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Florida International UniversityDepartment of Civil and Environmental Engineering

CEG 4011 L Geotechnical Engineering I LaboratoryProf. Luis A. Prieto-Portar PhD, PE, SE.

Lab Report #03

Particle-Size Analysis Hydrometer (ASTM D-422)

Performed on 18 February 2009

Team Members:

Member Attendance Writing Assignment Completed

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03- Particle-size Analysis (Hydrometer) of a Soil

1) Introduction: The Theory behind the experiment.

The hydrometer analysis is a widely used method of obtaining an estimate of the distribution of soil particle sizes from the No. 200 (0.075 mm) sieve to around 0.001 mm. The data is plotted on a semi-log plot of percent versus grain diameters and may be combined with the data from a mechanical (sieve) analysis of the material retained on the No. 200 sieve.

A hydrometer is an elongated glass bulb with a long, thin glass stem rising from the top of the bulb. The bulb is hollow except for a plug of lead in the bottom. If the bulb is inserted into a suspension, it will sink until the force of buoyancy is just sufficient to balance the weight of the hydrometer. The hydrometer is designed to sink into the suspension until the bulb is totally immersed, and the stem protrudes above the surface of the suspension. Because the length of stem that protrudes above the surface is a function of the density of the suspension, more of the stem protrudes for denser suspensions. It is thus possible to calibrate the hydrometer to read various densities. Soil hydrometers are typically calibrated to read in g/ml or g/liter. Hence, an appropriate hydrometer can be inserted into a suspension and a reading taken to obtain the average concentration of the solids in the fluid displaced by the hydrometer. Because the hydrometer calibration is affected by temperature and the specific gravity of solids, these factors will have to be taken into account during the experiment.

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In this procedure, a soil specimen is first dispersed in water, and then allowed to have the soil particles settle individually to the bottom. By using Stokes’ law, the velocity of the particles can be found with the following equation:

(Eqn-1)

where v = velocity (cm/sec),γs = unit weight of the solids (g/cm3),γw = unit weight of water ( 1 g/cm3),η = the viscosity of water (g s/cm2), andD = the diameter of the solid particles.

It is assumed that Stokes’ law can be applied to a mass of dispersed soil particles of various shapes and sizes.   Larger particles settle more rapidly than the smaller ones.  The hydrometer analysis is an application of Stokes’ law that permits the calculation of the grain size distribution in silts and clays, where the soil particles are given the sizes of equivalent spherical particles. The density of a soil-water suspension depends upon the concentration and specific gravity of the soil particles. If the suspension is allowed to stand, the particles will gradually settle out of the suspension, and the density will be decreased.  

George Gabriel Stokes

Time t = 0 Time t = t

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The velocity is expressed as the increasing depth of the hydrometer L in time t, or,

and solving for the particle diameter D,

(Eqn-2)

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An ASTM 152-H hydrometer in a dispersed soil water solution.

The hydrometer shown above is measuring the specific gravity of the soil-dispersed water suspension at the depth L, known as the effective depth. The magnitude of the effective depth L can be computed by,

(Eqn-3)

where L1 is the distance between from top of the hydrometer bulb (the “0” mark) to the solution surface mark. For example, suppose that the hydrometer reading of zero is L1 = 10.5 cm. Now suppose that the hydrometer reads L1 = 2.3 cm for a 50 g/liter reading. The hydrometer reading is,

L2 = 14 cm,

VB = volume of the hydrometer bulb = 67.0 cm2, and

AC = the cross-sectional area of the hydrometer cylinder = 27.8 cm2.

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The variation of L with the hydrometer reading is shown in Table 1.

Hydrometer Reading L (cm) Hydrometer

Reading L (cm)

0 16.3 26 12.01 16.1 27 11.92 16.0 28 11.73 15.8 29 11.54 15.6 30 11.45 15.5 31 11.26 15.3 32 11.17 15.2 33 10.98 15.0 34 100.79 14.8 35 10.6

10 14.7 36 10.411 14.5 37 10.212 14.3 38 10.113 14.2 39 9.914 14.0 40 9.715 13.8 41 9.616 13.7 42 9.417 13.5 43 9.218 13.3 44 9.119 13.2 45 8.920 13.0 46 8.821 12.9 47 8.622 12.7 48 8.423 21.5 49 8.324 12.4 50 8.125 12.2 51 7.9

Table 1. The variation of L with the hydrometer reading for an ASTM 152-H hydrometer.

To determine A for a soil with a specific gravity of the solids of Gs = 2.70 and with the water in the solution at a temperature of 25ºC, the viscosity of water is,

(Eqn-4)

This value can be confirmed from Table 2 that shows the variations of A with Gs and the water temperature.

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GsTemperature

17 18 19 20 21 22 232.50 0.0149 0.0147 0.0145 0.0143 0.0141 0.014 0.01382.55 0.0146 0.0144 0.0143 0.0141 0.0139 0.0137 0.01362.60 0.0144 0.0142 0.014 0.0139 0.0137 0.0135 0.01342.65 0.0142 0.014 0.0138 0.0137 0.0135 0.0133 0.01322.70 0.014 0.0138 0.0136 0.0134 0.0133 0.0131 0.0132.75 0.0138 0.0136 0.0134 0.0133 0.0131 0.0129 0.01282.80 0.0136 0.0134 0.0132 0.0131 0.0129 0.0128 0.0126

GsTemperature

24 25 26 27 28 29 302.50 0.0137 0.0135 0.0133 0.0132 0.013 0.0129 0.01282.55 0.0134 0.0133 0.0131 0.013 0.0128 0.0127 0.01262.60 0.0132 0.0131 0.0129 0.0128 0.0126 0.0125 0.01242.65 0.013 0.0129 0.0127 0.0126 0.0124 0.0123 0.01222.70 0.0128 0.0127 0.0125 0.0124 0.0123 0.0121 0.0122.75 0.0126 0.0125 0.0124 0.0122 0.0121 0.012 0.01182.80 0.0125 0.0123 0.0122 0.012 0.0119 0.0118 0.0117

Table 2. The variation of the constant A with the specific gravity of solids Gs.

The ASTM 152-H type of hydrometer is calibrated up to a reading of 60 at a temperature of 20 C for soil particles having Gs = 2.65. For example, a hydrometer reading of 30 at a given time t of a test means that there are 30 grams of soil solids (Gs = 2.65) in suspension per 1000 cc of soil-water mixture at 20 C at a depth where the specific gravity of the soil-water suspension is measured (that is, at L). We can use this to determine the percentage of soil still in suspension at time t from the beginning of the test and all the soil particles will have diameters smaller than D calculated from equation (2). Finally, there are three corrections that need to be made: (1) a temperature of the water FT, (2) a meniscus correction Fm, and (3) a zero correction Fz. These are as follows,

1. The temperature correction FT is used when the temperature is not 20 C.FT = -4.85 + 0.25T if T is between 15C and 28 C

This correction can be positive or negative.

2. The meniscus correction Fm is used with the upper level of the meniscus reading. This correction is always positive.

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3. Zero correction Fz. Since a deflocculating agent is added to the soil distilled water suspension for performing experiments, the zero reading is changed on the hydrometer. This correction can be positive or negative.

2) The required equipment.

1. ASTM 151-H hydrometer. The hydrometer is graduated in grams of soil colloids per liter (the Bouyoucos Scale). The temperature of standard is 68o F. The scale range is 5 to 60 grams with 1 gm divisions (ASTM 152H), which meets ASTM method D-422, and AASHTO method T-88. The total length of the hydrometer is 11" (280 mm).

2. Mixer. When performing the hydrometer method of testing sub grade soils this mixer is used for dispersing soil suspensions. The mixer operates at speeds above 13,000 RPM (no load) and has three speeds for maximum mixing flexibility. The mixer is furnished with a chrome- plated dispersion cup and a steel-plated stirring paddle. The front panel is stainless steel while the housing is die-cast aluminum. Dimensions are 19-7/16" x 6-9/16" x 7".

3. Two 1000 cc graduated cylinders4. Thermometer5. Constant temperature bath6. A deflocculating agent; in this experiment, a 4% solution of Calgon

(sodium-hexameta-phosphate).7. Spatula8. Beaker9. Electronic scale10. Plastic squeeze bottle11. Distilled water12. No. 12 rubber stopper.

Figure 2. The soil mixer machine.

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Figure 3. The thermometer (graduated in degrees Fahrenheit).

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Figure 4. ASTM 152-H hydrometer.

(3) The Procedure.

1) Place 50 g of a well-pulverized oven-dried soil into a dry 1000 ml beaker.2) Prepare the deflocculating agent (usually a 4% solution of Calgon which is

sodium hexa-meta-phosphate) by adding 40 g of the Calgon to 1000 cc of distilled water and mix thoroughly.

3) Take 125 cc of the Calgon mixture prepared in step 2 and add to the soil in the beaker from step 1. Allow to soak for 8 to 12 hours.

4) Take a 1000 cc graduated cylinder and add sufficient distilled water to the 125 cc of deflocculating agent with soil in order to reach 1000 ml. Mix the solution well.

5) The cylinder from step 4 is the temperature bath; record the temperature T in C.

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Put the hydrometer in the cylinder of step 5. Record the reading, making sure to use the top of the meniscus. This is the zero correction Fz, which can be positive or negative. Also observe the meniscus correction Fm.6) Using a spatula, thoroughly mix the soil prepared in step 3. Pour it into the

mixer cup. During this step, some soil will stick to the side of the beaker. Use the plastic squeeze bottle to wash the remaining soil in the beaker into the mixer cup.

7) Add distilled water to the cup to make it about 2/3 full, then mix for about 2 minutes with the mixer.

9) Pour the mix into the second 1000 cc graduated cylinder. Make sure that all the soil solids are washed out of the mixer cup. Fill the graduated cylinder with distilled water to bring the water level up to the 1000 cc mark.

Figure 7. Washing out soil solids with plastic squeeze bottle.

10) Secure a No. 12 rubber stopper to the top of the cylinder. Mix the contents well by using both hands to gently rotate the cylinder.

11) Place the soil-suspension cylinder next to the constant temperature bath. Record the time immediately. This is cumulative time t = 0. Insert the hydrometer into the cylinder containing the soil-water suspension.

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Figure 8. The two 1000 cc graduated cylinders ready to start taking measurements.

12) Take hydrometer readings at cumulative times t = 0.25 min., 0.5 min., 1 min., and 2 min. Make sure to always read the top of the meniscus.

13) Take the hydrometer out after two minutes and put it into the constant temperature cylinder next to it (step 5).

14) Take hydrometer readings at times t = 4 min., 8 min., 15 min., 30 min., 1 hour, 2 hours, 4 hours, 8 hours, 24 hours, and 48 hours. For each reading, insert the hydrometer into the cylinder containing the soil suspension about 30 seconds before the reading is due. After the reading is taken, take the hydrometer out and place it in the constant temperature cylinder from step 5.

15) Plot a grain size distribution graph on semi-log graph paper on excel with percent finer on the log scale

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(4) Calculations.

- For a hydrometer reading at t = 4 min: R = 10.115 and T = 22.8 °C.

- FT = -4.85 + 0.25T = +0.85

- FM = 0.5 and FZ = +4

- Rcp = R + FT – FZ = 6.965

- Hydrometer was calibrated for Gs = 2.65 so use Table 3 find a = 1.00

Gs a2.50 1.042.55 1.022.60 1.012.65 1.002.70 0.992.75 0.982.80 0.97

Table 3. The variation of a with the specific gravity of solids Gs.

- Find percent finer = = 13.93%

where Ws is the fry weight of soil used in the hydrometer analysis, and a is the

correction for the specific gravity

- Rcl = R + FM = 10.615

- Using Table 1 & interpolating, = 14.677cm

- Using Eqn-4, = 0.01287

- Using Eqn-2, = 0.024653 mm

Environmental ConditionsMeniscus correction (Fm) = 0.5

zero correction (Fz) = 3Temperature (t) = 22

Temperature Correction (Ft) = 0.65a (From Table) = 0.99

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(5) Data.Description of soil: Light brown silty sand

Hydrometer type: ASTM 151-H Specific gravity of solid, Gs = 2.65

Dry weight of soil, Ws = 50 g Temperature of test, T = 22.8 °C

Meniscus correction, FM = 0.5 Zero correction, FZ = +4

Temperature correction, FT = 0.85

Time (min)

Hydrometer reading, R

T (degree celsius) FT Rcp

Percent finer, (a*Rcp)/50 *100

or 2*a*Rcp

RclL

(cm) A D (mm)

0.25 10.125 22.8 0.85 6.975 13.95 10.625 14.675 0.01287 0.0986050.5 10.12 22.8 0.85 6.97 13.94 10.62 14.676 0.0697261 10.12 22.8 0.85 6.97 13.94 10.62 14.676 0.0493042 10.12 22.8 0.85 6.97 13.94 10.62 14.676 0.0348634 10.115 22.8 0.85 6.965 13.93 10.615 14.677 0.0246538 10.1125 22.8 0.85 6.9625 13.925 10.6125 14.678 0.017432

15 10.11 22.8 0.85 6.96 13.92 10.61 14.678 0.01273130 10.105 22.8 0.85 6.955 13.91 10.605 14.679 0.009003

1440 10.072 21.9 0.625 6.922 13.844 10.572 14.686 0.0013

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Log D vs Percent Finer

13.82

13.84

13.86

13.88

13.9

13.92

13.94

13.96

0.0010.010.11

Grain size, D (mm)

Per

cent

fine

r

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(6) Conclusions.Hydrometer analysis allows geotechnical engineers to determine grain size

distribution in soil samples. Whereas sieve analysis can separate particle up to 0.038 mm with a No. 400 sieve, hydrometer analysis can distribute fine soil particles up to a size of 0.001 mm.

There are many sources of error in this experiment. Human error in reading and recording hydrometer readings and instrumental error are two sources of error. Another source of error concerns the deflocculating agent and soil not soaking for 8 to 12 hours in the beaker because of laboratory time constraints. In addition, the rubber stopper was not applied to the graduated cylinder containing the soil suspension neither shaken as instructed in step 10 of the procedure. This prevented the thorough mixing of the soil with the water in the cylinder. The rough insertion of the hydrometer adds error since it introduces disturbance to the soil mix, causing turbulence. Moreover, the different size of grains in the sample introduces error since the bigger particles will flocculate faster than the smaller sizes and cause disturbance. Air bubbles floating on top of the liquid contributed to some error as well in reading the meniscus. Lastly, only tap water with its microscopic particles, rather than distilled water, was available at the laboratory at time of experiment.

Furthermore, it should also be noted that Table 1 is for an ASTM 152-H hydrometer; the hydrometer used in our experiment was an ASTM 151-H type.

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Hydrometer readings were taken at t = 0.25, 0.5, 1, 2, 4, 8, 15, 30, and 1,440 minutes. A hydrometer reading was not taken at t = 2,880 minutes. Since the hydrometer readings ranged from 10.125 to 10.105 and down to 10.072 at 1440 minutes, effective length did not change much as time passed. This experiment has various sources of error. This would contribute a high percent of error for this experiment. The sources of error include:

- Observational error- This is what is considered human error. When manually doing experiments, a lot of the readings are inaccurate. For example, reading the hydrometer, this must be read at the meniscus, while level with the hydrometer and then recorded. In this some error might occur.

- Equipment Error- Error may occur if the equipment is not calibrated properly. An example of this would be the hydrometer or the scale used to measure the soil sample. If any of the equipment is off, the experiment may lose accuracy and precision and create a small error.

- Another error for this experiment may include the surface tension on the hydrometer’s rod. This may change how the hydrometer sinks into the solution. Also the placing and removing the hydrometer from the cylinder may disrupt some of the displacement of the particles of the soil-water causing a false reading.

- If the readings were not recorded at the correct times, the resulting numbers could cause the calculations and the rest of the experiment to be off. Some of the readings for the hydrometer were not done exactly at the times required. For example, the last reading was collected on the Monday following the experiment.

- For this experiment tap water was used instead of the required distilled water. The tap water has tiny particles that may affect the results of the readings, where as the distilled water has none.

- The weight of the soil sample particles may have some error as well, since some particles are larger than others causing a slight disturbance.

- If the rubber stopper used in this experiment was not fastened tightly, then the cylinder was not able to be

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shaken properly resulting in a soil that is not uniformly mixed.

- Calculation error may have occurred causing false results.

This experiment may be improved if the sources of error are limited. Having the same person do the readings would minimize the human error of reading the measurements. Also complete the lab with patience. That way it can be sure that the hydrometer is carefully removed and placed into the cylinder. Also having smaller samples and accurate time readings will help reduce the error. This experiment was done in the time allowed for the lab class. Perhaps with more time, the data may have been collected more precisely and accurately.

(7) References.

1. Coduto, P. Donald. Geotechnical Engineering: Principles and Practices. New Jersey: Pearson Education, Inc., 1999.

2. L. A. Prieto-Portar, “Geotechnical Laboratory Notes”, web.eng.fiu.edu/prieto, Miami, 2009.

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Data Sheet

Grain Size Distribution: The Hydrometer Analysis

Group: ___________ Date: ______________ Location: _____________

Soil Description __________________ Hydrometer type ____________________

GS ____________ Dry Weight of soil, WS ____________ g

Temperature of test, T _________ Meniscus Correction, Fm _____________

Zero correction, Fz ____________ Temperature Correction, FT ___________

Time(min)

Hydrometer reading, R R

Percentfinner,

R L(cm) A

D(mm)