We have learnt about measures of gradation and also introduced different Atterberg limits
for fine-grained soils. We studied about the measure of gradation, practical significance
and applications of GSDs.
We also discussed about the different physical states of fine-grained soils like solid state,
liquid state and plastic state. We have defined different Atterberg limits at the interfaces
between different physical states. We have also discussed about the definitions of these
Atterberg limits. In this lecture we will be looking into how to determine this Atterberg
limits and the shrinkage phenomena involved in the drying of the soil. We will try to
look into some classification methods for distinguishing between silt and clay. Slowly
this process should lead to classifying both coarse-grained soils and fine-grained soils.
This lecture is with title Index Properties and Soil Classification Systems part-3.
As we have seen different physical states of fine-grained soil, initially when there
is high water content and this interface between liquid state and plastic state is called as
liquid limit. Interface between plastic state and semisolid state is called as plastic limit.
The difference between liquid limit and plastic limit is set as plasticity index. The interface
between semisolid and solid state is indicated as a shrinkage limit. And we said, that is
the minimum water content at which soil still maintains a complete saturation. After this
limit the soil completely changes into a dry state. Gradually in this zone, air starts
entering and then complete water in the voids is replaced by air to reach the final volume.
The three limits we defined are liquid limit, plastic limit and shrinkage limit. The difference
between the liquid limit and plastic limit is indicated as Plasticity index.
As we have discussed, let us look once again about the different physical states of the
fine-grained soils. If the water content of a clay slurry is gradually reduced by slow
desiccation that is allowing for drying gradually, the clay passes from a liquid state through
a plastic state and finally into a solid state. The water contents at which different clays
pass from one of these states into another is very important. These water contents may
be unique for particular clay. Water contents at these transitions can be used for identification
and comparison of different clays. These water contents like liquid limits, plastic limit
are used as a comparison for identifying different types of clays. Atterberg limits are water
contents where the soil behavior changes. We can put like as follows: Atterberg limits
are water contents, where the soil behavior changes from liquid state to plastic state,
and from plastic state to semisolid state, and the semisolid state into a solid state.
Let us look at this soil moisture scale which is presented in this slide. Here you see,
at liquid limit the soil is having most of the voids filled with water. At this liquid
limit, the soil is having water as many times the volume of the solids. The state above
this limiting line is called liquid limit and the state is called liquid state. At liquid
limit, the consistency is said to be very very soft that is at liquid limit the soil
is said to have a soft consistency and it is said to have a degree of saturation of
about 100 percent. At plastic limit that is interface between plastic to semisolid the
soil is said to have very stiff consistency.
In the plastic state most of the soil deposits do exists in the practice. Even at this particular water content
that is the plastic limit the soil still maintains 100 percent degree of saturation. From plastic
limit to shrinkage limit which is interfaced between semisolid to solid state the air starts
replacing the water in the voids and because of the gradual evaporation process the soil
tends to become extremely stiff at this particular state. Still, this is the minimum water content
in which the soil still maintains 100 percent degree of saturation.
After this, once the soil is allowed to dry then completely the air replaces the water
in the voids between the solid grain particles hence this is called air dry where the soil
is in a very hard state. From air dry to oven dry, for example if we allow the soil block
to dry then whatever hygroscopic moisture content which is there in soil block will
actually be lost. Below this shrinkage limit the soil is no longer completely saturated.
If soil reaches the shrinkage limit the partial saturation will try to come into picture by
losing the complete saturation. Here you see the block which is with more amount of water
which has again now become like a solid block where the grains are pushed together to see
that the soil grains are placed very close or tightly packed with minimum void ratio.
Having seen this and discussed about the shrinking nature of the soil let us try to look at the
shrinkage phenomena. We have discussed that at shrinkage limit the soil still maintains
100 percent saturation.
Let us consider the grains which are shown here, an idealized section through the soil,
assume that these are the grains and these are the different water surfaces which are
shown with different stages 1, 2, 3, 4, 5. When the soil changes from semisolid to solid
state in this curvilinear zone the water gradually gets replaced with air. Let us assume that
a compressible soil consisting of tiny grains that means grains as small as possible with
capillary pore space between the grains.
Let us assume that the menisci radius varies from R1 to R5 where R1, R2, R3, R4, R5 are
the radius of the different meniscus which are forming during the coarse of evaporation.
Assume that R1 is greater than R2, R2 is greater than R3, R3 is greater than R4 and R4 is greater
than R5. With continuous process of drying, the radius of the menisci continuously changes
and radius increases. If you look at that gradual process, that water surface which
was there at 1 transforms to 2, 3, 4 and 5. Let us try to look into the mechanics behind
these particular shrinkage phenomena.
If you look, when the pore spaces are completely filled with water and there is free water
in the surface of the soil, the meniscus is plane surface and tension in the water is
said to be 0. This is the meniscus surface what we are discussing, that is the tension
in the water is 0 and it maintains the free surface. Now, 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 the water. So surrounding
the grains the meniscus starts forming. At some time after evaporation has started the
menisci would have reduced to some position (say 2). That is, we are discussing about
at this stage that the menisci has come up to position 2. At this stage, the tension
in the water is said to be 2Ts by R2 where Ts is the surface tension of water and R2
is the radius of meniscus at the particular stage. Soil is compressed by stress equivalent
to 2Ts by R2. Let us look at this with a detailed figure that is, between the two grains how
this force acts to compress the soil grains.
So here consider the same surface tension of water which is acted with a radius of meniscus
R2. Tension in the water Tw can be estimated by equating the tensile force in water to
the vertical component of the surface tension force. Let us assume that the water is clean.
By assuming water is clean the tension in the water can be calculated as Tw is equal
to 2Ts by R2. If you see here, as R2 radius gets decreases that is it is becoming sharper
and sharper then the tension in the water keeps on increasing. As R2 decreases Tw the
tension in the water keeps on decreases. That is what actually happens as the soil starts
drying, the water surface or water menisci starts changing from position 1 to 2 and 2
to 3 with decreasing radius. As further evaporation occurs the fully developed meniscus in the
largest pore recedes to a small diameter and so it produces increased sigma dash and caused
further shrinkage. This stress acting between the grains acts like a compressive stress
and it pushes the grains together. So the grains will get compressed up to the maximum
extent possible to reach the minimum void ratio. Then soil tries to transform into a
very dense packing state.
As the evaporation continues the menisci continue to recede and the tension in the water continues
to increase. And the compression between the soil grains and the resultant shrinkage continue
to increase. Eventually, the meniscus will reach to smallest radius RS by the time meniscus
reduces to least possible radius of meniscus and the pores in the soil will not be there
to compress. That means most of the pores in the soil will already get compressed because
of the interactive forces at the grain to grain limit, hence the shrinkage phenomenon
occurs. What we have seen here is that, as the evaporation process continues the radius
of the menisci continues to decrease and when it reaches 5 the inter-granular force is very
very high where the grains are pushed closer so the soil undergoes a shrinkage phenomenon.
Having seen the shrinkage phenomena, we will go to the determination of these methods once
this plasticity index is defined. The plasticity index is nothing but a difference between
liquid limit and plastic limit.
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 specific
surface areas and charged particles like this will be able to hold large amount of water
between particles due to their charge field and polar nature of water particles. Clay
soils with high specific areas tend to exhibit very high plasticity indices. The plasticity
index is nothing but the measure of the degree of plasticity.
Clay soils with high specific surface area and charged surfaces are able to bind and
assimilate water molecules and the overall soil will still behave as a plastic solid.
Such soils will have high plasticity indices. Clay soils with high specific surface areas
that means finer is the particle, higher is the specific surface area and charged surfaces
are able to bind or assimilate water molecules and the overall soil will still behave as
a plastic solid. Soils with comparatively lower specific surface areas like sandy grains
will not be able to bind or assimilate water molecules and they will have much smaller
plasticity values. That means soils like silt or sandy silt will not exhibit higher plasticity
because with comparatively lower specific surface area they will not be able to bind
or assimilate the water molecules to the grains. So because of this phenomenon they will have
smaller plasticity indices values. So while designing an earth and fill for a particular
construction for example, for an embankment construction or so then deciding about the
plasticity index value is very very important. One classifies the soil based on the plasticity
index value. Suppose if the value of the plasticity index value is 0 basically it happens for
sandy soils then it is said that it is non-plastic in nature. So, if the plasticity index is
0 then it is said to be non-plastic in nature. If the plasticity value is less than 7 the
soil is said to be low plasticity.
For some type of construction like earth and fill materials low plastic soils are recommended
because it is easy to compact these particular types of soils. So, if the plasticity index
ranges between 7 and 17 they are said to be classified as medium plastic soil and if it
is greater than 17 then the soils are said to be very highly plastic soil. If the plasticity
index value is more than 17 it indicates a soil with very high plasticity. So having
defined about different Atterberg limits at the interfaces of different physical states,
now, it is time for us to look for, how to determine these different Atterberg limits
like liquid limits, plastic limit and shrinkage limit of the given soil. Let us look the determination
methodology for liquid limit.
Liquid limit is basically determined in the laboratory by using two widely accepted methods.
One is Casagrandes cup method, it is also called Casagrandes method. This is actually
postulated after Arthur Casagrande. Other one is the Cone Penetrometer method. Both
these methods are widely used. Out of these, Casagrandes liquid limit method is popular.
Here in this, the Casagrandes method runs like this. The laboratory determination of
the liquid limit by using Casagrandes method is shown. So, here a soil passing through
750 micron and soil passing through 75 micron or 200 number sieve has to be taken in a dry
state. It is placed with certain water content in the Casagrandes cup. The Casagrandes cup
has got a radius of 54mm. It is attached to a crank mechanism and it is placed on a hard
rubber base called Mcarthur rubber base. The soil mass is formed with certain water content.
In this method by using Casagrandes tool or ASTM standard tool, a groove of 2mm is required
to be made like this. The groove of the 2mm can be made by using Casagrandes tool which
has got a 2mm dent at the bottom of the tool or ASTM tool which has got similar arrangement
will also give a 2mm groove in the middle of the sample. Then it is a placed and rotated
in this direction as shown here at the rate of 2 revolutions per second gradually.
This particular methodology has been standardized by conducting number of experiments. This
is widely accepted standard method where this particular cup is subjected to tamping with
a distance of around 10mm to induce movement in the particular soil which is actually separated
with this 2mm groove. The number of blows required to close 13mm of this particular
portion of the soil is measured along the total length of the group. It is required
to be noted that the number of blows which are required to close 13mm length or half
inch length of the groove and if you know the corresponding water content we will get
a water content at which so many number of blows are required to close 13mm length of
the groove. By repeating this particular exercise with increasing water contents one finds variation
in water content with number of blows.
Number of blows required to close the two soil halves over a distance of 13mm is recorded
and the water content of the soil is determined. So the test is repeated several times that
is what being discussed. The test is required to be repeated at different water contents
and the number of blows which are required to close 13mm groove is required to be measured.
Each time the change in the water content of the sample is noted the graph of the water
content versus the number of blows is plotted.
Let us look how the graph looks like? The water content is plotted on the y-axis and
the number of blows required is plotted on the x-axis. These are the number of points
which we got for the soil which has been tested with number of water contents. So generally
soil is tested in dry state with higher water content. The line joining all these points
is called the flow curve the line and slope of this flow curve is called flow index which
is indicated as If. This flow index is nothing but it indicates the rate at which the soil
looses shearing resistance with an increase in the water content.
Now, if you plot number of points. Since the number of blows can be 1, 10, 100, 1000 this
is actually plotted on the logarithmic scale here. Here, if you consider two points on
this axis like W1 and N1.where W1 is the water content at N1 the number of blows and W is
the water content at N number of blows. The equation for the flow curve is written like
W minus W1 is equal to minus If log (N by N1). The slope of this curve is nothing but
W minus W1 is equal to minus If log (N by N1). So, here the water content correspond
to 25 number of blows is referred as a liquid limit. This is actually been fixed based on
number of correlation on different clays and it has been standardized to determine liquid
limit. One tends to do a minimum of three values on the right hand side of this particular
25 number of blows and minimum three values less than 25 number of blows to generate a
flow curve for particular soil and determine the flow index and liquid limit of a given
Second method is a Cone Penetrometer method. Before discussing Cone Penetrometer method,
one of the demerits which are going to be with liquid limit method is that most of the
soils do exists in intact state at a particular level. But what we do in a liquid limit test
in Casagrandes cup method is a disturbed condition state where the original disturbed condition
or remold state in which the representation of the bonds or soil fabric is not considered
or it will not be replicated. So now what we are doing is that, it remains in a certain
remold state with a certain soil fabric. The Cone Penetrometer method works out like this.
It has got the penetration of a standard cone into the saturated soil sample is measured.
The equipment has got a vertically mounted cone and with a standard load of 148g is placed
at the cone of this particular size. This particular truncated portion is going to have
around 30.5mm length or so.
It is a soil under cushion or a soil which is to be tested is to be placed in 50mm diameter
and 50mm height small cylindrical container in which the soil with certain water content
is placed. That cone is allowed to penetrate into the soil. So the penetration of the standard
cone into a saturated soil sample is measured for 30 seconds. If the penetration is less
than 20mm then the wet soil is taken out and mixed thoroughly with water and again the
test is repeated till the penetration is between 20 to 30mm. This is required to be carried
out. So water content corresponds to 25mm penetration is taken as a liquid limit. So we have discussed
about methods to determine the liquid limit. Let us now consider the method to determine
plastic limit. This is the second Atterberg limit: The water content at which the soil
starts crumbling, when it is rolled into a thread of 3mm diameter basically.
This is the standard method as of today to determine. For determining the plastic limit,
the soil is molded like this and made into a small thread of 3mm diameter. When it starts
rolling, the water content at which the soil starts crumbling is actually measured as a
plastic content. This is required to be done with repeated trails. The average value of
the number of the trails has to be taken into record as a plastic limit. This crumbled portion
has to be kept in oven-dried for about 105 degree C or so to determine plastic limit.
The typical Atterberg limits for sandy soil is said to be in non-plastic. Though a fine
sandy soil under certain moist states can exhibit some liquid limit but they are basically
with plasticity index 0, where it is called non-plastic. Silt is the particle with low
surface area and because of the limited capacity to simulate water to the particles, they exhibit
low Atterberg limits. Basically liquid limit will be in the range of 30 to 40 and plasticity
index will be in the range around 10 to 15 and they are actually medium plastic soils.
Clays will exhibit from 40 to 150 and plasticity index up to 15 to 100. The clays possessing
very high plasticity index values are called fat clays and the clays possessing low plasticity
index values are called lean clays. A fat clay and lean clay is actually the terminology
which is used generally in the practice. Soils possessing large values of liquid limit and
plasticity index are said to be highly plastic or fat clays. Those with low liquid limit
and plasticity index are called lean or slightly plastic soils. Depending upon the type of
the mineral and adsorbed cations the soil can have various liquid limits.
That is what it is being shown here in this particular table. Atterberg limit values of
clay minerals with various adsorbed cations. If you see here, different adsorbed cations
Na to the power plus, K power plus, Calcium power plus plus and Mg power plus plus is
shown and because of higher replacing power the thinning of the adsorbed layer occurs.
And because of that the liquid limit and plastic limit decreases.
For example, sodium based Montmorillonite clay can have a liquid limit of 344 percent
and plasticity index of around 251 percent. The calcium based Montmorillonite can have
a liquid limit about 166 and plasticity index of about 100. Sodium based Kaolinite is said
to have a very low liquid limit. With magnesium or calcium, it will have a liquid limit in
the range of 34 to 39 percent. Illite is falling in between kaolinite and Montmorillonite.
Here in this particular table Atterberg limit values of clay minerals with various adsorbed
cations are shown. As we can seen here, with Na to the power plus, K power plus, Calcium
power plus plus and Mg power plus plus there is a gradual decrease in the liquid limit
and the plasticity index values.
So, once we have determined liquid limit, plastic limit and plasticity index basically.
Now we are interested in accessing the soils consistency. These are basically carried out
by using two indices called liquidity index and consistency index. Liquidity index is
defined like this (W minus Wp) by Ip, where W is nothing but the water content in its
natural state, Wp is the plastic limit of a given soil and Ip is the plasticity index.
Ic the consistency index is nothing but difference of liquid limit and water content in natural
state to plasticity index.
If you consider here in this line, this is the solid state that is between shrinkage
limit to 0 water content, semisolid state that is from plastic limit to shrinkage limit
and plastic state between liquid limit to plastic limit. Above this is a liquid state.
In the solid state, the liquidity index value is said to be less than 0, contrary to this
in the solid state the consistency index will be greater than 1 because Ic is equal to (WL
minus W) by Ip. Because of this Ic is greater than 1. In each and every state if you compare
Ic plus IL is said to be equivalent to unity. So at plastic limit, liquidity index value
is 0 because the water content at plastic state W is equal to Wp and consistency index
is equal to 1. That is at this particular point the difference W1 minus Wp is nothing
but a plasticity index which is actually called Ic. Ic is equal to 1 at plastic limit.
Liquidity index is equal to 1 at liquid limit and at liquid limit consistency index value
is 0. At liquid limit, liquidity index is equal to 1. Above liquid limit that is in
the liquid state the liquidity index value is greater than 1 and Ic is less than 0. The
Ic that is consistency index value is less than 0 indicates that the soil is in very
very soft state. In a liquid state, if liquidity index value greater than 1 then the soil state
is again said to be in the very very soft state. So the two indices we explained is
basically to define the consistency of the soil. One is the consistency index which is
nothing but (WL minus W) by Ip, where WL is nothing but the liquid limit minus water content
in natural state to plasticity index of a given soil. Similarly liquidity index IL or
LI is indicated like (W minus Wp) by Ip, where W is the water content in natural state to
Wp is the plastic limit and Ip is the plasticity index. Basically we have a standard soil classification
methodology based on the soil consistency particularly with different ranges of liquidity
index values and consistency index values.
As we discussed, if Ic greater than 1 or Il less than 0, the soil is said to be in a very
stiff state. When Ic is in between 1 to 0.75 and 0 to 0.25, the soil is said to be in stiff
and in between 0.75 to 0.5 or 0.25 to 0.5, it is said to be in the medium soft. Similarly,
when the Ic¬ value is less than 0 and Il value is greater than 1, the soil is said
to be in the liquid state consistency. This is the standard soil classification based
on the soil consistency where the soil is said to be very stiff. If Ic is greater than
1 that means that most of the voids in the water is removed and if the value of Il is
less than 0, then it is called a very stiff consistency.
Here, if Ic is greater than 1 then it is said to be in the liquid state. So two extremities
are defined with these two indices that is liquidity index and consistency index. Another
index is called toughness index. The toughness index It indicates the rate of loss of shear
strength upon increase in water content. Suppose, for a given soil if the water content gradually
increase then this toughness indicates the rate of loss of Shear strength upon increase
in the water content. So with the assumption that the flow line is a straight line between
liquid limit and plastic limit the shearing resistance is proportional to number of blows.
The flow line is assumed to be linear between liquid limit and plastic limit, and shearing
resistance is proportional to number of blows. At liquid limit, number of blows required
Nl is equal to KSl, where Sl is the shear strength of a soil at the liquid limit. So
Nl is equal to KSl. where K is a constant and similarly for the same soil in same slopes,
then Np is equal to KSp that is number of blows at plastic limit is equal to K times
shearing resistance at Sp.
From this, if you substitute this in the equation of the flow curve where W1 is equal to minus
If log N1 plus C then substituting for Nl, KSl and substituting Np, KSp we get by subtracting
Wl minus Wp converting and writing as Ip is equal to If into log Sp by Sl. This is nothing
but Ip by If is equal to log (Sp by Sl). This ratio of plasticity index to the flow index
If is nothing but the slope of the flow curve called It is equal to Ip by If.
Generally for most of the clay soils It value varies from 1 to 3 and It is less than 1 then
soil is said to be easy to pulverize. Basically this happens with silt soils and clay soils.
Silt soil is easy to pulverize and break where the clay soil is very very difficult to break
because the toughness index value will be greater than 1. So having seen different methods
for determining liquid limit and plastic limit, once we know the liquid limit and plastic
limit we will be able to estimate the plasticity index, then show that we will be able to assess
the soils plasticity. When the soil is transforming from semisolid to solid state one more interface
limiting water content arises which is termed as shrinkage limit and the methodology which
is required to determine the shrinkage limit is like this.
For example, if you consider a original soil pack with solids and very high water content,
here when this particular soils pat is allowed to dry, the water which is evaporated is nothing
but V1 minus V2. This V1 minus V2 is the amount of water which is evaporated and then transforms
into a dry state once it allowed to dry. This is the soil pat at shrinkage limit and this
is the soil pat at the dry state. Let us look at the methodologies for arriving at shrinkage
limit. Once if you know the specific gravity of the soil or if you do not know the specific
gravity of the soil then what is the methodology is available for determining the shrinkage
limit? There are two approaches; one is by knowing the specific gravity or without knowing
the specific gravity.
Consider a soil sample which has been shown here with original soil pat and with volume
of water. All the voids in the soils are filled with water so it is a 2-phase system. Ws is
the weight of the solids,W1 is the initial weight of the soil pat and V1is the initial
volume of the soil. Once it is allowed to drying soil pat at shrinkage limit is V2 the
volume and Ws is the solids again. The weight of the water is remaining at the shrinkage
limit and W2 is wet weight of the soil pat at shrinkage limit. So V1 minus V2 is the
volume of the water which is lost during the process of evaporation. Now, weight of water
is nothing but the difference of W1 and Ws that is weight of soil mass minus weight of
water minus volume of water, W1 minusWs is nothing but the water which has been evaporated.
That is (V1 minusV2) into gamma w, this much weight of water has been evaporated. Once
the soil pat is allowed to dry because of the phenomena we have discussed there will
not be any volume change. So V2is equal to Vd . Here, from this process to this process
the air gradually replaces the water. That is, water gets gradually replaced by air so
it is transformed into a dry state. Here what we see is a plastic state, initially we took
a plastic state and once you allow it to dry it is transformed to a shrinkage state that
is at the shrinkage limit and from there into dry state. Here the soil pat is allowed to
dry in the air till the color changes from the dark color to light color and placed in
the oven at 110°C till its weight becomes constant. Basically we take glass containers
in which the inner surface of the glass containers is required to be lubricated to prevent any
cracking of the soil pats upon rain and allowed for drying gradually in the laboratory. So
with these assumptions let us try to determine shrinkage limit. Two approaches are there.
The first approach is that the specific gravity of the soil solids is not known. In that case
shrinkage limit is nothing but a water content which is the weight of water to weight of
solids. So weight of the water is nothing but (W1 minus Ws minusV1 minusV2) into gamma
w. That is what we have been discussed (W1 minus Ws minus V1 minus V2) into gamma w is
actually the volume lost equal amount of water which has been lost because of the evaporation.
By rewriting this particular expression, we can write shrinkage limit as is equal to Wi
that is initial water content is (W1 minus Ws) by (Ws minus V1 minus V2) by gamma into
(gamma w by Ws). So shrinkage limit is equal to [Wi minus (V1 minus V2) into (gamma w)
by Ws] into 100. So this is actually a process where in you are required to know the initial
water content. V2 is the volume at the end of the shrinkage limit or in the oven state.
So this V2 is required to be determined by a mercury displacement method. We have a standard
method in the laboratory where we immerse the dry soil pat in the mercury. The volume
of mercury being placed is calculated and the weight of the mercury which has been replaced
by mercury by the specific gravity that is going to give the volume of the soil pat.
In this approach, to measure the volume of the soil pat at the end of the drying is said
that there is a mercury displacement method. At the shrinkage limit or at the dry state
V2 is equal to volume of the displaced mercury by Gmercury which is nothing but 13.6. With
that we will be able to get V2. Once we know the V2 that is once you know initial volume
of the soil pat without even knowing the specific gravity of the solids we will be able to estimate
shrinkage limit of a given soil. Another approach is that, the specific gravity of the solids
is known to us. Then let us assume that volume of voids is equal to volume of water is equal
to V2 minus Vs. At the shrinkage limit as the soil is still completely saturated. So
all the voids are filled with water, volume of voids is equal to V2 minus Vs. So we can
write weight of water as V2 minus Ws by (Gsgamma w). That is Ws is equal to Gs Vs gamma w.
From there by writing Vs is equal to Ws by (Gsgamma w). We can write this particular
expression. By seeing this, WsL is equal to weight of water to weight of solids. So weight
of water is estimated like as [V2 minus Ws by (Gsgamma w)] into gamma w. by Ws gives
us the shrinkage limit. By rearranging and simplifying we can write V2 as Vd and Gs as
gamma s by gamma w. [(Vd minus Ws by gamma w) into gamma w] by Ws is shrinkage limit
where here Gs is equal to gamma s by gamma w which has been replaced.
Simplifying further we get shrinkage limit WsL is equal to (Vd gamma w by Ws) minus 1
by Gs. So now writing this gamma d is equal to Ws by Vd. That is Ws by Vd is substituted
here as gamma d that is gamma w by gamma d minus 1 by Gs For a dry soil gamma d is equal
to (Gsgamma w) by (1 plus e). So using soil gamma d is equal to (Gsgamma w) by (1 plus
e) and simplifying this particular expression will get shrinkage limit is equal to e by
Gs.e is the void ratio at the shrinkage limit that is the minimum void ratio for a given
soil. So e is equal to WsL Gs. So initial wet weight and initial wet volume is not required
in this approach. If you know the specific gravity of the solids, sometimes it is also
required;, the specific gravity of the solids can be determined by knowing the other values.
So in this approach we have seen the two methods. One method is determined by not knowing the
specific gravity and another one is by knowing specific gravity. Now let us define shrinkage
Shrinkage ratio is nothing but is a ratio of volume change expressed as percentage of a dry volume to
the corresponding change in the moisture content from initial value to shrinkage limit. So
shrinkage ratio is indicated by r. So r is equal to [(V1 minus V2) into 100 by (Wi minus
WsL). But Wi minus WsL) can be written as ((V1 minus V2) into (gamma w)) by Ws] The
Wi minus WsL is nothing but amount of water evaporated from the plastic state to shrinkage
So simplifying further we can write shrinkage ratio as r is equal to [(V1 minus V2) by V2]
into [Ws by (V1 minus V2)gamma w]. Simplifying further by canceling V1 minus V2, we get Ws
by (V2 gamma w). This can be again simplifies like by writing Ws by V2 that is nothing but
dry unit weight of soil mass Ws by Vd. The volume of the soil mass with solids and air
gamma d by gamma w which is nothing but Rw is equal to Gmdry that is nothing but mass
specific gravity of a given soil mass in dry state. So the shrinkage ratio is equal to
mass specific gravity of the given soil in dry state. So substituting in the previous
expression what we have derived WsL is equal to (gamma w by gamma d) minus 1 by Gs is equal
to (1 by R) minus (1 by Gs) so this is the expression what we derived. So Gs can be determined
by back calculating from the shrinkage ratio and shrinkage limit. So by knowing the shrinkage
limit and shrinkage ratio we will be able to cross check the specific gravity of the
solids. This is actually the procedure for determining the shrinkage limit. So having
seen, there is one more very important parameter called activity number.
Activity number is nothing but the ratio of plasticity index to percentage clay fraction.
So activity number is basically is used to define the swelling potential of the clays
basically for fine-grained soils. The skemton considers the change in the volume of the
clay during shrinking or swelling which is a function of plasticity index and amount
of the finer clay size particles. That is amount of clay particle size is finer than
that is less than 2 micron size. That is, the amount of the finer particles is finer
than 2 micron size. If you see the clay minerals and activity ratio, activity ratio is less
than 0.38 for kaolinite and in between greater than 0.38 and 0.9 for illite and greater than
2.45 for montmorillonite or BC soils that is block cotton soils. Montmorillonite soils
are liable to have very high activity ratio.
Once the activity number is determined we will be able to estimate the swelling potential
of the particular clays whether the clay is used to identifying this particular soil is
having the swelling nature or not, this activity number can be assertine. Actually this is
basically obtained by the percentage clay fraction finer than 2 micron and by knowing
the plasticity index. The activity number which is defined as ratio of plasticity index
to percentage clay fraction which is finer than 2 microns.
This particular graph is shown here. The clay fraction is less than 0.002mm expressed in
percentage which is shown here on the x axis. Plasticity index graph is shown on the y axis.
So here, if you see the kaolinite is exhibiting the value of 0.38 and illite has the value
in between 0.38 and 0.9. So this is actually the illite line. Somewhere here the montmorillonite
is actually having very high activity number which is 7.2. That is what we have discussed
that montmorillonite clays are known for swelling or a shrinkage or swelling in nature. There
are different slopes which are dictated if the soil falls in this range then they are
said to be inactive and if it is in between 0.75 to 1.25, if there are more than 1.25
and that the soil is above 2.45 then it is actually said to be very active.
Very active in the sense, the particular soil is prone for higher degree of swelling. So
we have seen different methods about determination of the liquid limit, plastic limit and shrinkage
limit. Now we have also studied about different methods which are available for determining
the size of the soils. Now it is time for us to classify the soil basically by knowing
different particle size distribution of coarse-grained soils as well as some information about on
the physical states of the fine-grained soils. With that we will be able to classify these
soils. So basically this classification methodology is to group the particular soils which are
having identical properties. So that for an engineer, once this particular group is known,
it is easy to identify and get first hand information about the soil behavior.