relative density

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


Vibratory table

Weight on sample

inside sleeve


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



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


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


100xee

eeR

minmax

measuredmaxd

(%)

1004831071360

7136070 x

emeasured

..

.

Solving and Rearranging the equation: Solving and Rearranging the equation:


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:


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?


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

relative density

Documents

dry density terms

maximum index density

point proctor test dry

increasing density emax

dry minimum

maximum kd e

example maximum kd

maximum index densities