Review of Relative Density Principles Relative Density principles apply to compaction of relatively clean, coarsegrained soils. Relatively clean usually taken to be less 12 % or less finer than the #200 sieve. Important for compaction study of filters 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 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 Review of Compaction Principles Compaction tests performed on clean sands may have this appearance w% 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 Compacting Clean Sands Vibration most effective energy for sands Use smooth-wheeled vibratory roller Relative Density Alternative to traditional compaction test is relative density tests Minimum Index Density Maximum Index Density Relative Density 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” 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 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 Maximum Index Density Weight on sample inside sleeve Vibratory table Maximum Index Density Weight on sample inside sleeve Vibratory table Maximum Index Density Sample densified by vibration Measure D height to determine new gd Plate on which weight sits during vibration 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 Gs g water e 1 g dry Minimum and Maximum Void Ratios First emax Calculate void ratio at Minimum gd Gs g water 2.65 62.4 1 1 0.7225 g dry 96.0 Next emin Calculate void ratio at Maximum gd Gs g water 2.65 62.4 1 1 0.5033 g dry 110.0 Relative Density Equation emax emeasured Rd (%) x100 emax emin Diagram below illustrates a relative density of about 40 % emin gdmax emeasured gd measured increasing density emax gd min 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: Gs g water 2.65 62.4 e 1 1 0.6133 g dry 102.5 Compute Relative Density Now, use the values of void ratio in the relative density equation: emax emeasured Rd (%) x100 emax emin 0.7225 0.6133 Rd (%) x100 49.9% 0.7223 0.5033 Compute Relative Density Relative Density Equation (rewritten in dry density terms) Solve for Example: g d maxg d g d min Rd (%) 100 g d g d max g d min 110.0102.5 96.0 Rd (%) 100 49.8% 102.5110.0 96.0 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 70 % Relative Density vs. 1 Point Proctor 130 125 70 % Relative Density 120 115 110 Best fit correlation 105 100 70 %RD = 1 Point line 95 90 90 95 100 105 110 115 120 Field 1 Point Proctor Test Dry Density, pcf 125 130 70 % Relative Density vs. 1 Point Proctor Conclusion is that the field 1 point Proctor dry test is about equal to 70 % relative density 50 % Relative Density vs. 1 Point Proctor 125 120 best fit line 50 % Rd 115 110 105 100 95 % of 1 point 95 90 90 95 100 105 110 115 Field 1 pointdry density 120 125 130 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 Relative Density Estimates from FW SML Study gD 70= 1.075 x gd 1pt -9.61, for RD70 and gd 1pt in lb/ft3 gD 50 = 1.07 x gd 1pt - 12.5, for RD50 and gd 1pt in lb/ft3 Relative Density Estimates from FW SML Study Example Relative Density Estimates – Given: 1 Point Proctor Test gd = 105.5 pcf – Estimate 70 % and 50% Relative Density – Given that measured gd is 98.7, evaluate state of compaction of sand. Review of Relative Density Class Problem - Relative Density – A soil’s 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 % Class Problem Solution Given: Minimum index density is 96.5 pcf Maximum index density is 111.5 pcf. emax Gs g water 2.65 62.4 1 1 0.7136 g min_dry 96.5 emin Gs g water 2.65 62.4 1 1 0.4831 g max_dry 111.5 Class Problem Solution Now, substitue a value for RD of 70(%) in the relative density equation emax emeasured Rd (%) x100 emax emin 0.7136 emeasured 70 x100 0.7136 0.4831 Class Problem Solution Solving and Rearranging the equation: 0.7136 emeasured 70 x100 0.7136 0.4831 0.7136 emeasured 70 100 .2305 0.16135 0.7136 emeasured emeasured 0.7136 0.16135 0.5225 Class Problem Solution Now, calculate a value for dry density at this void ratio: Gs g water e 1 g dry 2.65 62.4 1.55225 g dry Summary 2.65 62.4 0.55225 1 g dry g dry 165 .36 106 .5 lb 1.55225 ft 3 - The dry density corresponding to 70(%) relative density for this sample is 106.5 pcf 140 Other information on Relative Density 130 Dry Density, pcf Gravelly sand 120 sand and silty sand 110 100 90 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. 80 0 10 20 30 40 50 60 Relative Density, % 70 80 90 100 Other information on Relative Density 45 Chart is for silty sands (SM) Saturated Water Content, % 40 35 30 Average 25 20 15 Reference ભ Donovan, N.C. and Sukhmander Singh, "Liquefaction Criteria for the Trans-Alaska Pipeline." Liquefaction Problems in Geotechnical Engineering, ASCE Specialty Session, Philadelphia, PA, 1976. 10 5 0 10 20 30 40 50 60 Relative Density, % 70 80 90 100 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? Class Problem Solution Reading from the chart, the estimated Rd value is about 42 percent.