit weight: It is the ratio of the total weight to the total volume of the
soil. It is denoted by (ϒ) and is also referred as bulk unit weight(ϒb) or
weight density.
ϒ or ϒb = W/V
• Dry Density: The dry density is defined as the ratio of the mass of soil
solids to the total volume. It is denoted by (ρd).
ρd = MS/V
• Dry Unit weight: The dry unit weight is defined as the ratio of the
weight of soil solids to the total volume. It is denoted by (ϒd).
ϒd = WS/V

10. • Density of Solids: The density of solids is defined as the ratio of the
mass of soil solids to the total volume of soil solids. It is denoted by (ρs).
ρs = MS/VS
• Unit weight of Solids: The dry unit weight is defined as the ratio of the
weight of soil solids to the total volume of soil solids. It is denoted by
(ϒS).
ϒS = WS/VS
• Saturated Density: The saturated density is defined as the ratio of the
saturated mass of soil to the total volume. It is denoted by (ρsat).
ρsat = Msat/V

11. • Saturated Unit weight: The saturated unit weight is defined as the ratio
of the saturated weight of soil to the total volume. It is denoted by (ϒsat).
ϒsat = Wsat/V
• Submerged Unit weight: The submerged unit weight is the
effective mass per unit volume when the soil is submerged below
standing water or below the ground water table. It is denoted by
(ϒ’)
𝛾′
=
(𝛾𝑠𝑎𝑡 − 𝛾𝑤)
𝑉

12. Explanation of
Submerged
Unit Weight

13. • Specific Gravity: It is defined as the ratio of the weight of a given
volume of soil solids to the weight of an equal volume of distilled
water.
G = ϒS/ϒw or ρs/ρw
Typical values of specific gravity for different soils are given below:
Type of Soil Sp. Gravity Type of Soil Sp. Gravity
GRAVEL 2.65 - 2.68 SILTS 2.66 – 2.70
SAND 2.65 - 2.68 INORGANIC CLAY 2.68 – 2.80
SILTY SAND 2.66 – 2.70 ORGANIC SOILS below 2.0

14. • Mass Specific Gravity: The specific gravity of a mass of soil (including air, water and
solids) is termed as bulk or mass specific gravity Gm. It is expressed as
𝐺𝑚 =
𝛾
𝛾𝑤
𝑜𝑟
𝜌
𝜌𝑤

15. Relationship 3: Between 𝒏𝒂,𝒆 & 𝐒
We Know,
𝑉
𝑣 − 𝑉𝑤
=
𝑉
Also, 𝑆 = /
𝑉
𝑤
𝑉𝑣
Hence, 𝑆∗ 𝑉
𝑣 = 𝑉𝑤
𝑛𝑎=
𝑉
𝑣 − 𝑆 ∗ 𝑉
𝑣
𝑉
𝑎
𝑉
𝑣*(1 − 𝑆)
𝑛 =
𝑉
𝑎
𝑛 = 𝑛∗(1 − 𝑆)
Also, 𝑛 = e / 1 + e
Hence,
𝑎
𝑒∗ (1 − 𝑆)
𝑛 =
1 + 𝑒
𝑛𝑎 = ൗ
𝑉
𝑎
𝑉
𝑤

16. Relationship 4: Between e, G, w and S
Take Vs = 1, But e = Vv/Vs and Vv = e, therefore V = 1+e

17. 𝑤 =
𝑊
𝑤
𝑊
𝑠
=
𝛾𝑊 ∗ 𝑉
𝑤
𝛾𝑠 ∗ 𝑉
𝑠
Also, S = VW/VV and G = ϒS/ϒW
𝐻𝑒𝑛𝑐𝑒, 𝑤 =
𝑊
𝑤
𝑊
𝑠
=
𝛾𝑊 ∗ 𝑉
𝑤
𝛾𝑠 ∗ 𝑉
𝑠
=
𝛾𝑊 ∗ 𝑉
𝑣 ∗ 𝑆
𝐺 ∗ 𝛾𝑤 ∗ 𝑉
𝑠
………………. (1)
But Vv/Vs = e, so equation (1) becomes
𝑤. 𝐺 = S. 𝑒

18. We know that,
ϒ = =
𝑊 𝑊𝑠+ 𝑊𝑤
𝑉 𝑉
𝑉
ϒ =
ϒ𝑠*𝑉𝑠+ϒ𝑤*𝑉𝑤
…… (1) (ϒ𝑠 = Ws/Vs and ϒ𝑤=Ww/Vw)
From Fig. Vs = 1 and Vv = e
ϒ = 𝐺*ϒ𝑤*1+ϒ𝑤*𝑆*𝑒
𝑉
…….. (G = ϒs/ϒw) and (Vw = S*Vv)
1+𝑒
ϒ =
𝐺+𝑆*e *ϒ𝑤
……………….(2)
Relationship 5: Between ϒ, G, e and S

19. If soil is fully dry eq. (2) becomes,
𝐺.ϒ𝑤
ϒsat =
ϒd =
1 + 𝑒
If soil is fully saturated eq. (2) becomes,
𝐺 + 𝑒 *ϒ𝑤
1 + 𝑒
Relationship 6: Between 𝒂𝒄 andS
𝑐
𝑎 = /
𝑉
𝑎
𝑉
𝑣
1 − 𝑆
= 𝑉
𝑣
= ൗ
𝑉
𝑣 − 𝑉
𝑤
𝑉
𝑣

20. We know that, ϒ =
𝑊
𝑉
ϒ =
𝑊𝑠+ 𝑊𝑤
𝑉
𝑉
ϒ =
𝑊𝑠 + 𝑤*𝑊𝑠
……………. (w = Mw/Ms)
ϒ =
𝑊𝑠*(1 + 𝑤)
𝑉
ϒ = ϒ𝑑* 1 + 𝑤 ………….. (Ws/V = ϒd)
ϒ
ϒd =
(1 + 𝑤)
Relationship 7: Between ϒd, ϒand w

21. Relationship 8: Between ϒd, G, w and 𝒏𝒂
𝑉=𝑉
𝑎+ 𝑉𝑤+ 𝑉
𝑠
𝑉=𝑉
𝑎+
𝛾𝑤
+
𝑊
𝑤 𝑊𝑠
𝛾
𝑠
1 =
𝑉
𝑎
𝑉
+
𝑊
𝑤
𝛾𝑤 ∗ 𝑉
+
𝑊
𝑠
𝛾𝑠 ∗ 𝑉
1 =
𝑉
𝑎
𝑉
+
𝑊
𝑠 ∗ 𝑤
𝛾𝑤 ∗ 𝑉
+
𝑊
𝑠
𝛾𝑠 ∗ 𝑉
1 =
𝑉
𝑎
𝑉
+
𝛾𝑑 ∗ 𝑤
𝛾𝑤
+
𝛾𝑑
𝛾𝑠
1 − 𝑛𝑎 =
𝛾𝑑
𝛾𝑤
∗ (
1 + 𝑤
𝐺
)
𝛾𝑑 = 1 − 𝑛𝑎 ∗ 𝛾𝑤 ∗ 𝐺/(1 + 𝑤𝐺)

22. d
We know that, ϒ =
𝐺∗𝛾𝑤
(1+𝑒)
…… from Relationship 7
d
ϒ =
𝐺 ∗𝛾𝑤
1 − 𝑛
(1 + 𝑛 )
ϒd =
𝐺 ∗𝛾𝑤
(
1 − 𝑛 + 𝑛
1 − 𝑛
)
ϒd = 𝐺 ∗𝛾𝑤*(1 - n)
Relationship 9: Between ϒd, G and n

23. ϒsat =
We know that, from Relationship 5
1 + 𝑒
𝐺 ∗ ϒ𝑤 𝑒∗ϒ𝑤
ϒsat =
(1 + 𝑒)
+
(1 + 𝑒)
∗(1 − 𝑛)
𝐺 ∗ ϒ𝑤 𝑛 ∗ϒ𝑤
ϒsat =
(1 − 𝑛 + 𝑛/1 − 𝑛)
+
(1 − 𝑛 + 𝑛/1 − 𝑛)
ϒsat = 𝐺∗ϒ𝑤∗ 1 − 𝑛 + 𝑛 ∗ϒ𝑤
Relationship 10: Between ϒ, G, and n
(𝐺+ 𝑒)*ϒ𝑤

24. ϒsat =
We know that, from Relationship 5
1 + 𝑒
𝛾′ =
1 + 𝑒
𝐺 + 𝑒 .ϒ𝑤
− 𝛾
𝛾′ =
𝐺 ∗ ϒ𝑤 ∗ 𝑒 ∗ ϒ𝑤 − 𝛾𝑤 + 𝑒 ∗ 𝛾𝑤
(1 + 𝑒)
𝛾′ =
(𝐺 − 1) ∗ ϒ𝑤
(1 + 𝑒)
Relationship 11: Between 𝜸′, G, andn
(𝐺 + 𝑒).ϒ𝑤

25. We know that, from Relationship 11
𝛾′ =
(𝐺 − 1) ∗ ϒW
𝛾′ =
𝐺 ∗ϒ𝑤
−
(1 + 𝑒) (1 + 𝑒)
𝛾′ = 𝛾𝑑 − 𝛾𝑤 ∗ (1 − 𝑛)
𝛾𝑤
Relationship 12: Between 𝜸′, ϒ, andn
(1 + 𝑒)

26. Relationship 13: Between ϒsat, ϒd, ϒ, and S
We know that, from Relationship 5
𝛾 =
𝐺 + 𝑆 ∗ 𝑒 .ϒ𝑤
1 + 𝑒
𝛾 =
𝐺 ∗ϒ𝑤
+ 𝑆 ∗(
𝑒∗ ϒ𝑤
(1 + 𝑒) 1 + 𝑒
)
𝛾 = 𝛾𝑑 + 𝑆 ∗( −
(𝐺 + 𝑒) ∗ ϒ𝑤 𝐺 ∗ϒ𝑤
1 + 𝑒 1 + 𝑒
)
𝛾 = 𝛾𝑑 + 𝑆 ∗(𝛾𝑠𝑎𝑡 − 𝛾𝑑)

27. INDEX PROPERTIES OF SOIL: Those properties of soil which
are used in the identification and classification of soil are known as
Index Properties. Various index properties of soils are: -
a. Water content
b. In-situ density
c. Specific gravity
d. Particle size
e. Consistency
f. Density index

28. a) Oven drying method
b) Pycnometer method
c) Sand bath method
d) Alcohol method
e) Calcium carbide method
f) Radiation method
Methods of Water Content Determination
Laboratory
Methods
Field
Methods
Following are the methods used for water content
determination:

29. OVEN DRYING METHOD
This method employs use of thermostatically controlled oven for water content
determination. This is the most accurate method of water content determination.
Thermostatically
controlled oven
Vacuum Desiccator Weighing Balance
Containers with Lid

30. The following procedure is adopted as per IS 2720: Part 2
1. Clean the container, dry it and weight it with lid (M1).
2. Take the required quantity of the wet specimen in the container and close it
with lid. Take the mass (M2)
3. Place the container with its lid removed in the oven till mass becomes constant
(normally for 24 hours).
4. When the soil has dried, remove the container from the oven using tongs.
Replace the lid on the container. Cool it in a desiccator.
5. Find the mass (M3) of the container with lid and dry soil sample.
After all parameters are found out, find water content using following relation
w = M2 - M3/M3 – M1

31.  In This method, the soil sample is taken in a
evaporating dish. Sample is then mixed with
methylated spirit.
 Quantity of methylated spirit required is one
milli litre for every gram of soil.
 The methylated spirit is then ignited. The
mixture is then stirred with spatula.
 After the methylated spirit has burnt away
completely dish is allowed to be cooled and
mass of dry soil is obtained.
ALCOHOL METHOD

32. DISADVANTAGES:
 Cannot be used if soil contain large proportion of clay,
organic matter.
 Methylated spirit is volatile so extra care is required.
 Not accurate.
 After all parameters are found out, find water content using following
relation.
w = M2 - M3/M3 – M1

33. SAND BATH METHOD
• Sand Bath Method for the determination of soil water content is a
quick field method which is employed when an electric oven is not
available for drying of wet soil.
• Sand is kept on a tray to a height of about 3 cm.
• A container is filled with wet soil and dried by keeping on the sand
bath and heating with stirring. Few white papers are kept on top of the
wet soil in the container.
• The soil is said to be dry when these white papers turn brown. Finally,
dry soil is obtained, and the water content can be determined with the
help of the equation obtained for oven drying method.

34. This method of the determination of water content makes use of fact that
when water reacts with calcium carbide, acetylene gas is produced. This
test is performed as per IS 2720:Part 2 (1973).
CALCIUM CARBIDE METHOD

35. 1. Set up the balance, place the sample in the pan till the mark on the balance
arm matches with the index mark.
2. Check that the cup and the body are clean.
3. Hold the body horizontally and gently deposit the levelled, scoop-full of the
absorbent (Calcium Carbide) inside the chamber.
4. Transfer the weighed soil from the pan to the cup.
5. Hold cup and chamber horizontally, bringing them together without disturbing
the sample and the absorbent.
6. Clamp the cup tightly into place. If the sample is bulky, reverse the above
placement, that is, put the sample in the chamber and the absorbent in the cup.
7. In case of clayey soils, place all the 4 steel balls (3 smaller and 1 bigger) in
the body along with the absorbent.

36. 8. Shake the unit up and down vigorously in this position for about 15
seconds.
9. Hold the unit horizontally, rotating it for 10 seconds, so that the balls roll
around the inner circumference of the body.
10. Rest for 20 seconds.
11. Repeat the above cycle until the pressure gauge reading is constant and note
the reading. Usually it takes 4 to 8 minutes to achieve constant reading. This
is the water content (m) obtained on wet mass basis.
12. Finally, release the pressure slowly by opening the clamp screw and taking
the cup out, empty the contents and clean the instrument with a brush.
13. The water content on dry mass basis,
w = m/[100-m] * 100%

37. Methods of Specific Gravity Determination
The specific gravity of solids is frequently required for
computation of several soil properties such as void ratio, degree of
saturation, unit weight of solids, fine soil particle size, etc.
Methods used for determination are:-
1. Pycnometer bottle method
2. Density bottle method
3. Measuring flask method
4. Gas jar method
5. Shrinkage limit method

38. Density Bottle Method
PROCEDURE: (As per IS 2720: Part 3)
• Firstly, Weigh the bottle, with stopper to the nearest 0.001g (M1).
• Take the oven dried soil sample and transfer it the density bottle. Weigh the
bottle with the stopper and the dry sample (M2).
• Add de-aired distilled water to the density bottle just enough to cover the soil.
• Shake gently to mix the soil and water. Place the bottle containing the soil and
water after removing the stopper in the vacuum desiccator.
• Take out the bottle from the water bath and determine the mass of the bottle
and its contents (M3).
• Atlast fill the bottle with water and weigh as (M4) and using the relation
below find specific gravity of soil sample.
G =
𝑀2 − 𝑀1
)
𝑀2 − 𝑀1 − (𝑀3 − 𝑀4

39. Stepwise procedure to determine Specific Gravity
• Density Bottle of 50ml capacity, provided
with nose.
• The nose has a small opening on the top to
help escape of air.
Density Bottle

40. Pycnometer Method
PROCEDURE: (As per IS 2720: Part 3)
• The procedure for finding specific gravity using pycnometer is same as that of
density bottle.
• The capacity of bottle is different, which is 1000 ml.
• This method is widely adopted for finding the specific gravity of coarse
grained soil usually having size greater than 4.75 mm
• Pycnometer Bottle of 1000ml capacity, provided with
lid.
• The lid has a small opening on the top (2mm) to help
escape of air.
Pycnometer Bottle

41. A measuring flask of 250 ml capacity, with a graduation marked at that level .It
is fitted with an adaptor for connecting it to a vacuum line for removing
entrapped air. This method is similar to density bottle method. About 80-100 g
of oven drying sample is taken. Suitable for fine grained and medium grained
soil.
Measuring Flask Method
Gas Jar Method
In this method, a gas jar of about 1 litre
capacity is used. The jar is fitted with
rubber bung. The gas jar serve as
pycnometer. The method is similar to
pycnometer method.

42. Methods of Unit Weight Determination
The Unit Weight of soil is frequently required for computation of
several soil properties such as void ratio, degree of saturation, unit
weight of solids, etc. Apart this also helpful when finding the
bearing capacity of soil and compaction effort
Methods used for determination are:-
1. Core Cutter method
2. Sand Replacement method
3. Water Displacement method
4. Rubber balloon method.

43. 1. Measure the inside dimensions of the core cutter
2. Determine empty weight of core cutter (M1)
3. Level the surface, about 300 mm square in area.
4. Place the dolly over the top of the core cutter and press the core cutter into
the soil mass using the rammer.
5. Stop the process of pressing when about 15 mm of the dolly protrudes
above the soil surface.
6. Remove the soil surrounding the core cutter and take out the core cutter.
7. Remove the dolly. Trim the top and bottom surface of the core cutter
carefully using a straight edge.
8. Weight the core cutter filled with the soil (M2).
9. Remove the core of the soil from the cutter. Determine the water content
Core Cutter Method

44. Steps involved in core cutter test
Core Cutter details

45. M1
M2
Firstly Bulk density, is computed using following relation:
𝛒 =
𝑴𝟐 − 𝑴𝟏
𝑽
Secondly dry density, is computed using following relation:
𝛒d =
𝛒
𝟏 + 𝒘

46. Relative Density
 Relative density is the measure of compactness of cohesionless soil.
Relative density or density index is the ratio of the difference between the
void ratios of a cohesionless soil in its loosest state and existing natural state
to the difference between its void ratio in the loosest and densest states.
 Determination of relative density is helpful in evaluating compaction state
of coarse grained soils and also assessing the safe bearing capacity in case
of sandy soils.
The density index is defined as,
ID = (emax – e / emax – emin)
Where, emax = void ratio in the loosest state
emin = void ratio in the densest state
e = natural void ratio of the deposit

47. Relationship between Density Index and Void Ratio
Source: https://i1.wp.com/civilengineering.blog/wp content/uploads/2020/02/SmartSelect_20200214-183420_Amazon-Kindle.jpg?resize=400%2C400&ssl=1

48. The slope of the straight line AB, representing the relationship between ID and e is given by
tanθ =1/(emax – emin)
cotθ = (emax – emin)
Now, for an intermediate value e we have,
(emax – e) = ID*cotθ or
ID= emax− e*cotθ
Substituting the value of cotθ from equation ii, we get
ID= emax− e/emax− emin
From fig., we observe that when e = emax, ID = 0 and when e = emin, ID = 1. Now from
equation, we have
e = G*γw/γd−1
emax= G*γw/γdmin− 1
emin= G*γw/γdmax
− 1
[ID= γd − γdmin/ γdmax − γdmin]*[γdmax/γd]

49.  “Soil Mechanics & Foundation Engineering”, Dr. K.R.Arora
 “Basic & Applied Soil Mechanics”, Gopal Ranjan & A.S.R.
Rao
 “Soil Mechanics & Foundation”, B.C.Punmia, Ashok Kumar
Jain, Arun Kumar Jain
 “Soil Mechanics”, T.William Lambe
 “Geotechnical Engineering Hand Book”, Ernst and Sohn
 “Methods of Test for Soils (IS : 2720)”, Bureau of Indian
Standards
References