Relative density principles apply to compaction of clean, coarse-grained soils with less than 12% fines. Relative density tests involve measuring minimum and maximum index densities. Minimum index density results from loosely placing soil, while maximum results from vibrating soil. Relative density is calculated from these values and used to estimate compaction levels. A study correlated relative density to standard proctor tests. Estimates of 50% and 70% relative density can be made from proctor dry densities. Relative density charts also relate dry density, water content and soil type.

1. Review of Relative Density
Principles
 Relative Density principles apply to
compaction of relatively clean, coarse-
grained soils.
 Relatively clean usually taken to be less 12
% or less finer than the #200 sieve.
 Important for compaction study of filters

2. Objectives
 Explain basic principles
of compacting clean
sands and gravels
 Understand basic tests to
obtain reference
densities.
 Use 1 point compaction
test in design and quality
control
 Summarize minimum
and maximum index
density tests
 Detail the importance
of water content in
compacting clean
sands and gravels

3. Review of Compaction Principles
 Compaction Tests are not commonly
performed on soils with 12 % or fewer fines
 Small percentage of fines means soils
cannot easily hold water to examine range
of water and effect on dry density

4. Review of Compaction Principles
 Compaction tests performed on clean sands
may have this appearance
w %

5. Compacting Clean Sands
 Clean sands are compacted most easily at
either very dry or very wet water contents
 At intermediate water contents, capillary
stresses in voids resist compaction
 Bulking is term for this phenomenon

6. Compacting Clean Sands
 Vibration most effective energy for sands
 Use smooth-wheeled vibratory roller

7. Relative Density
 Alternative to traditional compaction test is
relative density tests
 Minimum Index Density
 Maximum Index Density
 Relative Density

8. Minimum Index Density
 Minimum index
density of clean
sand is that
resulting from
very loosely
filling a steel
mold. ASTM
Method D4254
Sand
dropped no
more than 1”

9. Minimum Index Density
 After filling the
mold, excess soil
is carefully screed
off. The volume
of this mold is 0.1
ft3. Knowing the
weight of soil in
the mold, the dry
density is easily
computed

10. Maximum Index Density
 Example Minimum dry density = 96 pcf
 Maximum index density of clean sand
results from vibration at high amplitude on
vibratory table for 10 minutes.
ASTM D4253
 Example Maximum dry density = 117.5 pcf

11. Maximum Index Density
Vibratory
table
Weight on
sample inside
sleeve

12. Maximum Index Density
Vibratory
table
Weight on
sample inside
sleeve

13. Maximum Index Density
Sample
densified by
vibration
Measure D
height to
determine
new gd
Plate on which weight
sits during vibration

14. Void Ratio and Dry Density
 The void Ratio is calculated for each state of
denseness of sample.
 Maximum void ratio occurs at minimum index
density - For Example Min.gd = 96.0 pcf
 Minimum void ratio occurs at maximum index
density For Example Maximum gd = 110.0 pcf
1

g
g


dry
water
s
G
e

15.  First Calculate void ratio at Minimum gd
Minimum and Maximum Void Ratios
 Next Calculate void ratio at Maximum gd
7225
0
1
0
96
4
62
65
2
1 .
.
.
.
max 




g
g


dry
water
s
G
e
5033
0
1
0
110
4
62
65
2
1 .
.
.
.
min 




g
g


dry
water
s
G
e

16. emax
emin
emeasured
gdmax gd min
gd measured
Diagram below illustrates a
relative density of about 40 %
increasing density
100
(%)
min
max
max
x
e
e
e
e
R measured
d



Relative Density Equation

17. Now, assume that the density of this
sand was measured in a compacted fill
and it was 102.5 pcf. Calculate a value
for relative density of the fill. First,
calculate the void ratio of the fill:
Calculate Void Ratio of Compacted Sand
6133
.
0
1
5
.
102
4
.
62
65
.
2
1 






dry
water
s
G
e
g
g

18. Now, use the values of void ratio in the
relative density equation:
Compute Relative Density
100
x
e
e
e
e
R measured
d
min
max
max
(%)



 
%
.
.
.
.
.
(%) 9
49
100
5033
0
7223
0
6133
0
7225
0



 x
Rd

19.  
 
100
min
max
min
max
(%) 



d
d
d
d
d
d
d
R
g
g
g
g
g
g
 
 
 
%
.
.
.
.
.
.
.
(%) 8
49
100
0
96
0
110
5
102
0
96
5
102
0
110





d
R 
Compute Relative Density
Relative Density Equation
(rewritten in dry density terms)
Solve for Example:

20. Fort Worth Relative Density Study
 NRCS lab in Fort Worth studied 28 filter
sands and used some published data
 Minimum and Maximum Index Densities
were performed on each sample
 A 1 point dry Standard Proctor energy mold
was also prepared for each sample.
 Values of 50% and 70% relative density were
plotted against the 1 point Proctor value

21. 70 % Relative Density vs. 1 Point Proctor
90
95
100
105
110
115
120
125
130
90 95 100 105 110 115 120 125 130
Field 1 Point Proctor Test Dry Density, pcf
70
%
Relative
Density
70 %RD = 1 Point line
Best fit correlation

22. Conclusion is that the field 1 point
Proctor dry test is about equal to 70
% relative density
70 % Relative Density vs. 1 Point Proctor

23. 50 % Relative Density vs. 1 Point Proctor
90
95
100
105
110
115
120
125
90 95 100 105 110 115 120 125 130
Field 1 pointdry density
50
%
Rd
95 % of 1
point
best fit line

24. Conclusion is that the 95 % of the
field 1 point Proctor dry test is
about equal to 50 % relative
density
50 % Relative Density vs. 1 Point Proctor

25. gD70= 1.075 x gd 1pt -9.61,
for RD70 and gd 1pt in lb/ft3
gD50 = 1.07 x gd 1pt - 12.5,
for RD50 and gd 1pt in lb/ft3
Relative Density Estimates from FW
SML Study

26. Example Relative Density Estimates
–Given: 1 Point Proctor Test
gd = 105.5 pcf
–Estimate 70 % and 50% Relative Density
–Given that measured gd is 98.7, evaluate
state of compaction of sand.
Relative Density Estimates from FW
SML Study

27. Class Problem - Relative Density
– A soil’s minimum index density is 96.5
pcf and its maximum index density is
111.5 pcf. The Gs value is 2.65
– Calculate the emin and emax
– Compute the void ratio and dry density
corresponding to a relative density value
of 70 %
Review of Relative Density

28. Given: Minimum index density is 96.5 pcf
Maximum index density is 111.5 pcf.
Class Problem Solution
7136
0
1
5
96
4
62
65
2
1 .
.
.
.
max 




g
g


min_dry
water
s
G
e
4831
0
1
5
111
4
62
65
2
1 .
.
.
.
min 




g
g


max_dry
water
s
G
e

29. Now, substitue a value for RD of 70(%)
in the relative density equation
Class Problem Solution
100
x
e
e
e
e
R
min
max
measured
max
d



(%)
100
4831
0
7136
0
7136
0
70 x
emeasured
.
.
.




30.  Solving and Rearranging the equation:
Class Problem Solution
100
4831
0
7136
0
7136
0
70 x
emeasured
.
.
.



2305
7136
0
100
70
.
. measured
e


measured
e

 7136
0
16135
0 .
.
5225
0
16135
0
7136
0 .
.
. 


measured
e

31.  Now, calculate a value for dry density at this void
ratio:
Class Problem Solution
1

g
g


dry
water
s
G
e 1
4
62
65
2
55225
0 
g


dry
.
.
.
dry
g


4
62
65
2
55225
1
.
.
. 3
5
106
55225
1
36
165
ft
lb
dry .
.
.


g
 Summary - The dry density corresponding to
70(%) relative density for this sample is 106.5 pcf

32. 80
90
100
110
120
130
140
0 10 20 30 40 50 60 70 80 90 100
Relative Density, %
Dry
Density,
pcf
sand and silty
sand
Gravelly sand
Reference - Donovan, N.C. and Sukhmander Singh, "Liquefaction Criteria
for the Trans-Alaska Pipeline." Liquefaction Problems in Geotechnical
Engineering, ASCE Specialty Session, Philadelphia, PA, 1976.
Other information on Relative Density

33. 5
10
15
20
25
30
35
40
45
0 10 20 30 40 50 60 70 80 90 100
Relative Density, %
Saturated
Water
Content,
%
Reference ભ Donovan, N.C. and Sukhmander Singh,
"Liquefaction Criteria for the Trans-Alaska Pipeline." Liquefaction
Problems in Geotechnical Engineering, ASCE Specialty Session,
Philadelphia, PA, 1976.
Average
Chart is for silty
sands (SM)
Other information on Relative Density

34. Class Problem
Given that the water content of a silty
sand that was obtained from a saturated
zone of a channel bank measured 24.5
percent
What is the estimated relative density
of the sand?

35. Class Problem Solution
Reading from the chart, the
estimated Rd value is about 42
percent.