Relative Density
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Transcript of Relative Density
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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
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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
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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
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Review of Compaction PrinciplesCompaction tests performed on clean sands may have this appearanceDr densityw %
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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
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Compacting Clean SandsVibration most effective energy for sandsUse smooth-wheeled vibratory roller
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Relative DensityAlternative to traditional compaction test is relative density testsMinimum Index DensityMaximum Index DensityRelative Density
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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
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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
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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
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Maximum Index DensityVibratory tableWeight on sample inside sleeve
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Maximum Index DensityVibratory tableWeight on sample inside sleeve
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Maximum Index DensitySample densified by vibrationMeasure D height to determine new gdPlate on which weight sits during vibration
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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
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Minimum and Maximum Void RatiosFirst Calculate void ratio at Minimum gd
Next Calculate void ratio at Maximum gd
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Relative Density Equation
emaxeminemeasureddmaxd mind measuredDiagram below illustrates a relative density of about 40 %increasing density
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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:
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Compute Relative DensityNow, use the values of void ratio in the relative density equation:
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Compute Relative DensityRelative Density Equation (rewritten in dry density terms)Solve for Example:
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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
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70 % Relative Density vs. 1 Point Proctor
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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
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70 %RD = 1 Point line
Best fit correlation
Field 1 Point Proctor Test Dry Density, pcf
70 % Relative Density
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70 % Relative Density vs. 1 Point ProctorConclusion 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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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
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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
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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
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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.
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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 %
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Class Problem SolutionGiven: Minimum index density is 96.5 pcf Maximum index density is 111.5 pcf.
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Class Problem SolutionNow, substitue a value for RD of 70(%) in the relative density equation
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Class Problem SolutionSolving and Rearranging the equation:
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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
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Other information on Relative Density
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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
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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, %
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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?
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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