CENG220L
SOIL MECHANICS LAB
Title: Relative Density
Date: 10/5/2023
Members: Mahdi Khalil- Loujat Faraj- Taleb Abboud- Abed Alaziz Dirani
Contents
Introduction: .......................................................................................................................... 3
Theory: .................................................................................................................................. 3
Equipment: ............................................................................................................................ 4
Procedure:.............................................................................................................................. 4
Minimum Dry Density ...................................................................................................... 4
Maximum Dry Density ..................................................................................................... 4
Results: .................................................................................................................................. 6
Determination of Minimum Dry Density ......................................................................... 6
Determination of Maximum Dry Density \ ...................................................................... 7
Analysis: ................................................................................................................................ 8
Errors: .................................................................................................................................. 10
Conclusion: ......................................................................................................................... 11
Reference:............................................................................................................................ 11
Introduction:
The relative density test is an important geotechnical test used to determine the relative
density of soil. It is used to evaluate the compaction level of soil, which is important in
assessing its suitability for construction projects. In this report, we will describe the
process of conducting a relative density test and discuss the results obtained.
Theory:
Relative density is defined as the ratio of the density of the soil in its compacted state to
the density of the same soil in its natural state. It is also known as the degree of
compaction. The test involves measuring the volume of a hole in the soil before and after
it has been filled with a known amount of sand. The soil's initial volume is determined by
excavating a hole of known dimensions. The sand is then poured into the hole, and its
volume is measured. The difference between the two volumes is the volume of the soil in
the hole. The mass of the soil is also measured. Using this information, the relative
density of the soil can be calculated using the following equation:
𝜋
𝑣𝑜𝑙𝑢𝑚𝑒𝑚𝑜𝑙𝑑 = ∗ 𝐷2 ∗ ℎ
4
𝑒𝑚𝑎𝑥 − 𝑒𝑓𝑖𝑒𝑙𝑑
𝐷𝑟 =
∗ 100
𝑒𝑚𝑎𝑥 − 𝑒𝑚𝑖𝑛
𝑒𝑚𝑎𝑥 = [ (𝛾𝑤 ∗ 𝐺𝑠)/(𝛾𝑑 𝑚𝑖𝑛 ) ] − 1
𝑒min= [ (𝛾𝑤 ∗ 𝐺𝑠)/(𝛾𝑑 𝑚𝑎𝑥 ) ] − 1
𝜌𝑠
𝐺𝑠 =
𝜌𝑤
𝑒=
𝑉𝑣
1
= ( 𝑉𝑣 + 𝑉𝑤 )
𝑉𝑠
𝑣𝑠
Equipment:





Metal mold
Balance
Funnel
Scoop
Shaking vibratory table
Procedure:
Minimum Dry Density
1. Determine the volume of the mold excluding the collar is through taking three readings
for the height (h) and inner diameter (D) of the mold.
2. Determine the mass of the empty mold excluding the collar.
3. Place the collar
4. Fill the mold to overflowing by using a scoop and a funnel and discharging the soil in a
circular spiral pattern from a height not exceeding 2" or 50mm above the top of the mold.
Maintain the height of the sand inside the funnel at all times.
5. Remove the collar and screen off the top of the mold to remove excess soil
6. Determine the weight of the mold including the loose soil and record the value.
7. Repeat steps 3 to 5 three times and average the three values of mass obtained
8. Calculate the dry density, dry unit weight and the void ratio of the sand.
Maximum Dry Density
1. Determine the volume of the mold excluding the collar is through taking three readings
for the height (h) and inner diameter (D) of the mold.
2. Determine the mass of the empty mold excluding the collar.
3. Place the collar
4. Fill the mold using the scoop to 1/3 of its height and level the surface
5. Place deadweight on the sand and position the mold on vibrating table. Vibrate for 3
minutes.
6. Remove the deadweight and fill the mold to 2/3 of its height and level the surface.
7. Place deadweight on the sand and position the mold on vibrating table. Vibrate for 3
minutes.
8. Remove the deadweight and fill the mold with the third layer and level the surface.
9. Place deadweight on the sand and position the mold on vibrating table. Vibrate for 3
minutes.
10. Remove the deadweight and the collar and screen off the top of the mold to remove
excess soil
11. Determine the weight of the mold including the compacted soil and record the value.
12. Calculate the dry density, dry unit weight and the void ratio of the sand.
Results:
Table 1
Mold dimensions
1
2
3
Average
Height (cm)
11.6
11.6
11.6
11.6
Internal
Diameter (cm)
Volume (m^3)
15.3
15.2
15.1
15.2
2.1 *10^-3
Determination of Minimum Dry Density
Table 2
Description
symbol
Values
Unit
Trial 1
Trial 2
Trial 3
Mm
4.929
4.929
4.929
Kg
Mass of mold with
dry sand
Mm,s
8.222
8.21
8.231
Kg
Mass of dry soil
Weight of dry soil
Ms
Ws
3.293
0.0323
3.281
0.03218
3.302
0.03239
Kg
KN
Volume of mold
Minimum dry unit
weight
Vm
𝜸𝒅,𝒎𝒊𝒏
15.42
M3
KN/m3
Average min. dry
unit weight
𝜸𝒅,𝒎𝒊𝒏,𝒂𝒗𝒈
15.37
KN/m3
emax
0.69
NA
Mass of mold
without collar
Maximum void
ratio
15.38
2.1*10^-3
15.32
Determination of Maximum Dry Density \
Table 3:
Description
symbol
Values
Unit
Mm
Trial 1
4.929
Trial 2
4.929
Kg
Mass of mold with
dry sand
Mass of dry soil
Mm,s
8.446
8.442
Kg
Ms
3.517
3.513
Kg
Weight of dry soil
Ws
0.0345
0.034462
KN
Volume of mold
Vm
Mass of mold
without collar
2.1*10^-3
M3
Maximum dry unit
weight
𝜸𝒅,𝒎𝒂𝒙
Average max. dry
unit weight
𝜸𝒅,𝒎𝒂𝒙,𝒂𝒗𝒈
16.415
KN/m3
emin
0.58
NA
Minimum void
ratio
16.42
16.41
KN/m3
Analysis:
After measuring the height (H) and the inner diameter (d) of the mold we can determine
the volume, which is:
𝑉=
𝜋𝑑 2 ℎ 3.14 ∗ 15.22 ∗ 11.6
=
= 2.1 ∗ 10−3 𝑚3
4
4
Then we can determine both minimum and maximum dry unit weight using the following
formula,
𝛾𝑑𝑚𝑖𝑛 𝑡𝑟𝑖𝑎𝑙1
𝑔
9.81
𝑊𝑠 𝑀𝑠 ∗ 1000 3.293 ∗ 1000 0.0323
𝐾𝑁
=
=
=
=
= 15.38 3
𝑉𝑚
𝑉
0.0021
0.0021
𝑚
𝛾𝑑𝑚𝑎𝑥 𝑡𝑟𝑖𝑎𝑙1
𝑔
9.81
𝑊𝑠 𝑀𝑠 ∗ 1000 3.517 ∗ 1000 0.0345
𝐾𝑁
=
=
=
=
= 16.42 3
𝑉𝑚
𝑉
0.0021
0.0021
𝑚
Where Ws is the dry weight of soil
In order to determine void ratios using:
1.
𝑒𝑚𝑎𝑥 = [ (𝛾𝑤 ∗ 𝐺𝑠)/(𝛾𝑑 min 𝑎𝑣𝑔 ) ] − 1 = (
2.65 ∗ 9.81
− 1) = 0.69
15.37
2.
𝑒min= [ (𝛾𝑤 ∗ 𝐺𝑠)/(𝛾𝑑 max 𝑎𝑣𝑔 ) ] − 1 = (
2.65 ∗ 9.81
− 1) = 0.58
16.415
Note: take the average of dry unit weight in both min and max for the trials then
determine void ratio.
3. To determine the unit weight and density corresponding to Dr = 90% for the given soil,
we need to use the following equation:
𝛾𝑑𝑟𝑦 =
Where:
1 + 𝑒𝑚𝑎𝑥
∗ 𝐺𝑠 ∗ 𝜌𝑤
1 +𝑒





γ_dry = dry unit weight
e_max = maximum void ratio
e = void ratio at Dr = 90%
Gs = specific gravity of soil solids
pw = density of water (assumed as 1 kg/m³)
First, we need to find the void ratio corresponding to Dr = 90%. For a given soil, the
relationship between relative density and void ratio can be approximated by the following
equation:
𝑒𝑚𝑎𝑥 − 𝑒𝑓𝑖𝑒𝑙𝑑
𝐷𝑟 =
∗ 100
𝑒𝑚𝑎𝑥 − 𝑒𝑚𝑖𝑛
Where:
 Dr = relative density
 emax = maximum void ratio
 emin = minimum void ratio
Rearranging the equation, we get:
𝑒 = 𝑒𝑚𝑎𝑥 −
(𝑒𝑚𝑎𝑥 − 𝑒𝑚𝑖𝑛 ) ∗ 𝐷𝑟
100
= 0.78 −
(0.78 − 0.43) ∗ 90
100
= 0.52
Now, we can calculate the dry unit weight as follows:
𝛾𝑑𝑟𝑦 =
1 + 𝑒𝑚𝑎𝑥
1 + 0.78
∗ 𝐺𝑠 ∗ 𝜌𝑤 =
∗ 2.65 ∗ 1 = 17.14 𝐾𝑁/𝑚3
1+𝑒
1 + 0.52
Therefore, the unit weight and density corresponding to Dr = 90% for the given soil are
17.14 kN/m³ and 1,740 kg/m³, respectively.
Errors:
Errors can occur in this test due to a variety of factors, including:
 Contamination: Any foreign material present in the sample can alter the relative
density measurement. Therefore, it is essential to ensure that the sample is pure
and free from any contaminants.
 Air bubbles: Air bubbles can get trapped in the sample during the test, causing
inaccurate results.
 Improper handling: The test equipment must be handled carefully to avoid any
errors in measurement.
 Human error: Errors can occur due to mistakes made by the operator, such as
incorrect recording of measurements or misreading of the instrument scale.
 Calibration issues: If the equipment is not calibrated properly or regularly, it can
result in incorrect readings.
 Sample size: The size of the sample can also affect the accuracy of the test. Too
small or too large a sample may lead to inaccurate readings.
It is important to take all these factors into consideration while performing the relative
density test to ensure accurate results.
Conclusion:
In conclusion, the relative density of granular soil is the ratio of the difference between
the maximum and minimum densities to the difference between the maximum and
minimum void ratios. This parameter is expressed as a percentage and provides an
indication of the degree of compaction of the soil.
It is essential for evaluating the suitability of soil for various engineering applications,
such as foundation design, slope stability analysis, and pavement design. The selection of
the appropriate test method depends on the type of soil and the required accuracy. It is
recommended to follow the standard procedures and guidelines outlined in the ASTM
standards to obtain reliable and accurate results.
Reference:




the lab handout
Soil mechanics course material
ASTM D4254
ASTM D4253