# Mod-01 Lec-06 Index properties

Welcome to lecture number 6 of module 1 of
advanced geotechnical engineering, so in this lecture we are going to discuss about index
properties. In the previous lectures we have understood about clay particle water interaction. And different methods to determine clay minerals
and sedimentation analysis, before introducing sedimentation analysis we also discussed the
method for determining gradation of coarse grain particles, when you have got a soil
which is more than which is having fines more than 12% then we need to dose sedimentation
analysis or it is also refer to as hydrometer analysis. So hydrometer analysis is basically used to
determine, the gradation of fine particles hydrometer is a device which is used to measure
the specific gravity of liquids. As you see in this slide you have a hydrometer with the
dimensions in millimeters and it has got a stem and a bulb at the bottom, this is used
basically to measure the specific gravity of the soil suspension. So with this it is
possible to measure the specific gravity from time to time as the soil settles the specific
gravity can be SS. For a soil suspension the particle start settling
right from the start and the unit weight of the soil suspension changes from 1 from time
to time. So here in this slide as it is guess it can
be seen that this is at the commence of the test and once the hydrometer is place, then
the specific gravity of the suspension is measured after elapsing at time t2 and again
the reading is taken and here you can see that the particles which are actually settled
at the base and after certain time t2, t3 and t4 and this situation of the settlement
of the particles is shown. So measurement of the specificity of the soil
suspension at a known depth at a particular time provides a point on the grain size distribution
curve. So here the process of the sedimentation of the dispersal specimen is shown here when
you have got at time T=0 you have got a suspension. And if you have a sampling depth at a depth
jet from the top surface of the suspension, it can be written in the form of a phase diagram,
as shown here with the total volume 1 and volume of the solids and volume of water and
with the weight of water on the right hand side and weight of solids on the right hand
side. So with this volume of solids is nothing but Ws /G s γW okay and the volume of water
which is nothing but 1 – you know this total volume, that is 1 this volume of water is
nothing but 1 – V s and substituting here you will get volume of water=1 – W s / G’s
γW. So the γI is nothing but the suspension at
any time nothing but weight of w water + weight of the solids /total volume 1, so that is
written here as weight of solids + γWV w whole /1, so / substituting for V W you will
get the initial unit weight of the net weight of a unit volume of the suspension γI as
γW + WS x GS – 1/GS, so this here the GS is nothing but the specific gravity of the
soil solids. In the process of the sedimentation of disperses
fun here at level x, if you assume here the size of the particles which have settled from
the surface to the depth jet in time TD this is from the Stokes law when you use we can
actually obtain D=√ of 18 μ /G s – 1x γW root over Z / TD so jet is the difference
depth where the measurement is being taken. So above this level x no particle of size
greater than will be present and in element depth of DJ you can see here this is a small
element depth the more this level exits at a depth jet from the surface of the suspension.
May is assumed that uniform and the particles of the same diameter exist, so the particles
are smaller than D and they actually have a uniform specific gravity it is assumed in
that particular elemental distance, if the percentage of the weight of the particles
finer than D already sediment to the original weight of the soil solids in the special suspension. Is say and that is if the percentage of the
weight of the particles finer than D which are already sediment to the original weight
of the soil solids in the suspension is say n then we can actually get the weight of the
solids per unit volume ohms unit volume of suspension at depth Z as N – x W / V where
WS is nothing but W / V. Unit weight of the suspension after elapsing time TD at a depth
Z is given / from the previous discussion γ z=γW x n – x W / V x GS – 1 / GS.
So with this we can actually obtain and – as GS / Gs – 1 x γz – γW x v / W where n – is
in percentage. So the process of sedimentation with the dispersal
specimen but here γZ is nothing but G ESS γW we are GSS is nothing but 1 + Rh /1000
x γW where Jsss is the specific gravity of the soil specific suspension, which is nothing
but the graduations on the hydrometer. The graduations on the hydrometer generally vary
from 0.95 to 1.03 or a length of the stem so RH is the reading on the hydrometer, what
it is noted during the process of experiment. So n – is obtained here as GS / G’s – 1 x
RH 1,000 x V / W, so which is simplified further we are for a volume of say thousand CC of
the soil suspension placed initially, we can actually get n -as GS / G’s – 1 x Rh / W is
nothing but the weight of the solids taken for the dry solids taken for the dispersion
analysis our sedimentation analysis. And as we actually keep the hydrometer in
the from time to time it is subjected to it is required to perform immersion Corrections,
so in order to calibrate or calibration of the hydrometer for the immersion here in this
slide, that two figures which are actually shown, one is before the immersion of the
hydrometer another, one is the after version of the hydrometer. Before immersion of the
hydrometer at level y y is the point at which the measurement is being made that is where
the center of the bulb is assumed to be occurring or assume to be there.
So HE height from the surface from that the distance from the center of the bulb to the
top surface of the soil specimen and when this said the surface top surface be xx and
the surface at which the you know center of the bulb meets is say yy, so when the bulb
is placed there is a raise in the water that raised in the water suspension region the
water suspension is given / V H / AJ because V H is but the volume of the hydrometer AJ
is nothing but the area of the jar in which the experiment is being performed.
So here it is assumed that Y, Y – which is actually you rises above the it is approximated
that 50% of the vh / a G – B it will be subjected to a that with the raise the raise is about
vh / 2 which is about the 50% of the raise of that excitation x –, so with that the
immersion correction can be obtained like this H E=here h + h / 2 + vh / 2 Ag the
distance – Vh / AG so after simplification it is obtained as h +h / 2 – vh / 2Aj so if
it is this immersion correction need to be applied approximately after say two to four
minutes of the you know readings whatever we take.
So the here then we discussed about the calibration of the hydrometer for you know basically for
immersion correction. Then the graduations which are actually there
as I said here from it starts from 0.952 to 1.030 or in the numbers it is our H=0 or
– 5 to 30 this is these are actually this graduated indicated on the stem of the hydrometer
and HE is the difference where the measurement which are which has been taken and these readings
which are achieve one and eighty two are unique for the hydrometer.
So need to be calibrated and then they vary over linear distance with these readings,
so the RH where conversion of our H x HE is done like this where our H=GS s – one in
2000 so the plot of our H with H II is valid for a particular hydrometer, that means that
each hydrometer will have a you know plot for our H and H E. So with the linear interpolation
if you see up to two minutes or four minutes where we do not have any immersion correction
with that H=He1 this distance and – H e1 – H e2 H e1- H t2 /30 x R H this is up to
44 minutes are here H e that is beyond four minutes H e1 – H t1 – HT 2 / 13 to R H – V
H / 2 A G, so this is after 4 minutes. So here it is summarized along with other
Corrections which are actually required for the you know hydrometer reading where n dash
=GS / G’s – 1 x R / w, w is nothing but the weight of the solids and R is the corrected
hydrometer reading which is used in this expression for calculating the percentage and W is the
weight of the solids taken for preparing the soil suspension, where R is nothing but R
h + CM that is meniscus correction + R – C T the temperature correction – CD.
So N combined that is if you have got a performed a sieve analysis and if the percentage of
the fines is say more than 12%, then the total soil taken for you know relation that is WT
and total soil passing 75 micron in a given soil mass which is taken for sieve analysis
and M combined can be obtained / getting n – / using / G’s – 1 x R / W and then putting
substituting in n combined=n – / x W 75 / WT you will be able to get the N combined.
So with that percentage the final and the particle size variation can be plotted and
where W 75 is nothing but the weight of the soil fraction passing seventh of a micron
WT is nothing but the total weight of the soil scaled skeleton for buying the sieve
and hydrometer analysis. So in the hydrometer Corrections apart from meniscus correction
cm, which is a meniscus correction which is applied always positive because the density
readings increased downwards that is that the suspension are the hydrometer readings
increased downwards. So because of that the meniscus correction
is always positive CT it is positive for temperature greater than 27 0 so RH will be less than
what it should be, so the reading will be less than what it should be. So because of
that the temperature correction is positive if the temperature is room temperature is
more than 27 0 negative 49, 27 degrees RH will be more than what it should be so because
of this it is higher, so what it is done is that the temperature correction is done negative.
And CD is always negative because in order to you know prevent of locking of the soil
particles while preparing the suspension the dispersion is not is used like sodium carbonate
or sodium alginate or use 2 d flock the soil. So dispersion as in concentration you know
to account for that the dispersion correction is always negative. So let us see after having
discussed the procedure let us see an example of or the hydrometer analysis with a particular
soil kaolin. Passing you know very fine kaolin soil, so
here the volume of the suspension is 1000 ml and the volume of the hydrometer is which
is taken for the test is about 90 CC and the weight of the dry soil taken is about 50 grams
and the specific gravity the soil is about 2.62, the cross section area of the jar is
AJ about 31 centimeter2 and room temperature is 27 0 dispersing agent correction about
CM=0.0004 meniscus correction CD=0.034, temperature correction CT=0.9965 and discuss
to the water taken as 8.55 8.54 x 10 two raised to – 7 kilo Newton second per meter 2. With this data for the given hydrometer that
is achieve one which is nothing here it is indicated ash – e one maximum depth maximum
depth to center of the bulk from our H 0.995 that is the topmost reading in the stem of
the hydrometer is 21 centimeter, HC2 that is closer to the center of the bulb maximum
depth to the center of the ball from for RH reading 1.030 is 9 centimeter. Let us say
at T at time T=minutes after placing the suspension and the reading which is actually
taken in the hydrometer is say 28.5 which is indicates that RH=1.0285.
Since H- E varies linearly with the RH the / using this presumption and the diameter
of the soil particle is actually calculated / using thousand x 1.8 μ /g RG s – one x
√ over h g 98 x 60 x T that is the time at which the you know the reading is being
taken and percentage finer n=G / G – 1 γ that is Rh + or – C that is a summation of
all the corrections in 2000/ this mass of the solids, which is actually taken for suspension. So here in this slide calculations are given
where H E H – E was obtained based on the hydrometer details where it is obtained as
9.14 and with immersion correction that is Vh / 2Ag it is obtained as 8.063. Now substituting
in the expression which was shown in the previous slide D=1000 x 1.8 545 x 10 to power of – 7/
the specific gravity – 1that is 2.62 -1 x √ of this 8.0 0 6 3/ 19 18 to 16 x 2 which
gives a particle size of 0.025 5mm. So with this you can actually calculate that
n -that is nothing but obtained as about 93%, so based on this for the different timings. When the calculations are done for time 0.5
minute, 1 minute immersion correction was not taken and 2, 5, 15, 30, 60 and then 121
14, 40 these are the reading these are the readings which are actually taken and these
are the corrected H – E and then D in particle size in millimeter, so once you plot this
the particle size on the log semi-log logarithmic scale and the percentage finer on the y-axis
we will get this gradation plot. So here this is the percentage finer on the
y-axis and particle size on the x axis with this is possible, that you will be able to
seethe percentage points. Here in this particular curing soil what has been taken the silt particles
are about 44% and clay particles are about 56%, that means that is basically silty clay
having the clay fraction about 56% and silt fraction about 44% and the 100%fine fractions. So limitations we have used the Stokes law
for calculating you know the come here arriving at the particle size distribution offline-grained
soils however we knew that the clay particles are hardly spherical but they are platelet
particles. So the soil particles are not truly spherical and the sedimentation is done in
a jar which is actually also induces some sort of limiting boundaries type. So for D
greater than 0.2 mm causes turbulence in water and for D

## One thought on “Mod-01 Lec-06 Index properties”

1. shammi kumar says:

Sir I want to know what is practical significance of toughness index
Which soil is better whose toughness index is lower or greater.