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Soil Mechanics definitions
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Review of Relative Density Review of Relative Density PrinciplesPrinciples
Relative Density principles apply to Relative Density principles apply to compaction of relatively clean, coarse-compaction of relatively clean, coarse-grained soils.grained soils.
Relatively clean usually taken to be less 12 Relatively clean usually taken to be less 12 % or less finer than the #200 sieve.% or less finer than the #200 sieve.
Important for compaction study of filtersImportant for compaction study of filters
ObjectivesObjectives
Explain basic principles Explain basic principles of compacting clean of compacting clean sands and gravelssands and gravels
Understand basic tests to Understand basic tests to obtain reference obtain reference densities. densities.
Use 1 point compaction Use 1 point compaction test in design and quality test in design and quality controlcontrol
Summarize minimum Summarize minimum and maximum index and maximum index density testsdensity tests
Detail the importance Detail the importance of water content in of water content in compacting clean compacting clean sands and gravelssands and gravels
Review of Compaction PrinciplesReview of Compaction Principles
Compaction Tests are not commonly Compaction Tests are not commonly performed on soils with 12 % or fewer finesperformed on soils with 12 % or fewer fines
Small percentage of fines means soils Small percentage of fines means soils cannot easily hold water to examine range cannot easily hold water to examine range of water and effect on dry densityof water and effect on dry density
Review of Compaction PrinciplesReview of Compaction Principles
Compaction tests performed on clean sands Compaction tests performed on clean sands may have this appearancemay have this appearanceD
r d
en
sity
w %
Compacting Clean SandsCompacting Clean Sands
Clean sands are compacted most easily at Clean sands are compacted most easily at either very dry or very wet water contentseither very dry or very wet water contents
At intermediate water contents, capillary At intermediate water contents, capillary stresses in voids resist compactionstresses in voids resist compaction
Bulking is term for this phenomenonBulking is term for this phenomenon
Compacting Clean SandsCompacting Clean Sands
Vibration most effective energy for sandsVibration most effective energy for sands Use smooth-wheeled vibratory rollerUse smooth-wheeled vibratory roller
Relative DensityRelative Density
Alternative to traditional compaction test is Alternative to traditional compaction test is relative density testsrelative density tests
Minimum Index DensityMinimum Index Density Maximum Index DensityMaximum Index Density Relative DensityRelative Density
Minimum Index DensityMinimum Index Density
Minimum index Minimum index density of clean density of clean sand is that sand is that resulting from resulting from very loosely very loosely filling a steel filling a steel mold. ASTM mold. ASTM Method D4254Method D4254
Sand dropped no more than
1”
Minimum Index DensityMinimum Index Density
After filling the After filling the mold, excess soil mold, excess soil is carefully screed is carefully screed off. The volume off. The volume of this mold is 0.1 of this mold is 0.1 ftft3. 3. Knowing the weight of soil in the mold, the dry density is easily computed
Maximum Index DensityMaximum Index Density
Example Minimum dry density = 96 pcfExample Minimum dry density = 96 pcf Maximum index density of clean sand Maximum index density of clean sand
results from vibration at high amplitude on results from vibration at high amplitude on vibratory table for 10 minutes. vibratory table for 10 minutes. ASTM D4253ASTM D4253
Example Maximum dry density = 117.5 pcfExample Maximum dry density = 117.5 pcf
Maximum Index DensityMaximum Index Density
Vibratory table
Weight on sample
inside sleeve
Maximum Index DensityMaximum Index Density
Vibratory table
Weight on sample
inside sleeve
Maximum Index DensityMaximum Index Density
Sample densified by
vibration
Measure height to
determine new d
Plate on which weight sits during vibration
Void Ratio and Dry DensityVoid Ratio and Dry Density The void Ratio is calculated for each state of The void Ratio is calculated for each state of
denseness of sample. denseness of sample. Maximum void ratio occurs at minimum index Maximum void ratio occurs at minimum index
density - For Example Min.density - For Example Min.dd = 96.0 pcf = 96.0 pcf
Minimum void ratio occurs at maximum index Minimum void ratio occurs at maximum index density For Example Maximum density For Example Maximum dd = 110.0 pcf = 110.0 pcf
1
dry
watersGe
First Calculate void ratio at Minimum First Calculate void ratio at Minimum dd
Minimum and Maximum Void RatiosMinimum and Maximum Void Ratios
Next Calculate void ratio at Maximum Next Calculate void ratio at Maximum dd
722501096
4626521 .
.
..max
dry
watersGe
5033010110
4626521 .
.
..min
dry
watersGe
emaxemin
emeasured
dmax d mind measured
Diagram below illustrates a relative density of about 40 %
increasing density
100(%)minmax
max xee
eeR measured
d
Relative Density EquationRelative Density Equation
Now, assume that the density of this Now, assume that the density of this sand was measured in a compacted fill sand was measured in a compacted fill and it was 102.5 pcf. Calculate a value and it was 102.5 pcf. Calculate a value for relative density of the fill. First, for relative density of the fill. First, calculate the void ratio of the fill:calculate the void ratio of the fill:
Calculate Void Ratio of Compacted SandCalculate Void Ratio of Compacted Sand
6133.015.102
4.6265.21
dry
watersGe
Now, use the values of void ratio in the Now, use the values of void ratio in the relative density equation:relative density equation:
Compute Relative DensityCompute Relative Density
100xee
eeR measured
dminmax
max(%)
%...
..(%) 949100
5033072230
6133072250
xRd
100
minmax
minmax(%)
ddd
ddddR
%.
...
...(%) 849100
09601105102
09651020110
dR
Compute Relative DensityCompute Relative Density
Relative Density EquationRelative Density Equation(rewritten in dry density terms)(rewritten in dry density terms)
Solve for Example:Solve for Example:
Fort Worth Relative Density StudyFort Worth Relative Density Study
NRCS lab in Fort Worth studied 28 filter NRCS lab in Fort Worth studied 28 filter sands and used some published datasands and used some published data
Minimum and Maximum Index Densities Minimum and Maximum Index Densities were performed on each samplewere performed on each sample
A 1 point dry Standard Proctor energy mold A 1 point dry Standard Proctor energy mold was also prepared for each sample.was also prepared for each sample.
Values of 50% and 70% relative density were Values of 50% and 70% relative density were plotted against the 1 point Proctor valueplotted against the 1 point Proctor value
70 % Relative Density vs. 1 Point Proctor70 % 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 %
Rel
ativ
e D
ensi
ty
70 %RD = 1 Point line
Best fit correlation
Conclusion is that the field 1 point Conclusion is that the field 1 point Proctor dry test is about equal to 70 Proctor dry test is about equal to 70 % relative density% relative density
70 % Relative Density vs. 1 Point Proctor70 % Relative Density vs. 1 Point Proctor
50 % Relative Density vs. 1 Point Proctor50 % 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
Conclusion is that the 95 % of the Conclusion is that the 95 % of the field 1 point Proctor dry test is field 1 point Proctor dry test is about equal to 50 % relative about equal to 50 % relative densitydensity
50 % Relative Density vs. 1 Point Proctor50 % Relative Density vs. 1 Point Proctor
D70 = 1.075 x d 1pt -9.61,
for RD70 and d 1pt in lb/ft3
D50 = 1.07 x d 1pt - 12.5,
for RD50 and d 1pt in lb/ft3
Relative Density Estimates from FW Relative Density Estimates from FW SML StudySML Study
Example Relative Density EstimatesExample Relative Density Estimates– Given: 1 Point Proctor TestGiven: 1 Point Proctor Testdd = 105.5 pcf = 105.5 pcf
– Estimate 70 % and 50% Relative DensityEstimate 70 % and 50% Relative Density
– Given that measured Given that measured dd is 98.7, evaluate is 98.7, evaluate
state of compaction of sand.state of compaction of sand.
Relative Density Estimates from FW Relative Density Estimates from FW SML StudySML Study
Class Problem - Relative DensityClass Problem - Relative Density– A soil’s minimum index density is 96.5 pcf A soil’s minimum index density is 96.5 pcf
and its maximum index density is 111.5 and its maximum index density is 111.5 pcf. The Gs value is 2.65pcf. The Gs value is 2.65
– Calculate the eCalculate the eminmin and e and emaxmax
– Compute the void ratio and dry density Compute the void ratio and dry density corresponding to a relative density value of corresponding to a relative density value of 70 %70 %
Review of Relative DensityReview of Relative Density
Given: Minimum index density is 96.5 pcf Given: Minimum index density is 96.5 pcf Maximum index density is 111.5 pcf. Maximum index density is 111.5 pcf.
Class Problem SolutionClass Problem Solution
713601596
4626521 .
.
..max
min_dry
watersGe
4831015111
4626521 .
.
..min
max_dry
watersGe
Now, substitue a value for RD of 70(%) Now, substitue a value for RD of 70(%) in the relative density equation in the relative density equation
Class Problem SolutionClass Problem Solution
100xee
eeR
minmax
measuredmaxd
(%)
1004831071360
7136070 x
emeasured
..
.
Solving and Rearranging the equation: Solving and Rearranging the equation:
Class Problem SolutionClass Problem Solution
1004831071360
7136070 x
emeasured
..
.
2305
71360
100
70
.
. measurede
measurede 71360161350 ..
5225016135071360 ... measurede
Now, calculate a value for dry density at this void ratio: Now, calculate a value for dry density at this void ratio:
Class Problem SolutionClass Problem Solution
1
dry
watersGe 1
462652552250
dry
...
dry
462652
552251..
.35106
552251
36165ft
lbdry .
.
.
Summary - The dry density corresponding to Summary - The dry density corresponding to 70(%) relative density for this sample is 106.5 70(%) relative density for this sample is 106.5 pcf pcf
80
90
100
110
120
130
140
0 10 20 30 40 50 60 70 80 90 100
Relative Density, %
Dry
De
ns
ity
, p
cf
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 DensityOther information on Relative Density
5
10
15
20
25
30
35
40
45
0 10 20 30 40 50 60 70 80 90 100
Relative Density, %
Sa
tura
ted
Wa
ter
Co
nte
nt,
%
Reference Donovan, N.C. and Sukhmander Singh, ભ"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 DensityOther information on Relative Density
Class ProblemClass Problem
Given that the water content of a silty Given that the water content of a silty sand that was obtained from a saturated sand that was obtained from a saturated zone of a channel bank measured 24.5 zone of a channel bank measured 24.5 percentpercent
What is the estimated relative density What is the estimated relative density of the sand?of the sand?
Class Problem SolutionClass Problem Solution
Reading from the chart, the Reading from the chart, the estimated Rd value is about 42 estimated Rd value is about 42 percent.percent.