# Lecture-3 (SM1).pdf

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ADDIS ABABA INSTITUTE OF TECHNOLOGYSCHOOL OF CIVIL AND ENVIRONMENTAL ENGINEERING

CENG 2141Soil Mechanics I

CENG 2141Soil Mechanics I

Instructor: Petros Fekadu11/2014

Mechanical Properties of Soil Comprises compressibility, shear strength &

bearing capacity.

Depends on (1) Grain-size distribution &(2) Consistency

Comprises compressibility, shear strength &bearing capacity.

Depends on (1) Grain-size distribution &(2) Consistency

2

Grain Size Distribution (GSD) GSD information can be of value in providing

initial rough estimates of a soils engineeringproperties such as permeability, strength,expansivity, etc.

When measuring GSDs for soils, two methods aregenerally used:

o For grains larger than 0.075mm sieving is used.o For grains in the range of 0.075mm > D > 0.5m,

the hydrometer test is used.

GSD information can be of value in providinginitial rough estimates of a soils engineeringproperties such as permeability, strength,expansivity, etc.

When measuring GSDs for soils, two methods aregenerally used:

o For grains larger than 0.075mm sieving is used.o For grains in the range of 0.075mm > D > 0.5m,

the hydrometer test is used.3

Grain Size Distribution Contd

In coarse grain soils ... By sieve analysisDetermination of GSD:

In fine grain soils ... By hydrometer analysis

4Sieve Analysis Hydrometer Analysis

soil/water suspension

hydrometer

stack of sieves

sieve shaker

Sieve Analysis

5

Procedure for Sieve Analysisa) Pour ovendried soil of mass M into the top sieve of the

stack;b) Shake and agitate the stack of sieves until all soil grains

are retained on the finest sized sieve through which theycan possibly pass;

c) Weigh the mass of soil Mi retained on each sieve;

d) For each sieve size used, compute Ni, the percentage bymass of the soil sample that is finer than the ith sievesize.

a) Pour ovendried soil of mass M into the top sieve of thestack;

b) Shake and agitate the stack of sieves until all soil grainsare retained on the finest sized sieve through which theycan possibly pass;

c) Weigh the mass of soil Mi retained on each sieve;

d) For each sieve size used, compute Ni, the percentage bymass of the soil sample that is finer than the ith sievesize.

6

100MM

seiveionRetained% ith

i

1i

thth )seiveionRetained(%100seive ithanFiner%

Some Commonly Used Measures(1) The "effective size" of the soil: D10(2) Average particle diameter (D50) is the

average particle diameter of the soil.(3) The Uniformity Coefficient:

Cu = D60/D10

(4) The Coefficient of Gradation:Cc= (D30)2/(D60xD10)

GSD measurements, which can beperformed quickly and inexpensively,tell us whether a given soil ispredominantly sandy, silty, or clayey.This simple information is often ofgreat help in trying to anticipate asoils possible mechanical properties.

(1) The "effective size" of the soil: D10(2) Average particle diameter (D50) is the

average particle diameter of the soil.(3) The Uniformity Coefficient:

Cu = D60/D10

(4) The Coefficient of Gradation:Cc= (D30)2/(D60xD10)

GSD measurements, which can beperformed quickly and inexpensively,tell us whether a given soil ispredominantly sandy, silty, or clayey.This simple information is often ofgreat help in trying to anticipate asoils possible mechanical properties.

7

Some Commonly Used Contd Empirically, D10 has been strongly correlated with the permeability of

finegrained sandy soils. Poorly-graded soils: Cu < 4 & steep gradation curve Well-graded soils: Cu > 4 , 1 < Cc< 3 & flat gradation curve Gap-graded soils: Cc < 1 or > 3 & one or more humps

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Example 2.4A sample of a dry coarse-grained material of mass1350 g was shakenthrough a nest of sievesand the following resultswere obtained. Plot theparticle size distributionand determine (a) theuniformity coefficient and(b) the coefficient ofcurvature.

Sieve opening Mass retained (g)

20 mm 52.5

10 mm 60

4.75 mm 120

2 mm 225

1 mm 225

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A sample of a dry coarse-grained material of mass1350 g was shakenthrough a nest of sievesand the following resultswere obtained. Plot theparticle size distributionand determine (a) theuniformity coefficient and(b) the coefficient ofcurvature.

1 mm 2250.6 mm 210

0.425 mm 172.5

212 m 82.5150 m 52.575 m 37.5Pan 112.5

Hydrometer Testing

Assuming that soil particles are perfect spheresdispersed in water with a viscosity , Stokes lawcan be used to relate the terminal velocity v of aparticle to its diameter D:

in which s is the density of soil particles and w isthe density of water.

The equation indicates that a larger particle willhave a greater terminal velocity when droppingthrough a uid.

The basis of hydrometer analysis is that when soil particles aredispersed in water, they will settle at different velocities because oftheir different sizes.

Assuming that soil particles are perfect spheresdispersed in water with a viscosity , Stokes lawcan be used to relate the terminal velocity v of aparticle to its diameter D:

in which s is the density of soil particles and w isthe density of water.

The equation indicates that a larger particle willhave a greater terminal velocity when droppingthrough a uid.

10

2ws D18

v

Hydrometer Testing Contd In the hydrometer laboratory test (ASTM 2004) a dry soil specimen

weighing 50 g is mixed thoroughly with water and placed in a graduated1000-mL glass ask.

A oating instrument called a hydrometer is placed in the ask to measurethe specic gravity of the mixture in the vicinity of the hydrometer center.

In a 24-hour period the time t and the corresponding depth z are recorded.The measured depth is correlated with the amount of soil that is still insuspension at time t .

From Stokes law, it can be shown that the diameter of the largest soilparticles still in suspension is given by

in which w is the unit weight of water. From the hydrometer readings and with the help of the above equation, one

can calculate the percent of ner particles and plot a gradation curve.

In the hydrometer laboratory test (ASTM 2004) a dry soil specimenweighing 50 g is mixed thoroughly with water and placed in a graduated1000-mL glass ask.

A oating instrument called a hydrometer is placed in the ask to measurethe specic gravity of the mixture in the vicinity of the hydrometer center.

In a 24-hour period the time t and the corresponding depth z are recorded.The measured depth is correlated with the amount of soil that is still insuspension at time t .

From Stokes law, it can be shown that the diameter of the largest soilparticles still in suspension is given by

in which w is the unit weight of water. From the hydrometer readings and with the help of the above equation, one

can calculate the percent of ner particles and plot a gradation curve.11

Dws t)1G(z18D

Example 2.5Estimate the diameter of the particles using Stokes lawand classify the soil as clay or silt. The vertical distancemoved by soil particles of a certain size over a period of60 s is 1 cm. is 0.01 g/(cm.s) and w = 1 g/cm3 at atemperature of 20C. Take Gs = 2.65.

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Consistency Soil consistency is defined as the relative ease with which a soil can

be deformed. The terms of soft, firm, or hard are used. Soil consistency provides a means of describing the degree and

kind of cohesion and adhesion between the soil particles as relatedto the resistance of the soil to deform or rupture.

Consistency largely depends on soil minerals and the water content. Cohesion is a measure of the interparticle molecular attraction and

bonds. Adhesion is similar to cohesion except with adhesion involves the

attraction of a water molecule to a non-water molecule (water-solidbond).

Soil consistency is defined as the relative ease with which a soil canbe deformed. The terms of soft, firm, or hard are used.

Soil consistency provides a means of describing the degree andkind of cohesion and adhesion between the soil particles as relatedto the resistance of the soil to deform or rupture.

Consistency largely depends on soil minerals and the water content. Cohesion is a measure of the interparticle molecular attraction and

bonds. Adhesion is similar to cohesion except with adhesion involves the

attraction of a water molecule to a non-water molecule (water-solidbond).

13

Atterberg Limits Atterberg limits are the limits of water content used to

define soil behavior. The consistency of soils according toAtterberg limits gives the following diagram.

14

Atterberg Limits Contd Liquid Limit (LL) is defined as the moisture content at which

soil begins to behave as a liquid material and begins to flow. Plastic Limit (PL) is defined as the moisture content at which soil

begins to behave as a plastic material. Shrinkage Limit (SL) is defined as the moisture content at which

no further volume change occurs with further reduction inmoisture content.(SL represents the amount of water required to fully saturate thesoil (100% saturation))

o The shrinkage limit is useful for the determination of the swellingand shrinkage capacity of soils.

Liquid Limit (LL) is defined as the moisture content at whichsoil begins to behave as a liquid material and begins to flow.

Plastic Limit (PL) is defined as the moisture content at which soilbegins to behave as a plastic material.

Shrinkage Limit (SL) is defined as the moisture content at whichno further volume change occurs with further reduction inmoisture content.(SL represents the amount of water required to fully saturate thesoil (100% saturation))

o The shrinkage limit is useful for the determination of the swellingand shrinkage capacity of soils.

15

Liquid Limit In the lab, the LL is defined asthe moisture content (%) requiredto close a 2-mm wide groove in asoil pat a distance of 0.5 in alongthe bottom of the groove after25 blows.

o Soil sample size 150g passing #40 sieve

o Equipment: Casagrande liquidlimit device

In the lab, the LL is defined asthe moisture content (%) requiredto close a 2-mm wide groove in asoil pat a distance of 0.5 in alongthe bottom of the groove after25 blows.

o Soil sample size 150g passing #40 sieve

o Equipment: Casagrande liquidlimit device

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Plastic Limit

The moisture content (%)at which the soil whenrolled into threads of 3.2mm(1/8 in) in diameter, willcrumble.

Plastic limit is the lowerlimit of the plastic stage ofsoil.

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The moisture content (%)at which the soil whenrolled into threads of 3.2mm(1/8 in) in diameter, willcrumble.

Plastic limit is the lowerlimit of the plastic stage ofsoil.

Plasticity Index Plasticity Index is the difference between the

liquid limit and plastic limit of a soil.PI = LL PL

After finding LL and PI, use plasticity chart toclassify the soil.

Table :Typical Atterberg limits for soils

Plasticity Index is the difference between theliquid limit and plastic limit of a soil.

PI = LL PL After finding LL and PI, use plasticity chart to

classify the soil.Table :Typical Atterberg limits for soils

18

Liquidity Index

.P

PLL I

wwI

It is a measure of soil strengthusing Atterberg limits

19

Activity (A) of a soil is the PI divided by the percent of clay-sizedparticles (less than 2 m) present.

From the activity, one can predict the dominant clay type present in asoil sample.High activity signifies large volume change when wetted and largeshrinkage when dried. Soils with high activity are very reactivechemically.Normally the activity of clay is between 0.75 and 1.25, and in thisrange clay is called normal. When A is less than 0.75, it is consideredinactive. When it is greater than 1.25, it is considered active.

Activity

(%)fractionClayIA P

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Activity (A) of a soil is the PI divided by the percent of clay-sizedparticles (less than 2 m) present.

From the activity, one can predict the dominant clay type present in asoil sample.High activity signifies large volume change when wetted and largeshrinkage when dried. Soils with high activity are very reactivechemically.Normally the activity of clay is between 0.75 and 1.25, and in thisrange clay is called normal. When A is less than 0.75, it is consideredinactive. When it is greater than 1.25, it is considered active.

Example 2.6

Number of blows 10 19 23 27 40

Water content (%) 120 99 79.6 73 55

Plastic limit and liquid limit tests were carried out on a clay soil with60% of particles smaller than 0.002 mm. Two determinations for theplastic limit gave water contents of 39.5 % and 40.5 %. A liquid limittest conducted on a soil sample in the cup device gave the followingresults:

(a) Compute the plastic limit (PL)(b) Extract the liquid limit (LL)(c) Determine the activity (A) and(d) Calculate the liquidity index and describe the consistency of thesoil with w =30%

21

Water content (%) 120 99 79.6 73 55

Plastic limit and liquid limit tests were carried out on a clay soil with60% of particles smaller than 0.002 mm. Two determinations for theplastic limit gave water contents of 39.5 % and 40.5 %. A liquid limittest conducted on a soil sample in the cup device gave the followingresults:

(a) Compute the plastic limit (PL)(b) Extract the liquid limit (LL)(c) Determine the activity (A) and(d) Calculate the liquidity index and describe the consistency of thesoil with w =30%

Assignment #11. Prove the following expressions:

(a) = Gsw(1 n)(1 + )

(b)

2. A cylindrical soil sample of 4 cm diameter and 8 cmlong with 5% air voids and 15% water by weight.Calculate the mass and the void ratio of the sample.Take Gs= 2.7.

d

d(max)

d(min)d(max)

d(min)dr

D

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1. Prove the following expressions:

(a) = Gsw(1 n)(1 + )

(b)

2. A cylindrical soil sample of 4 cm diameter and 8 cmlong with 5% air voids and 15% water by weight.Calculate the mass and the void ratio of the sample.Take Gs= 2.7.

d

d(max)

d(min)d(max)

d(min)dr

D

Assignment #1 ... Contd3. Calculate the weight of water that has to be added to 1m3 of soil to attain a 95% degree of saturation. Take d =18 kN/m3, w = 5% and Gs = 2.7.

4. Calculate the weight of water that has to be added to 1m3 of soil to attain a 95% degree of saturation. Take d =18 kN/m3, w = 5% and Gs = 2.7.

5. Determine the specific gravity of a soil sample if itsvolumes at a liquid limit (LL = 65%) and a shrinkage limit(SL = 22 %) are 34.8 cm3 and 19.9 cm3 respectively.

23

3. Calculate the weight of water that has to be added to 1m3 of soil to attain a 95% degree of saturation. Take d =18 kN/m3, w = 5% and Gs = 2.7.

4. Calculate the weight of water that has to be added to 1m3 of soil to attain a 95% degree of saturation. Take d =18 kN/m3, w = 5% and Gs = 2.7.

5. Determine the specific gravity of a soil sample if itsvolumes at a liquid limit (LL = 65%) and a shrinkage limit(SL = 22 %) are 34.8 cm3 and 19.9 cm3 respectively.

END OF CHAPTER-2

24

ASSIGNMENT#1 has to beDone in groups (5 students/Group)Submitted 2 weeks after the chapter ends.