06 - NPTEL

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay

06


Index properties


Review

Sedimentation analysis

Clay particle-water interaction

Identification of clay minerals


Hydrometer analysis

Hydrometer is a device which is used to measure the specific gravity of liquids.

0.995

1.030

20 - 40

130 - 150

10 - 20

50

60

50

29 -31 φ

4.7 φ

(All dimensionsare in mm)


Hydrometer Analysis-For a soil suspension, the particles start settling down right from the start, and hence the unit weight of soil suspension varies from top to bottom.

Measurement of specific gravity of a soil suspension (Hydrometer) at a known depth at a particular time provides a point on the GSD.


Process of Sedimentation of Dispersed Specimen

Ww

WSVS

VW1

VS = Ws/(Gsγw) Vw = [1 -Ws/(Gsγw)]

Initial unit weight of a unit volume of suspension γi = [γw + Ws(Gs-1)/(Gs)]

γi = [Ws+γwVw]/1


dws tz

Gd

γµ)1(

18−

=


z Size d of the particles which have settled from the surface through depth z in time td(From Stroke’s Law):XX

Note:

Above the level X – X, no particle of size > d will be present. In elemental depth dz, suspension may be uniform and particles of the size smaller than d exist.

dz


Process of Sedimentation of Dispersed Specimen If the percentage of weight of particles finer than d (already sedimented) to the original weight of soil solids in the suspension is N′ Then:

Weight of solids per unit volume of suspension at depth z = (N′)(W/V) (i.e. Ws = W/V)

Unit Weight of suspension after elapsing time tdat depth z is γz = [γw + N′(W/V)(Gs-1)/(Gs)]

N′ = [GS/(GS-1)[γz - γw](V/W)

N′ in %



But γz = GSSγw = (1 + Rh/1000) γw

Where GSS = Sp. Gravity of Soil Suspension (Graduated on hydrometer from 0.995 – 1.030)

Rh is the reading on Hydrometer

N′ = [GS/(GS-1)](Rh/1000) (V/W)

= (GS/(GS-1) (Rh/W) For V = 1000 c.c.


Calibration or Immersion correction for Hydrometer

Before the immersion of hydrometer

After the immersion of hydrometer

he

Vh/(2AJ)

H

h/2

Vh/(AJ)

h = height of the bulb

H = Height of any reading Rh

AJ = Area of C/S of Jar

Vh = Vol. of hydrometer

he = [H+h/2+Vh/(2AJ)-Vh/AJ) = (H+h/2) - Vh/(2AJ)

xx

yy

y´ y´

x´ x´


Conversion of Rh into He

Rh = 0; Gss = 1.00

Rh = 30; Gss = 1.030

He1he

He2

he = He1-[(He1-He2)/30]Rh up to 4 min.

he = He1-[(He1-He2)/30]Rh – Vh/(2AJ) after 4 min.

Rh = (GSS-1)103

Plot of Rh with He –Valid for a particular hydrometer


Hydrometer correctionsN′ = (GS/(GS-1) R/W R = Rh+ Cm ± Ct - Cd

Ncombined = N′[W75/WT]

Where, W75 = Wt. of soil passing 75µ

WT = Total wt. of Soil taken for combined Sieve and Hydrometer Analysis

Cm = Meniscus correction (Always + )Because density readings increase downwards

Ct = + for T > 27°C (Rh will be less than what it should be)= - for T < 27 °C (Rh will be more than what it should be)

Cd = Always Negative (Dispersion agent concentration!!)

R = Corrected observed reading


Given Data:Volume of suspension = 1000 mlVolume of hydrometer, Vh= 90 ccWeight of dry soil, Ms = 50 gSpecific gravity of soil, G = 2.62Cross- sectional area of jar, Aj = 31.0075 cm2

Room temperature, T = 27º CDispersing agent correction, Cm= 0.0004Meniscus correction, Cd= 0.0034Temperature correction, Ct = 0.9965Viscosity of water, = 8.545 x 10-7 kN-sec/m2

µ

Example on Hydrometer analysis (kaolin)


H’e1 = Maximum depth to centre of bulb from Rh = 0.995 = 21 cm

H’e2 = Maximum depth to centre of bulb from Rh = 1.030 = 9 cm

At t = 2 min, Rh = 1.0285

Since H’e varies linearly with reading Rh



0

20

40

60

80

100

0.001 0.01 0.1 1

Perc

ent

finer

(%)

Particle size (mm)

Example on Hydrometer analysis


Limitations of Stroke’s law-Soil particles are not truly spherical and sedimentation is done in a jar (For d > 0.2 mm causes turbulence in water and d < 0.0002 mm Brownian movement occurs (too small velocities of settlement) --- Can be eliminated with less concentrations.

-Floc formation due to inadequate dispersion

-Unequal Sp.Gr of all particles (insignificant for soil particles with fine fraction)


Measures of GradationD60 = dia. of soil particles for which 60 % of the particles are finer. (i.e. 60 % of the particles are finer and 40 % coarser than D60)

D10: Effective Particle Size D50 : Average Particle Size

(10 % Finer and 90 % coarser than D10 size)


Measures of Gradation

D30 = 0.3 mm

-Engineers frequently like to use a variety of coefficients to describe the uniformity versus the well-graded nature of soils.


Measures of GradationSome commonly used measures are:

The uniformity coefficient Cu = D60/D10

Soils with Cu < 4 are considered to be poorly graded or uniform. Cu > 4 – 6 Well Graded Soil

Coefficient of Gradation or Curvature

Cc = (D302)/(D60*D10)

Cc = 1- 3 Soil is well-graded.

Higher the value of Cu the larger the range of particle sizes in the soil


Typical characteristics of GSD curves

-Steep Curves ⇒ Low Cu values ⇒ Poorly graded soil (Uniformly graded).

(Cu < 5 for uniform soils)

-Flat Curves ⇒ High Cu values ⇒ Well graded soil.

-Most gap graded soils have a Cc outside the range.

(an absence of intermediate particle sizes)


Typical GSDs for Residual soilsYoung residual

Intermediate maturing

Fully maturing

GSD can provide an indication of soil’s history

⇒ A residual deposit has its particle sizes constantly changing with time as the particles continue to break down…


Typical GSDs for Transported soilsGlacial Glacial-Alluvial

River deposits may be well-graded, uniform or gap-graded, depending up on the water velocity, the volume of suspended solids, and the river area where deposition occurred.


Grain Size Curves for different soils


Particle size distribution of Bentonite, Illite, and Kaolinite clay

After Koch (2002)


Gradation

% Gravel = 0

% Sand =

(100 – 60) = 40

% Silt = (60 – 12)

= 48

% Clay = 12 %


Example problemDetermine the percentage of gravel (G), Sand (S), Silt (M), and Clay (C) of soils A,B and C

Soil A: 2%G; 98%S; 0%M; 0%C (Poorly-graded sand)

Soil C: 0%G; 31%S; 57%M; 12%C (Well graded sandy silt)

Soil B: 0%G; 61%S; 31%M; 7%C (Well graded silty sand)


Some applications of GSA in Geotechnology and construction

-Selection of fill material

-Road Sub-Base Material

-Drainage Filters

-Ground Water Drainage

-Grouting and Chemical Injection

-Concreting Materials

-Dynamic Compaction

Embankment

Earth Dams


Practical Significance of GSD-GSD of soils smaller than 0.075 mm (#200) is of little importance in the solution of engineering problems. GSDs larger than 0.075 mm have several important uses.

1) GSD affects the void ratio of soils and provides useful information for use in cement and asphalt concretes.

(Well graded aggregates require less cement per unit of volume of concrete to produce denser concrete, less permeable and more resistant to weathering)


Practical Significance of GSD

2) A knowledge of the amount of percentage fines and the gradation of coarse particles is useful in making a choice of material for base courses under highways, runways, rail tracks etc.,

3) To determine the activity of clay based on percentage clay fraction (<2µ)

4) To design filters (Filters are used to control seepage) and pores must be small enough to prevent particles from being carried from the adjacent soil.


Different physical states of fine-grained soil


Consistency of Fine-Grained Soils‘Consistency’ is the property of a material which is manifested by its resistance to flow.

-It represents the relative ease with which the soil may be deformed.

-Degree of firmness of a soil and is often directly related to strength.

-It is conveniently described as soft, medium stiff (medium firm), stiff (or firm), very stiff.

Note: These terms unfortunately are relative and have different meaning to different observers.


Consistency of Fine-Grained SoilsIn Soil Mechanics, it is required to determine the range of potential behaviour of a given soil type based only a few simple tests. Typical concerns are the following:

i) Soils might shrink or expand excessively in an uncontrolled manner after they have been placed in geotechnical structures (roadway subgrades, dams, levees, foundation materials, etc.)

ii) Soils might loose their strength and ability to carry loads safely.


Consistency of Fine-Grained Soils Tests used to detect potential problems for coarse-

grained soils (gravels and sands) are different than those used to detect potential problems for fine-grained soils (silts and clays).

Coarse-Grained soils:

- Water content is generally not a major factor

- Major factor leading to shrinkage is the structure of the soil skeleton.

Fine-Grained soils: Water content is a major factorWater Content Soils expand

Loose strengthSoils shrinkGain strength


Different physical states of fine-grained soilIf the water content of a clay slurry is gradually reduced by slow desiccation, the clay passes from a liquid state through a plastic state and finally into a solid state.

The water contents at which different clays passes from one of these stats into another are very different.

∴ Water contents at these transitions can be used for Identification and Comparison of different clays.

Atterberg limits are water contents where the soil behaviour changes…


Soil is no longer fully saturated

LL

PL

SL

Air dry

Oven dry

Physical State Consistency Sr

Liquid

Plastic

Semi-Solid

Solid

Very Soft SoftStiff

Very Stiff

Extremely Stiff

Hard

100 %

100 %100 %

Natural Soil Deposits

Hygroscopic Moisture

Soil-Moisture scale


Consistency of Fine-Grained SoilsIt was discussed that fine-grained soils have high SSAs and electrical charges on their particles. Because of this, fine-grained soils, and clays in particular can change their consistency quite dramatically with changes in water content.

Each soil type will generally have different water contents at which it behaves like a solid, semi-solid, plastic, and liquid. For a given soil, the water contents that mark the boundaries between the soil consistencies are so called Atterberg Limits.

[After Swedish Soil Scientist A. Atterberg (1902)]


Consistency of Fine-Grained Soils

Atterberg LimitsAtterberg limits are water contents where the soil behaviour changes.


Water Content

A

B

C

DEF

G

Va

Vs

Vd

Transition Zone

Vol. of Sample

Vw

LIQUID STATEPLASTIC

STATESEMI-SOLID STATE

SOLID STATE

VO

wlwpws wo

Transition Stages from Liquid to Solid state

Vol. Change of soil = Vol. of moisture lost


Atterberg LimitsLiquid Limit (LL) is the water content at which a soil is practically in a liquid state, but has infinitesimal resistance against flow which can be measured (2.7 kN/m2)

Plastic Limit (PL) is the water content at which a soil would just begin to crumble when rolled into thread of approximately 3 mm diameter.

Shrinkage Limit (SL) is the water content at which a decrease in water content does not cause any decrease in the volume of the soil mass.

(at SL Sr =1)


Idealized section through soil

Shrinkage Phenomena1

2

3

4

5

1

2

34

5

Water Surface

Imagine a compressible soil consisting of tiny grains with capillary pore space between the grains.

R1, R2, R3, R4, R5: Radii of menisci

(R1 >R2>R3>R4>R5)


Shrinkage Phenomenaa) When the pore spaces are completely filled with water and there is free water on the surface of the soil, the meniscus is plane surface (1) and tension in the water is zero.

b) As the evaporation removes water from the surface, a meniscus begins to form in each of the pores at the surface with a resulting tension in water.

c) At some time after evaporation has started the menisci would have reduced to some position (say 2).. At this stage, tension in the water is 2Ts/R2. Soil is compressed by stress equivalent to 2Ts/R2


Shrinkage Phenomena

Ts

TsTs

σ′ σ′

Ts

R2

Tension in water TW can be estimated, by equating Tensile force in water to the vertical component of surface tension force, as Tw = (2Ts/R2)

d) As the further evaporation occurs, the fully developed meniscus in the largest pore recedes to a small diameter!!

Produces increased σ′ and caused further shrinkage


Shrinkage Phenomenae) As the evaporation continues the menisci continue to recede and the tension in the water continue to increase and the compression between the soil grains and the resultant shrinkage continue to increase.

f) Eventually, the meniscus will reach the smallest radius (R5)… By the time, meniscus reduces to least possible radius of meniscus the pores in the soil will not be there to compress…

Hence, Shrinkage!!!


The Atterberg limits provide a good deal of information on the range of potential behaviour a given soil might show in the field with variations of water content.

Atterberg Limits


Plasticity Index or PI

It is the range of moisture content over which soil exhibits plasticity.

Plasticity is defined as that property of a material which allows it be deformed rapidly, without rupture.

IP = wL – wP (Greater the difference between wLand wP, greater is the plasticity of the soil).


Plasticity Index or PIPlasticity Index = LL – PL

This measures the range of water contents over which a given soil can pull water into its macro-structure, assimilate it, and still act like a solid.

Clay soils with high SSA’s and charged particles will be able to hold a large amount of water between platelets due to their charge field and the polar nature of water molecules.


Plasticity Index or PI

Clay soils with high SSA’s and charged surfaces are able to bind/assimilate water molecules and the overall soil will still behave as a plastic solid. Such soils will have high PIs.

Soils with comparatively lower SSA’s will not be able to bind/assimilate water molecules and thus will have much smaller PI values.


Classification of soil based on PI

PI Plasticity

0 Non-Plastic

< 7 Low Plastic

7 -17 Medium Plastic

> 17 Highly Plastic


Laboratory determination of Liquid Limit

Two Methods:

-Casagrandes Method (After Arthur Casagrande)

-Cone Penetrometer Method


2 rev/s


10mm

Hard Rubber Base

54 mm

2mm

Casagrandes Method

Soil Passing 200# Sieve



-Number of blows required to close the two soil halves over a distance of 13 mm is recorded and the water content of the soil is determined.

-The test is repeated several times. Each time change the water content of the sample. A graph of water content vs number of blows is plotted.


Equation of Flow curve: w – w1 = -If [log (N/N1)]

Flow curve and Flow IndexWater Content [%]

+++

++

+ +

+

No. of Blows (Log Scale)

Flow Curve

w1, N1

w, N

N > N1; w < w1

Slope of the flow curve = Flow Index If

25

wL

(indicates rate at at which soil looses shearing resistance with an increase in water content)


Cone Penetrometer Test

50 mm dia.

50 mm ht.

148g-The penetration of a standard cone into a saturated soil sample is measured for 30 seconds.

- If the penetration is less than 20 mm, the wet soil is taken out and mixed thoroughly with water and the test is repeated till the penetration is between 20 – 30 mm. The water content corresponds to 25 mm penetration is taken as Liquid Limit.


Determination of Plastic Limit Water content at which the soil crumbles when rolled into threads of 3 mm diameter.


Typical Atterberg Limits for SoilsSoil type wl wp IpSand NP

Silt 30 - 40 20 - 25 10 - 15

Clay 40 -150 25 - 50 15 -100

NP = Non-Plastic;

-Soils possessing large values of wl and Ip are said to be highly plastic or fat clays.

-Those with low wl and Ip are called lean or slightly plastic.


Atterberg limit values of clay minerals with various adsorbed cations

Cation Mineral

Na+ K+ Ca++ Mg++

Wl [%] Ip [%] Wl [%] Ip [%] Wl [%] Ip [%] Wl [%] Ip [%]

Kaolinite 29 1 35 7 34 8 39 11

Illite 61 27 81 38 90 50 83 44

Montmorillonite

344 251 161 104 166 101 158 99


Liquidity Index and Consistency Index

LLPLSL

w

0

Solid SemiSolid

Plastic Liqui

d

LI < 0 LI = 0 LI = 1 LI > 10<LI< 1

Ic > 1 Ic = 1 Ic = 0 Ic < 0

−=

p

pL I

wwI

−=

p

lc I

wwI


Soil classification based on soil consistencyIc Il Consistency

>1 <0 Very Stiff

1 – 0.75 0 – 0.25 Stiff

0.75 –0.50 0.25 – 0.50 Medium soft

0.50 – 0.25 0.50 – 0.75 Soft

0.25 -0 0.75 – 1.0 Very Soft

< 0 > 1.0 Liquid state


Toughness Index It

With the assumption that flow line is straight between wl and wp and Shearing resistance αNo. of blows

Nl = kSl Np = kSp ;

wl = -If log Nl+C --- (1) wp = -If log Np+C --- (2)

==

=

l

p

f

pt

l

pfp

SS

II

I

SS

II

log

log It <1 Soil is easy to crumble or pulverize.

It = 1 – 3 for most clay soils

Indicates the rate of loss of shear strength upon increase in w %


Distinction between Silt and Clay

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