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  1. 1. Source: GEOTECHNICAL ENGINEERING 7 Particle Size and Gradation 7.1 GRAIN SIZES AND ORDERS OF MAGNITUDE 7.1.1 Size Ranges or Grades The individual particles that make up a soil vary in size by orders of magnitude. For example, the size difference between a 0.002 mm clay particle and a 2 m diameter boulder is 6 orders of magnitude, or about the same as between a Volkswagen and the Moon. It therefore is convenient to define particle size grades by defining discrete ranges in particle sizes that define clay, silt, sand, gravel, cobbles, and boulders. Each size grade covers a range in particle sizes––that is, all gravel particles obviously are not the same size. ‘‘Clay’’ thus defined relates to a range in particle sizes without regard to their mineralogy. However, because of a relationship between weatherability of different minerals and particle size, most clay-size particles are composed of the special group of minerals designated as clay minerals. A particular soil therefore will consist of varying percentages of clay, silt, and sand sizes with occasional coarser material. 7.2 GRADATION CURVES 7.2.1 Logarithmic Grain-Size Scale Because of the broad range in particle sizes that can make up a particular soil, sizes are conveniently plotted on a logarithmic scale. The advantage becomes apparent by comparing Fig. 7.1, where sizes are plotted on a linear scale, with Fig. 7.2, where the size distribution for the same glacial till soil is plotted logarithmically. Figure 7.2 also shows the huge variations in particle sizes between some common soils deposited by wind, water, and ice. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) 143 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
  2. 2. Particle Size and Gradation 144 Geotechnical Engineering Figure 7.1 Plotting particle sizes to a linear scale emphasizes the wrong end of the size scale—the gravel and not the clay. Figure 7.2 Semilogarithmic graph of the same particle size data for the glacial till soil and for several other soils. 7.2.2 Particle Size Accumulation Curves The graphs in Figs. 7.1 and 7.2 show particle size data as ‘‘percent finer’’ than each size on a dry-weight basis. This is a particle size accumulation curve. Figure 7.3 shows the relationship between an accumulation curve and a bar graph or histogram representation of the same data. The data are obtained by passing soil through a succession of progressively finer sieves and weighing the amount retained on each sieve. The bar heights in the upper graph show each of these amounts. Mathematically the upper graph is the differential or slope of the lower graph, which is the particle size distribution curve. Conversely, the lower graph represents the integral of the upper graph. The median or average grain size can be read directly from a particle size accumulation curve, as shown by the arrows in Fig. 7.3. The median grain size is defined on the basis that 50 percent of a soil by weight is finer, and 50 percent is Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
  3. 3. Particle Size and Gradation Particle Size and Gradation 145 Figure 7.3 Relation between a particle size accumulation curve showing a median grain size and a histogram showing modal sizes. coarser. In Fig. 7.3 this percentage occurs at 0.021 mm, which is in the size range for silt. The median grain size is designated by D50. Another reference size that has been found to relate to the permeability or hydraulic conductivity of soils is D10. Example 7.1 What is D10 for the soil in Fig. 7.3? Answer: Slightly smaller than 0.001 mm. 7.2.3 Modes The highest bar on a histogram data plot indicates a dominant particle size, which is designated the mode. Although a mode is not the same as a median size, in Fig. 7.3 the two are close because of the symmetrical shape of the major portion of the histogram. This symmetry reflects a statistical normal distribution, not of particle sizes, but of logarithms of the particle sizes because particles settle out of a suspension according to the square of their diameter instead of their diameter. In Fig. 7.3 another mode occurs in the clay size range smaller than 0.002 mm, probably due in part to clay adhering to coarser grains when they settled out. Two or more modes also can indicate soil mixtures, as when two strata are combined in one sample or sand has infiltrated into interstices in a gravel deposit. B horizon soils are bimodal because of infiltration by clay from the A horizon. Engineered soils often are mixtures in order to improve their engineering properties. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
  4. 4. Particle Size and Gradation 146 Geotechnical Engineering While a histogram is instructive, an accumulation curve is easier to plot and is almost universally used in engineering. Modes occur on an accumulation curve where slopes are steepest, and component soil percentages are indicated where the curve flattens out. Example 7.2 Large samples of glacial till often contain a mix of different component soils. What are component percentages in the glacial till in Fig. 7.2? Answer: The first steep section of the curve is at 41%, which therefore represents one component soil. The second break is at 60% so the difference is 60 – 41 ¼ 19%, which represents a second component. Similarly, the third break at 90% defines 90 – 60 ¼ 30% for a third component, and a fourth component makes up the remaining 10%. The three components percentage are 41 þ 19 þ 30 þ 10 ¼ 100%. The respective soils are (a) mainly clay plus some silt, (b) all silt, (c) mainly fine sand, and (d) a mixture of coarse sand and gravel. 7.3 DEFINING SIZE GRADES 7.3.1 Making the Grades Not all sand particles are exactly the same size, which means that ‘‘sand’’ must cover a range of particle sizes, the only requirement being that they are smaller than gravel and larger than silt grains. Natural size boundaries occur between gravel and sand, between sand and silt, and between silt and clay, but the boundaries are transitional and somewhat arbitrary, and different organizations have adopted different definitions. Gravel particles require a higher water velocity to be moved than sand, and wind does not move them at all. Sand particles move by bouncing, or saltation, and silt grains are mainly carried in suspension, as the mud in muddy water or the dust in air. Clay particles are so fine that they are very slow to settle out of suspension and consist of separate mineral species, the clay minerals. 7.3.2 Sieve Sizes Soils are separated into size grades by sieving, or sifting through a series or ‘‘nest’’ of standardized wire mesh sieves arranged from the coarsest down to the finest. Common sieve sizes used in engineering are listed in Table 7.1. A sieve is a wire fabric, so the sieve number does not describe the size of the opening but designates the number of wires per inch or millimeter. As a matter of convenience some size grades are defined on the basis of standard sieve sizes: gravel, for example, commonly designates particles that are coarser than 2 mm, which is the size of the opening in a No. 10 (wires to the inch) sieve. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
  5. 5. Particle Size and Gradation Particle Size and Gradation 147 No. (wires per inch) Opening, mm Comment Table 7.1 (Lid) –– Standard sieve sizes 4 4.75 Gravel used in geotechnical 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.0 . . . . . . . . . Size separating gravel and sand engineering 20 0.85 À 40 0.425 60 0.25 Sand 140 0.106 # 200 . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.075 . . . . . . . . . Size separating sand from silt (Pan) –– Silt and clay fall on through and collect in the pane One complication is that sieve openings are not round; they are approximately square. Spherical particles can pass through regardless of their orientation, but few soil grains are spheres. Sieves therefore are vigorously shaken or vibrated for a prescribed time in a sieve shaker in order to achieve reproducibility of the data. 7.3.3 Details of the Gravel-Sand Size Boundary Although the most common size boundary between sand-size and gravel-size particles is 2 mm, this size separation is not universal, even within geotechnical engineering. The Unified Soil Classification System used in earth dam and foundation engineering makes the separation at the No. 4 (3/16 in.) sieve, and material from 4.76 to 2 mm in diameter is considered ‘‘very coarse sand.’’ These and other size boundaries are indicated in Fig. 7.2 Because the boundaries differ, it is important that they be defined or included on graphs showing the particle size distribution, as indicated by the vertical lines and grade names across the bottom in Fig. 7.2. 7.3.4 The Sand-Silt Size Boundary As silt particles are fine enough to be carried in suspension they show little or no rounding of corners, whereas sand particles typically are abraded and rounded at the corners and edges from having been transported and bounced along by wind or water. However, the boundary is transitional, and for convenience it often is defined on the basis of a sieve size. In geotechnical engineering practice the boundary between sand and silt usually is that of a 200-mesh sieve opening, 0.075 mm or 75 mm (micrometers). The earlier designation was ‘‘microns.’’) Sand therefore presents a range in particle sizes between 0.074 and 2 mm diameter, a size ratio of 27. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
  6. 6. Particle Size and Gradation 148 Geotechnical Engineering Soil scientists prefer to make the separation between sand and silt at 0.020 mm or 20 mm. However, as shown by the loess and sand soils in Fig. 7.2, the natural boundary may be closer to the No. 200 sieve (0.074 mm) or even slightly larger. Geologists sometimes use 1/16 mm ¼ 0.067 mm, sometimes rounded off to 0.06 mm. However, the occurrence of a natural break in the general vicinity tends to diminish the influence on constituent percentages. 7.3.5 The Silt-Clay Size Boundary The most widely accepted size definition of clay is particles that are finer 0.002 mm or 2 mm. An earlier definition was based on the resolving power and eyepiece calibration of a light microscope at the U.S. Bureau of Soils, and set the boundary at 0.005 mm (5 mm). Later mineralogical investiga- tions showed that this boundary is too high, but meanwhile it became estab- lished and still is occasionally used in geotechnical engineering. The 0.005 mm size also requires less interpolation from measurements that routinely are made after 1 hour and 1 day testing time. This is discussed in more detail in section 7.4.6. 7.3.6 Silt-Clay Boundary Based on Physical Properties Another approach is to define clay on the basis of its plasticity or moldability with water, as silt is crumbly while clay is sticky and can be molded into different shapes. These relationships are quantified by two simple tests called Atterberg limits. These tests and the relationship to engineering soil classifications are discussed in Chapter 12. The limits define a moisture content range over which a soil can be molded. This range is the plasticity index, which is a fundamental soil property in geotechnical engineering. In order to avoid possible confusion between the two approaches, a clay content based on particle size may be referred to as clay-size material. 7.4 MEASURING PARTICLE SIZES 7.4.1 General Approach to Size Measurement Some shortcuts are in order because so many particles must be measured in order to obtain statistical reliability. One shortcut is to use sieves and screen a representative soil sample. Another approach that is used for particle sizes too small to be separated on sieves is to disperse the soil in water and make a determination based on the sedimentation rate, with largest particles settling the fastest. One of the most important steps in analysis is obtaining a representative soil sample. Large samples are spread out on a flat surface and ‘‘quartered,’’ Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
  7. 7. Particle Size and Gradation Particle Size and Gradation 149 that is, cut into four pie-shaped sectors and then combining opposing sectors and returning the other half of the sample to the bag. This procedure is repeated until the soil sample is small enough to be managed. A more rapid method for quartering uses a ‘‘riffle-type’’ sample splitter that has parallel shuts, with half directing the sample one way and the other half the other. Soils are air-dried prior to quartering and sieving, but as discussed in Chapter 6, if a soil contains halloysite clay mineral, it should be saved and sealed against drying. 7.4.2 Sedimentation Analysis Sieving is appropriate for measuring the amounts of sand and gravel in a soil, but silt and clay sizes are too small to be separated by sieving. Also, clay particles tend to be aggregated together into coarser particles and to occur as coatings on coarser particles. Gravel is removed by sieving, and the rest of the soil normally is soaked in water and then agitated and dispersed using a chemical dispersing agent. The suspension then is tested by measuring sedimentation rates, and finally the part of the soil that is retained on a fine sieve is dried and analyzed by sieving. The general procedure is as follows. After sieving to remove gravel and coarser particles, the soil is soaked in water containing a small amount of a chemical dispersing agent, usually sodium hexametaphosphate, a water softener that is available in the detergent department of a supermarket. The dispersing agent forces substitution of sodium ions for exchangeable calcium ions on the clay by creating an insoluble phosphate precipitate. The suspension then is agitated for a set amount of time with a standardized mechanical or air-jet stirring device. Ideally this will separate but not break individual soil grains. The soil suspension is diluted to 1 liter in a vertical flask and stirred in preparation for starting the test. The starting time is noted and the suspension is allowed to settle for various time intervals. After each time interval, the density of the suspension is determined at a particular depth with a hydrometer. An alternative method is to sample the suspension with a pipette, then dry and weigh the sample. The larger the weight of particles remaining in suspension, the denser the liquid, and the higher the hydrometer will float. An engineering hydrometer is calibrated to read directly in grams of soil per liter of suspension. Readings normally are taken after 1 minute and at various time intervals to 1 hour and then after 24 hours. After the sedimentation analysis is completed, the soil is washed on a fine sieve to remove the silt and clay particles, then dried and the sand fraction analyzed by passing through a series of sieves. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
  8. 8. Particle Size and Gradation 150 Geotechnical Engineering Figure 7.4 Sampling theory in sedimentation analysis: at a particular sampling depth the suspension contains a representative sample of all sizes smaller than the size that will settle to that depth. 7.4.3 Sedimentation and the Percent Finer A sedimentation analysis automatically measures the amounts finer than a specific grain size. This is illustrated in Fig. 7.4: after a certain time all particles larger than a certain depth have settled a calculated distance and therefore cannot occur at depths shallower than that distance. On the other hand, finer particles remain suspended and therefore are measured. After each hydrometer reading the hydrometer is removed so that particles will not settle on the bulb. Removal stirs a small portion of the upper part of the suspension, but the effect is small so long as particles move horizontally and not vertically relative to the suspension—as the instrument is removed, the level of the suspension goes down, and when it is replaced the level goes back up. The depth to the center of volume of the submerged part of the hydrometer is the effective sampling depth that is used in the calculations, and depends on the depth of sinking. This depth is obtained from a calibration chart or table, Table 7.2. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
  9. 9. Particle Size and Gradation Particle Size and Gradation 151 Hydrometer reading, g/l Depth, mm Table 7.2 5 155 Depth to hydrometer 10 147 center of volume 15 138 20 130 25 122 30 114 35 106 40 97 45 89 50 81 Note: Adapted from ASTM Designation D-422. Temperature also must be controlled and measured to enable correction for changes in the fluid viscosity. 7.4.4 Stokes’ Law of Sedimentation In 1851 a British mathematician, G. G. Stokes, solved for the settlement velocity of spherical particles in a suspension by equating their buoyant weight to viscous drag on the outer surfaces. Surface area increases in proportion to the radius while weight increases as the radius cubed, so the larger the particle, the faster it will settle. The classic derivation for Stokes’ formula in the cgs system is R ¼ 6%rv ð7:1Þ where R is the resisting force in g cm/s2, r is the particle radius in cm, is the fluid viscosity in poise or g-cmÀ1sÀ1, and v is the settlement rate in cm/s. Equating to the buoyant weight of a spherical soil grain gives 4 6%rv ¼ %r3 ð À w Þg ð7:2Þ 3 where and w are respectively the density of the soil grain and that of water, and g is the acceleration of gravity. Solving for velocity v gives 2ð À w Þgr2 v¼ ð7:3Þ 9 Thus, the settlement rate v depends on the square of the particle radius r. Experiments have confirmed the validity of the formula for particles between 0.001 and 0.10 mm in size, that is, for silt and most clay particles. Sand sizes are influenced by mass displacement considerations that slow their rates of sinking, Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
  10. 10. Particle Size and Gradation 152 Geotechnical Engineering and sizes smaller than about 0.001 mm settle more slowly. In 1827 an English botanist, Robert Brown, noticed that pollen grains suspended in water jiggled about when observed in a microscope, a movement that now is called Brownian motion. This grabbed the attention of an employee of the Swiss patent office, who wrote a brief paper attributing it to random molecular bombardment. The employee’s name was Albert Einstein, who later became famous for another matter. Particles smaller than about 0.001 mm tend to remain in suspension and are referred to as colloidal size particles. According to eq. (7.3) the rate of settling depends on the specific gravity of the particles, which varies depending on the mineral. Because sedimentation is a bulk test, an average specific gravity is used in the calculations for particle size. A method for measuring average specific gravity is described later in this chapter. However, the assumption that all grain densities are average means that particles of dense minerals will be reported as larger than their true dimensions because they settle faster. Sedimentation rate is influenced by the fluid viscosity, , which in turn depends on temperature. A standardized temperature of 208C (688F) is used for laboratory analyses. Other temperatures may be used with appropriate correction factors based on viscosity tables. An obvious limitation of Stokes’ Law is that it applies only to spherical particles, whereas silt grains are angular and clay particles flat. Particle sizes determined from sedimentation rates often are reported in terms of ‘‘equivalent particle diameters.’’ 7.4.5 Simplifying Stokes’ Law In eq. (7.3), a particle radius in cm equals the diameter 0.05D in mm. The settling velocity in cm/s equals 600L/T, where L is the settling distance in mm and T is time in minutes. Substituting values for the acceleration of gravity and the viscosity gives pffiffiffiffiffiffiffiffiffiffiffiffiffiffi D ¼ K L=10T ð7:4Þ where D and L are in mm and T is in minutes. K depends on the specific gravity of the soil and temperature of the solution; with a representative soil specific gravity of 2.70, and a standardized temperature of 208C, K ¼ 0.01344. Other values for this coefficient for different specific gravities and temperatures are given in ASTM Designation D-422. Example 7.3 A soil suspension is prepared containing 50 g/l. After 60 minutes the hydrometer reads 22 g/l. The temperature is controlled at 208C. (a) What particle diameter is being measured, and (b) what is the percent of particles finer than that diameter? Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
  11. 11. Particle Size and Gradation Particle Size and Gradation 153 Answer: (a) The effective depth of the hydrometer is obtained by interpolation of data in Table 7.2, which gives L ¼ 127 mm. From eq. (7.4), pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D ¼ 0:01344 127=10 Â 60 ¼ 0:0062 mm ¼ 6:2 mm: (b) P ¼ 100 Â 22/50 ¼ 44%. 7.4.6 Interpolating the Percent 2 mm Clay from Hydrometer Analyses The sedimentation time for a hydrometer analysis to measure 2 mm clay is approximately 8 hours, which is inconvenient with an 8-hour working day. However, as this part of the accumulation curve often is approximately linear on a semilogarithmic plot, the percent 2 mm clay can be estimated from a proportionality of the respective logarithms. As an approximation, P002 ¼ 0:4P001 þ 0:6P005 ð7:5Þ 7.5 USES OF PARTICLE SIZE DATA 7.5.1 Median Grain Size As previously mentioned, the size that defines 50 percent of the soil as being finer and 50 percent coarser is the median grain size, designated as D50, and is read from the intersection of the particle size distribution curve with the 50 percent line, as shown in Fig. 7.3. The median approximates but is not the same as a mean or average particle size, which would be very difficult to determine because it would involve measuring many individual particles and calculating an average. 7.5.2 Effective Size and Uniformity Coefficient A measurement that often is made for sand is the effective size, D10, or the size whereby 10 percent of the particles are finer, and was shown by an engineer, Allen Hazen, to correlate with the permeability of filter sands. Hazen defined the uniformity coefficient, Cu, as the ratio D60/D10. The uniformity coefficient can be as low as 1.5 to 2 for washed sands that are nearly all one size. For engineer- ing uses a soil is said to be ‘‘well graded’’ if it contains a wide range of particle sizes. A well-graded sand-gravel mixture may have a uniformity coefficient of 200–300. Example 7.4 The sand in Fig. 7.2 has approximate values of D10 ¼ 0.12 mm and D60 ¼ 0.20 mm, from which Cu ¼ 1.7. For engineering purposes this soil would be described as ‘‘poorly graded.’’ Because D10 is off the chart for fine-grained soils, another measure for degree of uniformity suggested by a geologist, Trask, is the ‘‘sorting coefficient,’’ So, which Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
  12. 12. Particle Size and Gradation 154 Geotechnical Engineering Table 7.3 Sieve number Weight percent retained Weight percent finer Mechanical analysis (particle diameter in mm) on each sieve data and Sieve analysis: determinations of No. 4 (4.76) 0 100 weight percents finer No. 10 (2.0) 4 100 – 4 ¼ 96 than sizes indicated No. 20 (0.84) 4 96 – 4 ¼ 92 No. 40 (0.42) 3 92 – 3 ¼ 89 No. 60 (0.25) 7 89 – 7 ¼ 82 No. 100 (0.147) 4 82 – 4 ¼ 78 No. 200 (0.075) 13 78 – 13 ¼ 65 Sedimentation analysis: (0.025) Hydrometer reading ¼ 52 (0.010) ‘‘ 31 (0.005) ‘‘ 21 (0.001) ‘‘ 8 is defined as (D75/D25)1/2. A more complicated calculation also may be made to obtain a statistical standard deviation. 7.5.3 Example of Mechanical Analysis Measurement of soil particle sizes is called a ‘‘mechanical analysis.’’ Data from a mechanical analysis are shown in Table 7.3. The percent 0.002 mm clay is estimated from eq. (7.4), which gives D002 ¼ 0.4 Â 8 þ 0.6 Â 21 ¼ 16 percent finer than 0.002 mm. The various size grades are as follows: Size grade Calculated percent by weight Gravel (retained on No. 10 sieve) 4 Sand (retained on No. 200 minus % gravel) (100 – 65) – 4¼ 31 Silt (coarser than 0.002 mm minus % gravel and sand) (100 – 16) – 4 – 31¼ 49 Clay (finer than 0.002 mm) 16 Colloidal clay (finer than 0.001 mm) (8) Total 100 7.5.4 Granular vs. Fine-Grained Soils Concrete mixes are designed based on a concept that largest particles are touching, and progressively finer particles fill in the voids. The same concept applies to soils, and a broad range of particle sizes is considered to be ‘‘well Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
  13. 13. Particle Size and Gradation Particle Size and Gradation 155 graded.’’ If coarse grains are in contact and voids between them are filled with smaller particles, the soil must increase in the volume, or dilate, in order to shear. This adds appreciably to the shearing resistance. In many soils the silt and clay content are high enough to separate larger soil grains so that shearing can occur through the silt-clay matrix without dilatancy, which causes a marked reduction in the soil shearing strength. Artificial mixtures of sand plus clay show that this property change occurs at about 25 to 30 percent clay. The two distinct modes of behavior distinguish ‘‘granular soils’’ from ‘‘fine-grained soils.’’ 7.5.5 Soil Mixtures In Fig. 7.5 a poorly graded silt soil is combined with a poorly graded sand to obtain a more uniform grading. In this example the mix is 50–50, and the construction lines are shown dashed. A better grading could be obtained by reducing the percentage of A and increasing that of B. The effectiveness of an improved grading can be determined with strength tests. Geologists refer to a well- graded soil as being ‘‘poorly sorted,’’ which means the same thing even though the connotations are different. Flat portions of a particle size accumulation curve indicate a scarcity of those sizes, and a soil showing this attribute is said to be ‘‘gap-graded.’’ Gap grading tends to give lower compacted densities and strength, and higher permeability. 7.5.6 Soil as a Filter Filters are barriers that can transmit water while retaining soil particles that otherwise would be carried along in the water. Filter soils usually are sands. A common use of a filter is in the toe drainage area in an earth dam, where control Figure 7.5 Combining two poorly graded soils A and B to obtain a more uniform grading A þ B. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
  14. 14. Particle Size and Gradation 156 Geotechnical Engineering of seepage is important to prevent water from emerging on the earth slope where it might lead to piping and failure. Geotextile filters generally are more expensive but are easier to install than are layers of sand, and are less likely to be damaged or compromised during construction. Design Protective filters act as a drain while resisting clogging by fine particles. They also cannot permit a breakthrough, and may be required to provide insulation against frost action. The finer sizes of particles in a soil filter tend to control its performance. Generally the filter F15 size is compared with the D85 size for the base soil. (To avoid confusion the filter size is designated with F instead of D.) A conservative and acceptable guide for design is F15/D8555. An additional requirement for the retention of clay, for example in the core of an earth dam, is that F1550.5 mm. Example 7.5 Is the sand in Fig. 7.2 an appropriate filter for an earth dam constructed from the glacial till in the same figure? Answer: The sand has F15 ¼ 0.12 mm, and the till has D85 ¼ 0.4 mm. Then 0.12/ 0.4 ¼ 0.355, so the filter should perform adequately. In addition F1550.5 mm so there should be little or no clay penetration. Question: What if the dam is constructed from the loess in the figure? 7.5.7 Geotextile Filters The apparent opening size (AOS) of geotextile fabrics is defined as O95, which is the size for 95 percent of glass beads of a particular size grade to pass through during sieving (ASTM Designation D-4751). One criterion in regard to filtration of soil is that O95/D8552 or 3, where D85 is for the soil. 7.5.8 Grouting Grouting is pumping of a fluid under pressure into a soil so that it either (a) permeates the soil, referred to as injection grouting, or (b) displaces the soil, called compaction grouting. The determination of whether a grout will inject into the soil pores or displace the soil is mainly dependent on the relations between the respective particle sizes. Injection grouting is a common remedial treatment used to solidify loose foundation soil and rock underneath buildings, dams, and other structures. Injection grouting also is used to seal leaks under dams or lagoons, to seal off and contain buried hazardous wastes, and to seal off the groundwater aquifers in preparation for tunneling. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
  15. 15. Particle Size and Gradation Particle Size and Gradation 157 Compaction grouting is a relatively new procedure that normally is intended to laterally compact and densify loose soil to reduce settlement under a foundation load. Regardless of the grouting procedure the maximum grouting pressure is limited by the overburden pressure of the soil, or lateral planar injections can lift the soil. When this occurs, pumping pressure should decrease while the pumping rate increases, referred to as the grout ‘‘take.’’ If the lateral stress existing in the soil is lower than the vertical pressure from overburden, the pumping pressure at which the ‘‘take’’ occurs is that which causes vertical radial cracking and is used as an approximate measure of lateral stress in the soil. This is called ‘‘hydraulic fracturing.’’ It was first developed in the petroleum production industry to increase the flow of oil into oil wells. Grout Materials The most common grout materials for rocks and soils are aqueous suspensions of Portland cement and/or fly ash. Sand-cement mortar may be used for grouting rubble that has large voids. Bentonite sometimes is used as a sealing grout, but has the disadvantage that it will shrink and crack when it dries out. The first injection grout was developed by Joosten in Germany and uses chemical solutions of sodium silicates and calcium chloride, which react to make insoluble calcium silicate and sodium chloride. Some more recent chemical solution grouts have been removed from the market because of potentially toxic effects on groundwater. Emulsions of asphalt in water are sometimes used as grout for sealing cracks and joints in basements. Soil Groutability For injection grouting the particle size ratio is reversed from that used design- ing filters, D15 for the soil and G85 for the grout. To ensure success, the ratio should be substantially higher than the corresponding ratio of 5 used for filters. Tests by the U.S. Army Corps of Engineers suggest that the ratio of soil D15 to cement G85 should be a minimum of 20. G85 for Portland cement typi- cally is about 0.040 to 0.050 mm. The smaller figure represents high-early strength cement, and also is fairly representative of fly ashes. Specially ground cements may have G85 of only 0.005 mm. Bentonite is composed of montmorillonite particles that expand on wetting, with an effective hydrated G85 of about 0.030 mm. Example 7.6 Can any of the soils of Fig. 7.2 be injection grouted with cement grout? Answer: The soil with the largest D15 is the sand, with D15 ¼ 0.12 mm. For cement, assume G85 ¼ 0.050 mm. Then D15/G85 ¼ 2.4 ( 20, so this sand cannot be injected with cement Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
  16. 16. Particle Size and Gradation 158 Geotechnical Engineering grout. The sand still may be a candidate for compaction grouting or injection grouting with chemical solutions, depending on the properties that are required. As a general guide: Gravel or very coarse sand can be injection grouted with cement and/or fly ashs. Medium to fine sand can be compaction grouted with cement/fly ash or injection grouted with sodium silicate or specially ground fine cement. Silt can be compaction grouted. Clay cannot be grouted, but expansive clay can be stabilized by a diffusion process of hydrated lime, which is much slower than the other processes. Partly because of the difficulty in controlling injection grouting and knowing where the grout goes, compaction grouting has become increasingly popular in recent years. 7.6 DESCRIBING PARTICLE SHAPE 7.6.1 Particle Shape and Engineering Behavior The shapes of soil grains can influence engineering behavior, as round grains obviously are more likely to slip and roll than angular fragments that mesh or interlock together. For this reason crushed rock normally creates a stronger surface of a ‘‘gravel’’ road than do the more rounded particles of gravel. On the other hand gravel, having been through many cycles of pounding against a beach or river bottom, is more likely to be harder and less likely to degrade into dust. The main effect of angularity is harshness, or the tendency for the soil to dilate or increase in volume during shearing, a matter that can be quantified with strength tests. Grain shapes closely relate to their mineralogy and origin; quartz sand grains derived from disintegration of granite tend to be round, whereas grains of feldpar derived from the same rock are more angular, and grains of mica are flat. Alluvial gravel generally is well rounded, sand less so, and silt not at all. Dune sand not only shows rounding, but the grain surfaces are etched from repeated impacts. The measurement of shapes of individual grains can be time-consuming, but measurement of grain profiles can be digitized and automated. A chart that can be used to estimate shape, or ‘‘sphericity,’’ is shown in Fig. 7.6. Sphericity theoretically is the ratio of a grain surface area to that of a sphere, but can be approximated by dividing the intermediate grain width by its length. As this does Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
  17. 17. Particle Size and Gradation Particle Size and Gradation 159 Figure 7.6 Chart for evaluating the shapes of individual soil grains from their profiles, 1.0 representing the approach to a sphere. not take into account the shortest grain dimension, it tends to overestimate sphericity of flat particles such as mica. 7.6.2 Special Problems with the Shape of Mica Grains Especially troublesome, is that mica particles are flat and also are springy, so compacting a soil with a high content of mica is like trying to compact a bucket of springs. Although micaceous soils are not common, their behavior is such that they are given a special category in some engineering classifications, and the glitter is not gold. 7.7 TEXTURAL CLASSIFICATION OF SOILS 7.7.1 Describing Different Proportions of Sand þ Silt þ Clay The first step in characterizing grain sizes in a soil is to take the soil apart and assign the component parts to size grades, namely gravel, sand, silt, and clay. Next let us describe the products when we put them back together. A naturally occurring gravel deposit almost inevitably will contain some sand, and a naturally occurring silt deposit almost inevitably will contain some clay, so when does it stop having ‘‘silt’’ for a soil name and start being a ‘‘clay’’? ‘‘Clay’’ therefore can mean either (a) clay mineral, (b) clay size, or (c) a deposit or soil that is mainly clay but also contains other minerals and grain sizes. Engineers tend to use a term such as ‘‘clay’’ interchangeably for its several meanings, and should be certain that it is used in a context that ensures that everybody will know what it means. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
  18. 18. Particle Size and Gradation 160 Geotechnical Engineering Figure 7.7 A soil textural chart based on the 0.075 mm definition of silt size and the 0.002 mm definition of clay size. 7.7.2 Soil Textures and Particle Sizes Soil scientists who do soil mapping in the field originally proposed the term ‘‘texture’’ to describe the ‘‘feel’’ of moist soil squeezed with the fingers. A soil might have a gritty or sandy feel, or it might have a smooth feel, more like modeling clay. ‘‘Loam’’ came to mean a somewhat loose and crumbly feel that is great for agriculture. Soil textures are quantified by relating them to the percentages of sand, silt, and clay. The various ranges are shown on a triangular ‘‘textural chart’’ such as Fig. 7.7. Boundaries on textural charts have been changed from time to time as size definitions have changed, but the concept remains valid and useful. The textural chart is read by entering any two of the three percentages and moving onto the chart in the directions of the corresponding short lines around the edges. For example, the boundary between clay and clay loam is at 30 percent clay-size material. It will be seen that a clay texture can contains as much as 55 percent sand. However, to qualify as a sand texture the soil must contain over 80 percent sand. Textural terms apply to the non-gravel portion of a soil, so the percentages are adjusted for gravel content. If the gravel content exceeds 10 percent the soil is ‘‘gravelly.’’ Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
  19. 19. Particle Size and Gradation Particle Size and Gradation 161 Example 7.7 What is the textural classification for the soil in Section 7.5.3? Answer: The soil contains 31% sand and 49% silt. These figures are adjusted for the 4% gravel content: 31/0.96 ¼ 32.6% sand and 49/0.96 ¼ 51.0% silt. The texturally is ‘‘silty clay loam.’’ 7.8 SPECIFIC GRAVITY OF SOIL PARTICLES 7.8.1 Definition and Use Specific gravity is defined as the density of a material divided by the density of water at 48C, which is water at its densest. According to eq. (7.3) the specific gravity is required in order to interpret settlement analyses. Some representative specific gravities for different minerals are shown in Table 7.4. Most sands have a specific gravity of 2.65–2.68; most clays, 2.68–2.72. 7.8.2 Measurement A common method for measuring the specific gravity of a large object is to weigh it in air and then submerge it in water. The difference equals the weight of the water displaced, a discovery made by Archimedes in his search for a way to determine the purity of gold. The weight divided by the weight lost therefore Gold 19.3 Terribly expensive Table 7.4 Silver 10.5 Pocket change Specific gravities of Galena (PbS) 7.5 Cubes that look like silver but aren’t some selected solids Pyrite (FeS2) 5.0 Cubes that look like gold but aren’t Hematite (Fe2O3) 4.9–5.3 Red iron oxide in soils Limonite (Fe2O3 nH2O) 3.4–4.3 Yellow or brown iron oxides in soils Iron silicate minerals 2.85–3.6 Dark minerals in basalt, granite Calcite (CaCO3) 2.72 Most abundant mineral in limestone Micas 2.7–3.1 Flakey Quartz(SiO2) 2.65 Most abundant mineral in soils Feldspar (Na and Ca silicates) 2.55–2.65 Most abundant mineral in rocks Kaolinite 2.61 Clay mineral Smectites 2.2–2.7 Expansive clay minerals Glass 2.2–2.5 Lead glass ¼ 3 Halite (NaCl) 2.1–2.3 Rock salt Liquid water (H2O) 1.00 At its densest, 48C Ice (H2O) 0.918 Floats on liquid water Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
  20. 20. Particle Size and Gradation 162 Geotechnical Engineering represents the weight divided by the weight of an equal volume of water, which by definition is the specific gravity: W G¼ ð7:6Þ W À Wb where G is the specific gravity and W and Wb are the weight and buoyant weight respectively. A slightly different procedure is used for soils and is a bit more tricky. A flask is filled with water and weighed; call this A. Then W, a weighed amount of soil, is put into the flask and displaces some of the water, giving a new total weight, C. As shown in Fig. 7.8, the weight of the water displaced is (A þ W À C). Hence, W G¼ ð7:7Þ AþWÀC Experimental precision is unhappy with subtracting a weight from the denominator, so measurements are exacting. Recently boiled or evacuated distilled water ensures that there is no air that might come out of solution to make bubbles, and clay soils are not previously air-dried. Less critical is a temperature-dependent correction for the specific gravity of water, which at 208C is 0.99823. (Specific gravities are reported to three significant figures.) Details are in ASTM Designation D-854. It will be noted that weights and not masses are measured, even though the data are usually recorded in grams. Example 7.8 A flask filled to a reference mark with water weighs 690.0 g on a laboratory scale. When 90.0 g of soil are added, the filled flask weighs 751.0 g. The water temperature is 208C. (a) What is G? (b) What effect will the temperature correction have? (c) What if as a result of measurement error the soil weight is 1 g too high, an error of 1.1%? Fig. 7.8 Using a pycnometer to measure specific gravity. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
  21. 21. Particle Size and Gradation Particle Size and Gradation 163 Answer: (a) G ¼ 90/(690.0 þ 90.0 – 746.0) ¼ 2.65. (b) Dividing by 0.998 to correct for water temperature does not affect the answer. (c) G0 ¼ 91/(690 þ 91 – 746) ¼ 2.53. A suggested assumed value would be more accurate. Problems 7.1. Plot a particle size accumulation curve for soil No. 4, Table 7.5, by enter- ing the data on a computer spreadsheet and selecting the logarithmic option for the particle sizes. (Optionally this can be done manually using 5-cycle semilogarithmic paper.) (a) Evaluate the effective size and unifor- mity coefficient. (b) What is the median grain size? (c) Defining clay as 50.002 mm, silt as 0.002–0.074 mm, sand as 0.074–2.0 mm, and gravel as 42.0 mm, what are the percentages of clay, silt, sand, and gravel? 7.2. Classify soil No. 4 according to the chart in Fig. 7.7 after adjusting the percentages for gravel content. 7.3. Plot a particle size accumulation curve for soil No. 1, Table 7.5. (a) Identify the median and mode(s). (b) If there are two modes, what is the approxi- mate percentage of each soil in the mixture? (c) Using the size grades defined in Problem 7.1, find the percentages of clay, silt, sand, and gravel. (d) Adjust the grade percentages for gravel and classify the soil by the chart in Fig. 7.7. 7.4. Calculate the effective size and uniformity coefficient for soil No. l. Answer: D10 ¼ 0.0039 mm, Cu ¼ 192. 7.5. By inspection indicate which of the soils in Table 7.5 should be designated as gravelly. 7.6. For the first five soils in Table 7.5 compare measured 0.002 mm clay contents with those interpolated from the 0.001 mm and 0.005 mm clay contents by eq. (7.5). 7.7. What is meant by a ‘‘well-graded’’ soil? What is the reason for considering such a soil to be well graded? 7.8. Which soils in Table 7.5 can be injection-grouted with a mixture of Portland cement, fly ash, and water? 7.9. Soil No. 12 in Table 7.5 is to be separated from No. 14 by means of a filter. From the two particle size accumulation curves, define (a) desirable characteristics of a geotextile filter, (b) the gradation(s) required for soil filter(s): if a single filter layer is not adequate, use two. (c) Select appropriate soil(s) from the table to use as filter(s). Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
  22. 22. 164 Table 7.5 Sieve number and Sedimentation Mechanical analysis size of opening (mm) size (mm) of soils: percentage Soil 1 in. 3 in. 3 in. No. 4 No. 10 No. 40 No. 60 No. 100 No. 200 0.050 0.005 0.002 0.001 LL PI 4 8 Soil passing various No. 26.7 18.8 9.4 4.75 2.00 0.42 0.25 0.149 0.074 No. Geotechnical Engineering sieve sizes 1 100 90 80 72 67 56 44 34 24 21 11 7 4 29 7 1 2 100 99 98 97 96 91 80 71 63 34 25 18 39 14 2 3 100 99 96 92 80 73 41 31 23 76 21 3 4 100 97 84 66 50 32 24 5 4 4 54 16 4 5 100 96 85 61 34 31 13 10 7 69 7 5 6 100 95 88 80 54 25 14 5 35 10 6 7 100 99 98 95 9 7 6 80 9 7 8 100 97 76 60 45 35 21 10 35 17 8 9 100 95 88 81 65 59 18 11 6 27 5 9 10 100 99 97 93 70 58 56 44 42 24 17 11 41 12 10 11 100 98 92 82 50 42 35 28 25 12 8 5 38 16 11 Particle Size and Gradation 12 100 93 77 64 48 24 20 16 12 11 8 7 6 13 4 12 13 100 99 84 48 12 8 –– –– –– –– N.P. 13 14 100 99 95 93 68 49 34 86 49 14 15 100 79 60 48 34 30 14 11 9 24 8 15 Any use is subject to the Terms of Use as given at the website. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. 16 100 94 89 87 85 81 73 39 24 12 59 43 16 17 100 98 94 48 42 33 26 22 13 11 10 47 24 17 18 100 98 97 96 94 91 90 89 86 80 42 27 16 45 17 18 19 100 45 38 30 22 20 10 7 4 16 6 19 20 100 98 96 95 93 89 64 44 29 84 53 20 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com)
  23. 23. Particle Size and Gradation Particle Size and Gradation 165 7.10. Combine soils 1 and 3 in Table 7.5 in such proportions that the resulting mixture contains 20 percent 5 mm clay. Draw the particle size accumulation curve of the mixture. References and Further Reading Grim, Ralph E. (1962). Applied Clay Mineralogy. McGraw-Hill, New York. Koerner, Robert M. (1990). Designing with Geosythetics, 2nd ed. Prentice-Hall, Englewood Cliffs, N.J. Mitchell, J. K. (1993). Fundamentals of Soil Behavior, 2nd ed. John Wiley Sons, New York. Sherard, J. L., Dunnigan, L. P., and Talbot, J. R. (1984). (a) ‘‘Basic Properties of Sand and Gravel Filters,’’ and (b) ‘‘Filters for Silts and Clays.’’ ASCE J. Geotech. Engr. Div. 110(6), 684–718. Sherard, James L. (1987). ‘‘Lessons from the Teton Dam Failure.’’ Engng. Geol. 24, 239–256. Reprinted in G. A. Leonards, ed., Dam Failures, Elsevier, Amsterdam, 1987. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.