Review of Relative Density Principles

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

Dr density
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
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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

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Maximum Index Density
Weight on sample inside sleeve
Vibratory table
12
Maximum Index Density
Weight on sample inside sleeve
Vibratory table
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Maximum Index Density
Sample densified by vibration
Measure D height to determine new gd
Plate on which weight sits during vibration
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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

15
Minimum and Maximum Void Ratios

• First Calculate void ratio at Minimum gd

• Next Calculate void ratio at Maximum gd

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Relative Density Equation
Diagram below illustrates a relative density of
about 40
emeasured
emax
emin
?d measured
?dmax
?d min
increasing density
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Calculate Void Ratio of Compacted Sand

• 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

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Compute Relative Density

• Now, use the values of void ratio in the relative
  density equation

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Compute Relative Density

• Relative Density Equation(rewritten in dry
  density terms)
• Solve for Example

?
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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

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70 Relative Density vs. 1 Point Proctor
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70 Relative Density vs. 1 Point Proctor

• Conclusion is that the field 1 point Proctor dry
  test is about equal to 70 relative density

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50 Relative Density vs. 1 Point Proctor
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50 Relative Density vs. 1 Point Proctor

• Conclusion is that the 95 of the field 1 point
  Proctor dry test is about equal to 50 relative
  density

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Relative Density Estimates from FW SML Study
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
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Relative Density Estimates from FW SML Study

• Example Relative Density Estimates
• Given 1 Point Proctor Testgd 105.5 pcf
• Estimate 70 and 50 Relative Density
• Given that measured gd is 98.7, evaluate state of
  compaction of sand.

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Review of Relative Density

• Class Problem - Relative Density
• A soils 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

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Class Problem Solution

• Given Minimum index density is 96.5 pcf
• Maximum index density is 111.5 pcf.

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Class Problem Solution

• Now, substitue a value for RD of 70() in the
  relative density equation

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Class Problem Solution

• Solving and Rearranging the equation

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Class Problem Solution

• Now, calculate a value for dry density at this
  void ratio

• Summary - The dry density corresponding to 70()
  relative density for this sample is 106.5 pcf

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Other information on Relative Density
33
Other information on Relative Density
Chart is for silty sands (SM)
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?

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Class Problem Solution

• Reading from the chart, the estimated Rd value is
  about 42 percent.