CE 240Soil Mechanics & Foundations

Lecture 1.3

Soil Particles(Das, Ch. 2)

Outline of this Lecture

1.Engineering consideration of soil particles

2.Sieve test3.Hydrometer test4.Particle distribution5.Shape of soil particles

Definitions for SOIL

Engineering definitions:Civil Engineering:

Soil is the earth material that can be disaggregated in water by gentle agitation.

Construction:Soil is material that can be removed by conventional means without blasting.similar to the definition of regolith in geological terms.

Agronomy definition:Soil consists of the thin layers of the earth’s crust formed by surface weathering that are able to support plant life.

Soil particles

The description of the grain size distribution of soil particles according to their texture (particle size, shape, and gradation).

Major textural classes include:gravel (>2 mm);sand (0.1 – 2 mm);silt (0.01 – 0.1 mm);clay (< 0.01 mm).

Furthermore, gravel and sand can be roughly classified as coarse textured soils, wile silt and clay can be classified as fine textures soils.

For engineering purposes, soils can also be divided into cohesive and non-cohesive soils. Non-cohesive means the soil has no shear strength if no confinement.

Cohesive soil contains clay minerals and posses plasticity.

In engineering practice, plasticity is defined as the ability to be rolled into thin thread before breaking into pieces.

Clay is cohesive and plastic. For example, mud sticking on shoes in a rainy day when one walk in a field.

Sand is non-cohesive and non-plastic.

Procedure for grain size determination

• Sieving - used for particles > 75 µm

• Hydrometer test - used for smaller particles (φ < 75 µm)– Analysis based on Stoke’s Law,

velocity proportional to diameter

A sieve test apparatus in a soil mechanics laboratory, (Das, Fig. 2.15)

A set of soil test sieves

Sieves and scale

sieve # Sieve opening (mm)4 4.7510 2.0020 0.85040 0.42560 0.250100 0.150200 0.074

Sieve Test

First of all, let’s discuss the sieve that is the essential tool to study particle size distribution for the grain size greater than 0.075 mm (75 microns).

U.S. Standard Sieve Sizes

Sieve test procedure:

0, the total mass of the soil sample (ΣM) under sieve test;1, determine the mass of soil retained on each sieve and the pan at last (i.e., M1, M2, M3, …. Mn, and Mp).2, the sum of soil mass retained on each sieve plus the mass in the pan should be equal to the total mass (ΣM= M1+M2 +M3+…. +Mn+Mp).3, determine the cumulative mass of soil retained above each sieve, for the ith sieve we have ΣMi = M1+M2+M3+…. +Mi .4, the mass of soil passing the ith sieve is

ΣM - ΣMi = ΣM – (M1+M2 +M3+…. +Mi ).5, the percent of soil passing the ith sieve (percent finer) is

100iM MFM

Σ −Σ= ×

Σ

Example: If you have a soil sample with a weight of 150 g, afterthorough sieving you get the following result.

sieve# size(mm) W(g) % accum% 100-accum%

4 4.750 30.0 20 20 8020 0.850 40.0 26.7 46.7 53.360 0.250 50.0 33.3 79 21100 0.150 20.0 13.3 92 8200 0.074 10.0 6.67 98 2

The last column shows the percentage of material finer than that particular sieve size by weight.

Gradation:

Gradation is a measure of the distribution of a particular soil sample. Larger gradation means a wider particle size distribution.

Well graded poorly sorted (e.g., glacial till)

Poorly graded well sorted (e.g., beach sand)

The range of grain size distribution is enormous for natural soils. E.g., boulder can be ~1 m in diameter, and the colloidal mineral can be as small as 0.00001 mm = 0.01 micron

=> It has a tremendous range of 8 orders of magnitude.

Fine-grained soil

The hydrometer test uses Stokes equation (for the velocity of a free falling sphere in suspension) to determine grain size distribution smaller than #200 sieve.

The grain size distributions of soils are commonly determined bysieve (smallest being #200) and hydrometer procedures. In the hydrometer analysis the soil smaller than #200 sieve is placed in suspension and by use of Stokes' equation for the velocity of a free falling sphere the equivalent particle size and percent of soil in suspension are computed.

For soils with both fine and coarse grained materials a combinedanalysis is made using both the sieve and hydrometer procedures.

Procedure for grain size determination

• Hydrometer test - used for smaller particles– Analysis based on Stoke’s Law, velocity proportional to diameter

Figure 1 Schematic diagram of hydrometer test

Procedure for grain size determination

• Hydrometer test - used for smaller particles– Analysis based on Stoke’s Law, velocity proportional to diameter

Figure 1 Schematic diagram of hydrometer test

Stokes LawA sphere falling freely through a liquid of infinite extent will accelerate rapidly to a certain maximum velocity and will continue at that velocity as long as conditions remain the same. The relationship of the terminal velocity to the physical properties of the sphere and the liquid are expressed by Stokes' Equation as shown in the following page.

2

18s wv Dρ ρη−

=

wherev: velocity of the particle settlementρs: density of soil particlesρw: density of soil particlesη: viscosity of waterD: diameter of soil particles

From the Stokes’ equation, rearranging the factors we can get

18 18

s w s w

LD vt

η ηρ ρ ρ ρ

= =− −

with s s wGρ ρ=

where Gs is the specific gravity of the soil particle, We get

18( 1)s w

LDG t

ηρ

=−

With the use of the SI units and choose g-sec/cm2

for viscosity h, and 1 g/cm3 for the density of water ρw, and the length L in cm, and time t in minute, and D in mm, we can get

30 ( )( )1 (min)s

L L cmD mm KG t t

η= =

−

Since both viscosity and specific gravity of soil particles are temperature dependent, so does parameter K. Table 2.6 in the textbook gives the K value as the function of temperature.

ASTM 152H Hydrometer and the definition of L (Das, Fig. 2.17 and Fig. 2.18)

1 21 ( )2

BVL L LA

= + −

whereL1: the length of the hydrometer stem;L2: the length of the hydrometer bulb;Vb: the volume of the hydrometer bulb;D: cross-section area of the cylinder;

Stokes' Law is applicable to spheres varying from 0.02 mm to 0.0002 mm in diameter. As applied to soil particles falling through water, inaccuracies for using the Stokes’ equation to determine the particle size occur due to the following factors:

1, Soil particles are not spheres;

2, The fluid is not of infinite extent;

3, The specific gravity of individual particles may vary;

4, Turbulence caused by larger particles falling;

5, Brownian movement of smaller particles;

6, Disturbance due to insertion and removal of the hydrometer;

7, The test is actually used for diameters as large as 0.07 mm.

Scanning electron micrograph of soil composed of fine sand, silt and clay

100 mµ

Sandstone

However, by proper sample and laboratory technique all except Item 1 (soil particles are not always spherical) in the 7 factors can be controlled or minimized so that the resulting inaccuracies can be ignored in normal testing. The shape of soil particles will vary from cubes to flakes with each of the shapes between these limits having different influence. Nevertheless, the results of the hydrometer analysis are valid if they are considered equivalent grain diameter rather than actual grain diameter.

Useful links for hydrometer testhttp://geotech.uta.edu/lab/Main/Hydrometer/

The particle distribution curves for 3 soil samples (West, Fig. 7.1)

There are a number of ways to characterize the particle size distribution of a particular soil sample.

D10:

D10 represents a grain diameter for which 10% of the sample will be finer than it. Using another word, 10% of the sample by weight is smaller than diameter D10. It is also called the effective size and can be used to estimate the permeability.

Hazen’s approximation (an empirical relation between hydraulic conductivity with grain size)

k (cm/sec) = 100D10D10

Where D10 is in centimeters. It is empirical because it is not consistent in dimension (cm/sec vs cm2).

Uniformity coefficient Cu:

Cu = D60/D10

where D60 is the diameter for which 60% of the sample is finer than D60.

The ratio of two characteristic sizes are the uniformity coefficient Cu. Apparently, larger Cumeans the size distribution is wider and vice versa. Cu = 1 means uniform, all grains are in the same size, such as the case of dune sands . On the other extreme is the glacial till, for which its Cu can reach 30.

from Cu = D60/D10 , then D60 = CuD10

Coefficient of gradation Curvature Cc

Another shape parameter, as the second moment of grain size distribution curve, is called the coefficient of curvature, and defined as

Cc = (D30 D30)/(D10 D60)

A soil is thought to be well graded if the coefficient of curvature Cc between 1 and 3, with Cu greater than 4 for gravels and 6 for sands.

Sorting Coefficient S0

Another parameter for measruinguniformity used mostly by geologists, and defined as

S0 = sqrt(D75/ D25)

It is not frequently used by geotechnical engineers.

West, Figure 7.1

D10

D60D60 D60

D10 D10

Preliminary Soil ClassificationThere are six (6) classification systems, each one is designed for a particular field.

1) Wentworth Scale• For Geology, not engineering geology;

3) USDA Scale• Agriculture;

3) BPR Scale• Road construction

4) ASTM Scale• Ceramic industry;

5) AASHTO Scale• Highway engineering;

6) USC Scale• Civil Engineering, construction;

We go through briefly of the first 3 systems and leave the last 2 to a more detailed discussion in 2 weeks.

(West, Figure 8.8)

Soil Classification (cont.)

1) Wentworth Scale

• For Geology, not engineering geology. Wentworth scale uses 2 as the base and mm as the primary unit. The subdivisions are based on a ratio of 2.

-3 -2 -1 0 1 2 31/8 ¼ ½ 1 2 4 83φ 2φ 1φ 0φ -1φ -2φ -3φφ-scale

(West, Figure 8.9)

Soil Classification (cont.)

2) USDA Scale• USDA scale intentionally sets silt/clay

boundary lower than the Wentworth scale (0.004 mm) and ASTM scale (0.005 mm), it is 0.002 mm. The reason behind this classification is:

• Fine-sized quartz and feldspar grains may occur at 0.005 mm, but definitely not smaller than 0.002 mm. However, quartz and feldspar are not plastic at all. Inclusion of these quartz grains into clay complicates many problems. USDA intends to coincide clay size with clay minerals.

(West, Figures 8.10 and 8.11)

clay

sand silt

clay

sandsilt

Reading Assignment:

Das, Ch. 2

Homework:

2.3, 2.8, 2.9