Review of Relative Density PrinciplesRelative 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

ObjectivesExplain basic principles of compacting clean sands and gravelsUnderstand basic tests to obtain reference densities. Use 1 point compaction test in design and quality controlSummarize minimum and maximum index density testsDetail the importance of water content in compacting clean sands and gravels

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

Review of Compaction PrinciplesCompaction tests performed on clean sands may have this appearanceDr densityw %

Compacting Clean SandsClean sands are compacted most easily at either very dry or very wet water contentsAt intermediate water contents, capillary stresses in voids resist compactionBulking is term for this phenomenon

Compacting Clean SandsVibration most effective energy for sandsUse smooth-wheeled vibratory roller

Relative DensityAlternative to traditional compaction test is relative density testsMinimum Index DensityMaximum Index DensityRelative Density

Minimum Index DensityMinimum index density of clean sand is that resulting from very loosely filling a steel mold. ASTM Method D4254

Sand dropped no more than 1

Minimum Index DensityAfter 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

Maximum Index DensityExample Minimum dry density = 96 pcfMaximum index density of clean sand results from vibration at high amplitude on vibratory table for 10 minutes. ASTM D4253Example Maximum dry density = 117.5 pcf

Maximum Index DensityVibratory tableWeight on sample inside sleeve

Maximum Index DensityVibratory tableWeight on sample inside sleeve

Maximum Index DensitySample densified by vibrationMeasure D height to determine new gdPlate on which weight sits during vibration

Void Ratio and Dry DensityThe 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 pcfMinimum void ratio occurs at maximum index density For Example Maximum gd = 110.0 pcf

Minimum and Maximum Void RatiosFirst Calculate void ratio at Minimum gd

Next Calculate void ratio at Maximum gd

Relative Density Equation

emaxeminemeasureddmaxd mind measuredDiagram below illustrates a relative density of about 40 %increasing density

Calculate Void Ratio of Compacted SandNow, 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:

Compute Relative DensityNow, use the values of void ratio in the relative density equation:

Compute Relative DensityRelative Density Equation (rewritten in dry density terms)Solve for Example:

Fort Worth Relative Density StudyNRCS lab in Fort Worth studied 28 filter sands and used some published dataMinimum and Maximum Index Densities were performed on each sampleA 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

70 % Relative Density vs. 1 Point Proctor

Chart1

93.44623593550631

97.46284907054225

100.69598228408732

104.56408578847294

103.77398609573996

108.32740477249148

108.222672464914

105.9634062786892

108.24238364319412

106.60171411683577

109.3113482056256

109.33333333333333

114.15562913907284

107.77751518535436

111.64859437751005

115.46467847157501

111.36153141536313

112.80312809155937

114.05070595457336

113.4732044198895

114.81075052421745

117.53117814148519

121.81538461538462

120.07261538461537

122.13490959666204

120.9848118743528

124.25923718712752

&A

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70 %RD = 1 Point line

Best fit correlation

Field 1 Point Proctor Test Dry Density, pcf

70 % Relative Density

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

50 % Relative Density vs. 1 Point Proctor

Chart2

89.16436081903709

94.09071639894506

97.38908720040796

100.70560204784877

100.84558285902737

104.23841217019253

104.18620361560419

103.14044227954234

104.77287878686478

103.7999040767386

105.82159624413146

105.96923076923078

109.19683257918552

105.01792012208197

107.61483870967743

110.71814119749777

108.3536964224272

109.8168624353408

111.05116557083085

110.82005395683453

111.82546683079943

113.8058939096267

117.17970401691332

116.5546294979377

118.13677130044843

118.21011804384487

120.4579642365887

105.36439643024895

111.1110514541387

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95 % of 1 point

best fit line

Field 1 pointdry density

50 % Rd

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

Relative Density Estimates from FW SML StudygD70= 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 StudyExample Relative Density EstimatesGiven: 1 Point Proctor Test gd = 105.5 pcfEstimate 70 % and 50% Relative DensityGiven that measured gd is 98.7, evaluate state of compaction of sand.

Review of Relative DensityClass Problem - Relative DensityA soils minimum index density is 96.5 pcf and its maximum index density is 111.5 pcf. The Gs value is 2.65Calculate the emin and emaxCompute the void ratio and dry density corresponding to a relative density value of 70 %

Class Problem SolutionGiven: Minimum index density is 96.5 pcf Maximum index density is 111.5 pcf.

Class Problem SolutionNow, substitue a value for RD of 70(%) in the relative density equation

Class Problem SolutionSolving and Rearranging the equation:

Class Problem SolutionNow, 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

Other information on Relative Density

Chart2

81.584.589938391

98103109112.5100.5110.75

116125129132120.5130.5

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.

Relative Density, %

Dry Density, pcf

Other information on Relative DensityChart is for silty sands (SM)

Chart3

37.586737929236.252168883738.9704322155

24.495567276422.988539309426.0794844253

14.190247402712.326015037616.1991184859

Prepared by NSMC &D&RPage &P

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.

Average

Relative Density, %

Saturated Water Content, %

Class ProblemGiven that the water content of a silty sand that was obtained from a saturated zone of a channel bank measured 24.5 percentWhat is the estimated relative density of the sand?

Class Problem SolutionReading from the chart, the estimated Rd value is about 42 percent.

Results of study published as technical note in ASCE Journal of Geotechnical Engineering, October, 1996