# Lecture – 23 Flow of water through soils – IV

Welcome to fourth lecture under the topic
flow of water through soils. In the previous lecture we have discussed about fluid flow
through soils and flow of water through a porous media. Then we also discussed about
changes in geostatic stresses with flow of water through soil. And we have introduced
an upward flow condition, a flow condition which is defined as a quick sand condition.
And we have looked into some typical examples governing the quick sand condition. In this
lecture we are going to learn about factors affecting the permeability. Before discussing
about the factors affecting permeability, let us look into the methods which are available
for measuring permeability in the laboratory. As introduced in the previous lecture, permeability
can be measured in the laboratory as well as in the field. For the field we have got specific methods
which are required to be executed to compare the laboratory permeability or sometimes to
access the permeability under in-situ conditions. Now in this particular lecture we are going
to study about flow of water through soils, particularly the measurement and then their
factors affecting this coefficient of permeability which is nothing but the Darcy’s coefficient
of permeability. Before looking into this the particular problem is given to practice
as a continuation of the previously solved problems. The problem statement is as follows.
Determine and plot the total vertical stress, pore water pressure and effective vertical
stress distribution at levels A, B and C shown in this cross sectional diagram. So here in
this slide the 2 layers of soils are shown. The upper layer is silty clay having specific
gravity of solids has 2.7, natural water content as 45.2 % and coarse sand which is lying below
this silty clay is under artesian conditions. So the head of the water above this natural
ground water table is 4 meters. So in view of the concepts already introduced, first
determine the total vertical stress at point A, B and C which are at elevations A, B and
C. Then considering the flow which is taking place in the vertical direction, determine
the pore water pressure at A, at B and at C. Then subtracting pore water pressure from
total stress determine the effective stress. And from the given data it is also possible
to estimate seepage velocity. So this can be estimated by knowing coefficient of permeability.
Let us consider the coefficient of permeability for this type of soil is say 1 × 10 to the
power of minus 7 meter per second. By knowing the hydraulic gradient or with which the flow
is occurring, we can compute the discharge velocity or superficial velocity which is
V=ki. By knowing the natural void ratio or the void ratio from the water content w
=45.2 % and specific gravity of solids 2.7, we can compute the void ratio of a soil. The
soil being saturated e=w Gs will be valid. So from these concepts we can determine e.
From their the porosity can be calculated Sn=e by 1+ e. By using relationship between
seepage velocity and discharge velocity the relationship what we derived in the previous
classes is Vs=V by L. By using the computed value of N and computed value of discharge
velocity, we can calculate seepage velocity. So this is how the problem works out. What
you are required to determine is total vertical stress at elevation A, B and C and pore water
pressure at A, B and C by considering the upward flow because the sand layer below is
under artesian conditions. Let us look into the permeability and drainage
characteristics of soils. Before introducing the methodologies for determining the permeability’s
in the laboratory, let us look into the ranges of the values of the permeability’s of soils.
So coefficient of permeability k meter per second which is given here. The zone with
yellow is shown with a permeability ranging from 10 to the power of zero to 10 to the
power of minus 6 meter per second. And the zone with pink color shown is ranging
from 10 to the power of minus 6 to 10 to the power of minus 8 meter per second. And practically
impervious zone which is indicated with orange color is 10 to the power of minus 8 to 10
to the power of minus 11 meter per second. So you can see the range of the values of
the permeability for a sandy type of soil or a gravelly type of soil. The permeability
is as high as 1 meter per second. For a clayey type of soil, a pure or homogeneous clayey
type of soil the permeability can be as low as 10 to the power of minus 11 meter per second.
So the contestation behavior could be attributed to the soil type which will be discussing
during the later part of the lecture. So here from the drainage point of view, many
times we are required to select a particular material for performing drainage. For example
under parking lots or under food paths or under market yard pavement paths or below
the road sub grade. So the drainage which is very important in such type of locations.
So the good drainage conditions for a soil can prevail if the permeability is in the
range of 10 to the power of 0 to 10 to the power of minus 6 meter per second. One can
have seen the tendency of decreasing the susceptibility or the qualification for a good drainage material
decreases this direction. The poor is the region from 10 to the power of minus 6 to
10 to the power of minus 8 meter per second and practically impervious from 10 to the
power of minus 8 to 10 to the power of minus 11 meter per second. The types of soils which
will come in this particular type of zone are clean gravels or clean sands or clean
sand with gravel mixtures. So if you have got a clean gravel and clean
sands and clean gravel and sand mixtures then they can be qualified to some extend as a
good drainage material. In case if you have very fine sands, organic and inorganic silts,
mixtures of the sand, silt and clay like glacial till and stratified clay deposits, so stratified
clay deposits in the sense like waved clay deposits, in those cases the permeability
requirement is 10 to the power of minus 6 to 10 to the power of minus 8 meter per second.
And the qualification as a drainage material or a rating is poor. And here homogeneous
clay below the zone of weathering can have permeability in the range of 10 to the power
of minus 8 to 10 to the power of minus 11 meter per second. And this can be a practically
impervious material as far as the drainage point of view, but this particular property
can be used or is being used for constructing or preventing the migration of pollutants
and contaminants. Let us look into the measurement of the soil
permeabilities. This particular slide we have already seen, once again let us look into
this particular slide. The value of the coefficient of permeability k depends upon average size
of the pores and is related to particle sizes and their packing. So here the larger particles
can have larger pores spaces and smaller particles can have smaller pores spaces. So here average
size of the pores and it is related to the particles size and their packing. And particle
shape it can be angular or sub angular or rounded. So we have discussed earlier the
particles with rounded arrangement can have large pore spaces. So in those cases the permeability
can be high. For example if the particles are with sub
rounded or angular in shape then the flow can be affected because of the interaction
of the water, when it is flowing through those pore channels passing through particles having
angular shape. And the soil structure that is arrangement of the particles. Incase of
a single grained structure for bulky particles it can have two extremes like loose arrangement
and dense arrangement or in the case of natural arrangement it can be medium dense or medium
very dense arrangement. So depending upon the arrangement it can have
the effect on the permeability. When it comes to this soil structure for fine grain soils,
it all depends upon the physico-chemical environment surrounding the particles. So that can influence
the permeability value to a large extend. This is what we discussed in the previous
lectures, the ratio of the permeabilities of typical sands and gravels to those of typical
clays is of the order of 10 to the power of 6. As you have seen in the previous slide
the clay and sand have got a distinct difference in the permeability values. So typical sands
and gravels to those of the typical clays is of the order of 10 to the power 6. So one
million times difference can be there. A small proportion of the fine material in a coarse
grained soil can lead to a significant reduction in the permeability. So let us look into the methods for measuring
the permeability. We have discussed that the number of tests can be used to measure or
estimate the permeability. Laboratory methods basically the two methods which are popular,
one is constant head test which is basically used for highly permeable soils. And other
method which is called falling head test which is basically used for relatively impermeable
soils which is meant for clayey soils or silty clay or silten clay mixtures. Indirect methods
for computation from the grain size distribution and oedometer test. In the field methods we
have discussed about two methods one is pumping methods and borehole methods. Particularly
the packer’s tests are very famous. So here we are not discussing about the field
methods but there are field methods which are available based on the pumping test for
an unconfined layer or a confined layer under an impermeable layer or under a permeable
layer. So packer’s tests are very famous in determining the permeability value in the
field. Let us discuss about the two laboratory methods called constant head test and variable
head test or falling head test for determining the permeability in the laboratory. And indirectly
for a typically clean sands or mixtures of silt and sand to some extent, the determination
of the permeability by using a correlation between an effective particle size and coefficient
of permeability is very useful in estimating the permeability value. Before looking into the laboratory measurement
of the permeability, the two important aspects which are required to be understood are has
to be ensured or discussed. So in this slide in determining the permeability of coarse
grain material, large quantities of flow occur in short periods of time. Because of the large
pore spaces the large quantities of flow occur in a short period of time. Contrary to this
incase of fine grain soils, small quantities of flow occur over a long periods of time.
So the two distinct differences are in case of coarse grain soils, large quantities of
flow occur over a short period of time and incase of fine grain soils small quantities
of flow occur over a long period of time. So two aspects that need careful attention
for all types of soils, the first aspect is to ensure that the flow occurs only through
the soil and not at the interface between soil and the mould in which of the soil is
contained during the permeability test. The soil sample is fully saturated before recording
observations. So this has to be ensured that the importance of saturation of the sample
is very much required. Otherwise the air which is there in the voids of the soil mass can
influence the permeability value, can hinder with or can influence the flow channels which
are developing through the soil mass. So here the two aspects, one is to ensure
that the flow occurs only through the soil not at the interface between the soil and
the mould in which the soil is contained. The soil sample is fully saturated before
recording observations. So one of the first methods for determining the permeability of
relatively permeable soils, basically the soils which are coarse grain in nature they
are determined by using constant head permeability test. The setup for this is explained in this
slide. It shows like this, a soil sample having a thickness L which is shown here and which
is surrounded by two porous stones. One porous stone is placed above and one porous stone
is below and a constant head water level is maintained as shown here in this figure. The extra surplus water is collected here.
And the water level is maintained here. So here because of this the flow occurs with
a hydraulic gradient h over L. So the flow occurs in the downward direction so here a
relatively sandy soil is shown and A is the area of the cross section of the specimen
perpendicular to the direction of the flow. So this is an arrangement for constant head
test. So in order to calculate the flow or coefficient of permeability what one has to
do is that after establishing a steady state seepage conditions collect an amount of water
say in q at given time t. For a given time t suppose you collect an amount of water in
a measuring jar which is q. So based on that by using the relation theory of continuity
equation we can say that q is equal to Avt. Where A is the area of the cross section over
which the flow is occurred and v is the discharge velocity with which the flow is taking place
and t is the time over which this flow q has been collected, i is the hydraulic gradient
which is nothing but h over L, L is the length of the specimen where h is the head which
is driving the flow. So the head loss between these two levels
is h. So q is equal to AK into h by L that is V has been substituted by adopting the
Darcy’s law conditions Ki, K which is the coefficient of permeability, i is h by L in
time t. So after rearranging we can write k is equal to QL by Aht. So by following this
method or by repeating the similar experiment for 3 or 4 times, then average value of the
coefficient of permeability k can be determined. So this is basically a method for coarse grain
soils, so this has to be conducted either on the disturbed samples or on the remolded
samples and it is not possible to perform this particular test on undisturbed samples. Let us look the main feature of the constant
head test. It is suitable for soils having a coefficient of permeability in the range
of 10 to the power of minus 2 to 10 to the power of minus 5 meter per seconds. Like as we introduced previously it should
have the permeability in the range of 10 to the power minus 2 to 10 to the power of minus
5 meter per second which applies to clean sand and sand-gravel mixtures with less than
10 % fines. So the fines cannot be more than 10 %, if it is more than 10 then the variable
head test or falling head test has to be considered. It can be suitable for soils when used in
their completely disturbed or remolded states such as for drainage materials and filters
to confirm that their performance will be adequate. So many times it is required or
this is performed for checking or qualification of these particular materials as drainage
materials or a filter materials. So the main features of constant head test
is basically used for coarse grain soils or soils having permeability in the range of
10 to the power of minus 2 to 10 to the power of minus 5 meter per second. And which applies
to clean sand and sand gravel mixtures with less than 10% fines or so. So it can be suitable
only for soils when used in their completely disturbed or remolded states such as for drainage
materials and filters to confirm that their performance will be adequate. So having seen the constant head test for
determining the permeability of coarse grain soils in the laboratory. Let us look into
the variable head or falling head test method. This particular arrangement which is shown
here is having a soil sample which is relatively impervious, a clayey soil sample which is
placed at a certain unit weight and water content. And surrounded by two porous stones,
one is placed above and one is below and it is connected with a tube having an area of
cross section a. And the bottom portion is connected with a stem which is shown here.
So cross-sectional area of the stand pipe which is connected to this particular arrangement
is a, that is this cross section area that is having a small diameter d and here A is
the cross-sectional area of this soil through which the flow is occurring. Now let us assume that at time t is equal
to zero, the head is h1, at time t1 the head is say h2. That means at time t=0 the head
is h1. Now a time t=t1 the head is now h2. So there is a drop of the head from h1 to
h2. So let h be the head of the water at any time t. So let in time dt the head drop by
amount dh. So here assume that let h be the head drop at any time t. So dh is the small
head drop in a small time dt. So by using this deliberation let us try to bring out
a theoretical deduction. So that we can determine an expression for determining the coefficient
of permeability based on falling head test. So here if you look into it by dropping amount
of water from h1 to h2, minute amount of water is trickled into the soil. So here the water
which is passing into the soil, incase of constant head test we establish that the water
is passing through the soil. So the amount of water which is flowing into the soil is
very less incase of falling head or variable head test. Considering the previous discussion
the quantity of the water flowing through the sample in time dt from the Darcy’s law
can be estimated like this. Like we did in the constant head test. The dQ=kiA (dt), so dt is the time over
which the head loss dh has occurred. So dh is the small head and h is the head at time
t. So dQ is equal to k into i in which i is equal to h by L, A is the cross section area
of the sample and dt is the time. So k into h by L into A into dt, so this quantity of
discharge can also be expressed as minus A dh where dh is the small drop which has occurred
over a time dt. So this is negative because as the time increases, head decreases so because
of this it is expressed as small discharge, dQ is equal to minus A into dh where A is
the cross sectional of the sand pipe which is above the system which is shown in the
previous slide. Now equating this quantity of the discharge which is dQ=-a (dh) and
dQ=k. h by L. A (dt). And integrating between the heads h1 and h2, where h1 is the head
at t is equal to t0 and h2 is the head at which t is equal to t1 over the small change
head dh. So kA by L where the time is t is equal to t0-t1, by simplifying and rearranging
we will get k is equal to 2.303 aL by At log10 (h1 by h2). So by using this expression one can determine
the permeability of fine grain soils especially clayey soils by using variable head test or
falling head test. So here a is the area of the cross section of the stand pipe, L is
the length of the sample and A is the area of the cross section of the soil sample through
which the flow is taking place and t is the time over which the difference in heads h1
into h2 is measured. So by repeating this particular experiment for 2 or 3 times an
average value of the coefficient of permeability can be determined and can be registered. So
these permeability values what we determine by using the experiment, they can range from
10 to the power of minus 8 meter per second to 10 to the power of minus 11 meter per second.
So this is a procedure how we have to determine the falling head test permeability of a given
soil particularly a fine grain soil by using falling head test. So main features are the major differences
between constant head test and falling head test, they can be classified like this. In
the constant head test permeability is computed on the basis of the fluid that
passes through the soil samples. While in the falling head test, k is the coefficient
of permeability is computed on the basis of fluid flowing into the sample. So here the
amount of discharge that is the flow which is taking place into the sample. So with the constant head test, time is required
to accumulate the fluid volume necessary to perform computation. Extreme care would be
required to prevent leaks in the apparatus and evaporation of discharged water. Incase
of the falling head test the duration of the test is shortened and care is required to
prevent evaporation of water in the inlet tube. So evaporation of the water in the inlet
tube can influence the results, so that has to be taken so that the evaporations are minimal.
So having seen the laboratory methods and as we mentioned, there are also methods for
determining permeability in the field like pumping test or borehole test and the packer’s
tests are famous. We are not discussing these methods for determining
permeability in the field. After having introduced the methods for measuring permeability, let
us look into the various factors which we can influence the coefficient of permeability.
So this factor affecting the permeability can be understood with the help of the two
basic equations. They have been postulated that interconnected voids are visualized as
a number of capillary tubes through which the water can flow. So all these interconnected
flow channels or tubes are assumed as a thin capillary tube or through which the flow is
taking place. So the first to give one expression that is
Kozeny and Carman equation where he has included the mini aspects or mini factors which can
influence the permeability. So this is expressed in the form of a Darcy’s equation v=ki.
So this particular part is nothing but coefficient of permeability k. Another equation reflecting
the influence of premeant and soil characteristics on k was proposed by Taylor 1948 using Poiseuille’s
law which is shown here, which can be read like this V=C into (de square) (gamma w
by mew) (e cube by 1+e) (i). So if you look for Kozeny and Carman equation which was proposed
by Kozeny and Carman basically for coarse-grained or gravelly soils. V=1 by Cs Ss T square
and (gamma w by mew) (e cube by 1+e) (i). So both the equations assume interconnected
voids are visualized as a number of capillary tubes through which the water flow is occurring.
So we will discuss this Kozeny and Carman equations in depth and based on that we will
evolve at the factors affecting permeability. Let us look into the factors affecting permeability
and in the case of Kozeny and Carman equation, the soil is assumed as an assemblage of particles
and the flow can take place in a microscopic way through a tortuous path. So this particular
path or this particular length of the flow passing through these contact points of the
solid grains is called as tortuous path. So the tortuosity is defined as the ratio
of the tortuous length to the imaginary length which is assumed as flow through soil which
can pass through the voids as well as through the solid grains in imaginary length. So that
length is L, so the tortuosity is nothing but ratio of L1 by L. So which is indicated
here in this Kozeny and Carman equation as t. So it can have a different tortuous lengths
passing through this contact points and through the voids in the soil mass. In the Kozeny
and Carman equation which is introduced in the previous slide where the v is the discharge
velocity, Cs is the shape factor. For granular soil Cs=2.5, Ss is the surface area per unit
volume of the solids and T is the tortuosity factor which is root two for granular soils.
And this particular Kozeny and Carman equation can be simplified as k which is Darcy’s
coefficient of permeability which is capital K time’s gamma w by mew. So here the capital K which is defined as
intrinsic permeability or absolute permeability which is a function of soil skeleton and which
is constant for a particular soil type. So the
k which is indicated here in this equation is nothing but 1 by Cs Ss T square and (e
cube by 1+e). So here the units for the k are indicated as Darcy’s. 1 Darcy’s=0.987
into 10 to the power of minus 8 centimeter square. So the absolute permeability units
are nothing but they are centimeter square or Darcy’s. So this is basically a property of soil and
which is a function of the soil skeleton. The relationship between k which is coefficient
of permeability and absolute permeability is k=capital K time’s gamma w by mew. So
if you look into this with an increase in viscosity then the coefficient of permeability
can be less and this particular absolute permeability value, if there is any change in void ratio
then there is a change in the absolute permeability. And the tortuosity, then the specific surface
area and then shape factor are included. So that is how this is indicated as which takes
care of the soil skeleton properties. Let us look into the list of factors affecting
permeability. They can be listed like this, shape and size of the soil particles. One
is the shape and size of the soil particles and void ratio that is k, as void ratio increases
k value increases. That means the soil with higher void ratios can have higher permeability.
Degree of saturation that is k increases with increase in value of saturation. So at partially
saturated soil because of the entrapped air within the voids can have low permeability.
Composition of this soil particles, particularly for clayey soils where the minerologies will
come into the picture to a large extend. Particularly for silt and sands the mineralogy may not
influence in a big way. Soil structure that is the type of arrangement
whether it is single grain or incase of clayey soils whether it is a fine grain soil or whether
it is a flocculent structure or dispose structure matters a lot. Or compactive effect that is
the one which is not listed here and which also can influence the permeability. And viscosity
of the permeant or density and concentration of the permeant, so these are the factors
which can influence the coefficient of the permeability. We also discussed that based
on the Taylor’s equation, relationship between k is proportional to de square which indicates
that with increase in grain size then increase in the permeability value can be seen. That
is if d e happens to be an effective particles size, a large effective particle size can
have the larger permeability. So that is the one which we discussed is that
factors affecting permeability, the effect of the grain size. So Hazen has proposed a
relationship between or a correlation based on permeability values determined with sands
or which are having the different effective particles sizes. So this particular graph
which is shown here d10 which is plotted on logarithmic scale and coefficient of permeability
k in meter per second is plotted on y axis. The different soils like silt, silty sands,
sand with fine, medium and coarse and gravel are selected. And here once the values are plotted the regression
which is obtained is indicated by the regression equation which is named here as a Hazen’s
equation after William Hazen. It is k=C (d10 square) where C is equal to 10 to the power
of minus 2. Then we can determine the coefficient of permeability in meter per second if you
use C=10 to the power of minus 2 and d10 in mm. So this equation which indicates that
the larger the effective particles size the larger is the coefficient of permeability.
And this particular relation is basically valid for k value for clean sands or sands
with silts less than 5 % fines or so. So C is a constant which includes the effect
of the shape of the pore channels in the direction of the flow and
total volume of the pores. So this is very important equation as far as determining the
coefficient of permeability based on the particle size distribution. So this is the one of the
significance of the particle size distribution we have discussed while discussing about the
Cs or Ss or a particle size distribution of soils. So here the Hazen’s empirical relationship
is shown here which is nothing but k=C (d10 square) where C is a constant which is obtained
from this regression. So the zone which is circled here that is which is highlighted
here shows silt and sandy particles. So this is where the large points are there. So that
is the reason why it is said that it is valid for sandy soils. Another question is that why the d10 is only
selected. The d10 is selected because the smaller particles control the size of the
pore channels. Suppose if there are large particles, there is a chance that this large
particles which are having large pore spaces can be filled with small particles then pores
space can be reduced. So that is the reason why the well graded sand have low permeability
compared to the uniformly graded sand. Because of the large void ratio the uniformly graded
sand will have large permeability. So in factors affecting permeability we are discussing about
the effect of grain size. The permeability of the granular soils depend mainly on the
cross-sectional areas of the pore channels. That is what we have discussed and we are
highlighting once again that the permeability of the granular soils depends mainly on the
cross sectional area of the pore channels. Since the average diameter of the pores in
a soil at a given porosity increase in proportion to the average grain size. The permeability
of the granular soils might be expected to increase as the square of the some of the
characteristic grain size. That is the reason why the Taylor’s in 1948 has used k is proportional
to around d e square. That is how the Taylor’s equation what we discussed earlier has k is
proportional to d e square. In the factors effecting the coefficient of permeability,
another factor is that the degree of saturation. If you look into it k is proportional to Sr.
At low saturation there will be reduction in flow channels available for flow. So here
after Das (1987) the chart which is shown here is the degree of saturation is on the
x-axis and coefficient of permeability on y axis in mm per second is shown here. For a medicine sand with u=0.797. As we can
see with an increase in the degree of saturation increase in the coefficient of permeability
can be noted. That means the air which is strapped inside the soil voids is sent out
because the permeability value increases. Another important parameter which influences
the permeability is the soil structure. The permeability of a soil deposit is significantly
affected by its in-place soil structure that is in-situ soil structure. A loose granular
soil would have a higher void ratio than a dense soil and therefore would permit greater
flow. That is the reason why we have discussed that well graded sand and uniformly graded
sand. The well graded sand have low permeability compared to the uniformly graded sand. That
means the gradation or particle size composition also very important if you consider the flow
through a soil. A fine grained soil with flocculent structure will have higher permeability than
soil with dispersed structure. So this we have discussed while discussing
about the comparison characteristics of soils. So here if you connect back that for a given
compactive effort if you have got say fine grain soil with a flocculent structure and
dispersed structure. The soils with flocculent structure have got more permeability than
disperse structure. Incase of flocculent structure the more or less we will get the isotropic
condition, the permeability will be same in all directions. The flow will be less tortuous.
Incase of a dispersed structure the flow is more of anisotropic condition, the horizontal
permeability is different form vertical permeability. That means the flow which is taking place
is perpendicular to the direction of this orientation of the plates. Basically they
are face to face orientation which are parallel arrangement indicates that the flow will be
more tortuous. That means more time it takes to flow in perpendicular
to the plane of the orientation of the plate particles in dispersed structure rather than
the flow across this particular plane that is along the plate shape particles. So the
permeability along the plate shape particles will be very high compare to it’s perpendicular
direction. So the same topic what we discussed is shown here. A fine grain soil with flocculent
structure will have higher permeability than soil with dispersed structure. So the soil
with dispersed structure is shown here. So here the flow normal to the particle orientation
is found to have a more tortuous path and leading to a very low permeability in this
direction. Compared to the flow parallel to the particle
orientation if you consider it is less tortuous and can have more permeability. So the disperse
structure will have a low permeability overall compared to flocculent structure and also
the flow is anisotropic condition, horizontal permeability is different from vertical permeability.
The horizontal permeability which is parallel to the orientation particle is very high compared
to the vertical permeability that is flow normal to the particle orientation. So even
at similar void ratios clay with an undisturbed flocculated structure will possess larger
void openings than the same clay having a dispersed structure. We also discussed like a flocculated structure
because of the stress like arrangement have got a three dimensional random arrangement
with large opening or spaces or large pore spaces. So larger the pore spaces the more
is the flow, that is what we have discussed k is proportional to the d which is the size
of the pores spaces. Incase of dispersed structure because of the orientation in which the random
arrangement takes place, where the phase two phase orientation takes place and because
of that the less flow takes place for the dispersed structure. Then low void ratio prevails
for a disperse structure. That means the low void ratio in the sense relatively when you
compare with the flocculate structure the flow will be very less in case of dispersed
structure. So here flow through the clusters of the particles
of clayey soil is shown. So because of this particular reason we can have a flow path
like this and it can be like this. So the clusters or packets of clay particles are
shown. So because of this the soil with flocculate structure or flocculent structure exhibits
isotropic condition, the permeability will be same in all directions. Incase of dispersed
structure it exhibits anisotropic conditions and the permeability of soil is severally
affected by the type of the structure. Similarly another factor which is required
to be discussed is the compactive effort. Incase of granular soils or sandy soils it
can be loose compaction or dense compaction. Incase of clayey soils as we have already
studied it can have a low or reduced compaction or proctor compaction or standard proctor
compaction or modified proctor compaction. So if you recall the variation of gamma d
versus water content can be obtained like this. This is for the reduced compaction and
this is for standard proctor compaction and this for modified proctor compaction. With
an increase in compaction energy there will be decrease in the opto moisture content,
increase in the dry unit weight. And this line is the zero air voids line. So if you
select for a particular standard proctor compaction the structure can be some what like this.
Here flocculent and here it can be dispersed. So by using the same logic what we discussed,
the permeability value on the dry side of optimum will be very high compared to the
flow of the soil with the same void ratio or same dry unit weight. The soil with a flocculent
structure can have higher permeability compared to the soil with a dispersed structure. The
discussion we already had because of the type of the soil structure prevailing at that particular
void ratio. So with an increase in compactive effort the
k value decreases. That means like modified proctor compaction can induce more packing
of the soil particles. Because of that the permeability value decreases. Similarly on
the wet side of the optimum the permeability value decreases. So if you look into this
particular relationship by using this particular expression what we are discussing is gamma
d and water content. Then you got a proctor compaction curve, this is the maximum dry
unit weight and optimum water content. So if you plot the permeability value here k
which is in meter per second and water content. This side is the dry side of optimum and this
is the wet side of optimum. So here on the dry side of optimum the soil can have high
permeability and the permeability value decreases. For a given typical soil on the wet side of
the optimum the coefficient of permeability will be less. On the dry side of the optimum
the coefficient of permeability will be high. So that particular reason is attributed to
the type of the soil structure which is prevailing at that particular moist compacted state or
this natural state. As we increase the water content say for example for compaction process
the orientation of these particles changes. That is that the structure is gradually transforming
from flocculent to a disperse structure. So as we increase the compactive effort then
this also shows that the dry side of permeability value will be less. This is for say a standard
proctor compaction with modified compaction it can have a value slightly less compared
to this standard proctor compaction. So the increase in compactive effort decreases the
coefficient of permeability. So here again we connected back to the type of the soil
structure which is prevailing in that moist compacted state for a given soil. So having seen the compactive effort, now
let us look into the effect of soil type. The volume of the water that can flow through
a soil mass is related more to the size of the void openings than the number or total
number of voids. So the k of the coarse-grained soils is greater than k of the fine grains
soils. That is the reason we have to understand particularly by keeping in view of the environment
surrounding the particles. So a k coarse-grained soil is greater than k fine grain soils. Even
though the void ratios are frequently greater than for fine-grained soils. So though the void ratios are very high for
fine grain soils, we always see that the k of the coarse grained soils is greater than
k of the fine grained soil. The reason is because we have seen that as a void ratio
increases the permeability value increases. But it will not happen like this for coarse
grained soils and fine grained soils. That means there are other additional factors which
influence this particular behavior. So k of the coarse grain soils is a function of particle
size, gradation, particle shape and roughness and void ratio of the soil medium. If it comes
to the k of the fine grained soil, that is a function of type of the clay mineral and
adsorbed ions surrounding the clay particles. Here the particle forces dominate these particular
arrangements. Let us discuss why the k of the coarse-grained
soils is more than k of the fine grain soils. So if you look into the effect of the soil
type, the concept can be assumed and explained by using the flow through a conduit pipe.
So this is for a coarse grain soil or a sandy soil where V maximum is occurring at the center
and V minimum is occurring at the wall. So this is how the flow takes place. So this
particular variation is attributed to the frictional drag at the edges as well as some
viscous drag which is taking place when the flow is taking place through the sand grains.
So this is nothing but the pores space or the pore channel diameter through a sandy
soil. When it comes to clayey soil as we all know we have a clay particle, if this is the
surface of the clay particle and this is another clay particle having a part of the adsorbed
and double layer water is shown here. So this situation is different, where this particular
coating of adsorbed water layer is absent incase of sandy soil. So here in this case as you can see here flow
through pore channel in a clayey soil with more developed double layer. Suppose if the
layer is depressed because of the some cation exchange which is taking pace there can be
more water flow because the double layer is depressed which is shown here. Incase if the
double layer is fully developed then we will see that the less water flow takes place.
The reasons we will discuss in the next slide where we are trying to explain this particular
phenomena of having k for coarse grained soils through the concept of flow of water through
a conduit. So if you look in to here this particular
distribution is attributed to friction developed at the conduit wall and the viscous friction
developed in the moving fluid. So because of this reason V occurs maximum here and then
minimum here. So some energy is lost here. But whereas in case of the flow of water which
is taking place through the clay particle, one reason is that the friction drag which
is taking place, the flow is attached almost to the wall and because of that very less
flow occurs. In addition to that the adsorbed ions will try to keep the water very close
to the clayey particles. Because of that the flow which is taking place through this fine
grain soil is very less. So the same concept is explained here. For fine grained soils
when void spaces are very small, all lines of flow are physically close to the wall of
the conduit and therefore only low velocity flow occurs. Mostly the velocity of the flow
is occurring along the boundaries of this double layer which are there. So depending upon the development of the double
layer whether it is depressed or completely that also influence the flow condition. Incase
of a depressed double layer relatively more flow occurs for a completely developed double
layer. In clays, flow in already small channels is further hampered because of the some of
the water in the voids is held or adsorbed, to the clay particles, reducing the flow area
and further restricting the flow. In case of the clays the reasons are, particularly
clays are fine grain soils because of the type of the environment surrounding the particle
that is physicochemical environment surrounding the particle influences the flow conditions. Incase of a sandy soils this is not absent
because of the loss of the frictional drag which is occurring at edges except that the
velocity is maintained with high flow. So because of that when the flow is high that
is seepage velocity is high for a coarse-grained soil than a fine grained soil. Because of
this reason the soils particularly with sands or basically forming coarse-grained soils
they exhibit very high permeability compared to fine-grained soils. So we can say that
the k of the clay is very less compared to k of sand. So another factor which is discussed is the
effect of the permeant. Like as you seen k is proportional to gamma w by mew. So variation
of the gamma w with temperature is negligible. So we can see that as mew increases the coefficient
of permeability decreases. So higher mew the lower coefficient of permeability, so effect
of specific surface area if you look into it we have discussed in the kozeny-carman
equation k is proportional to 1 by Ss square, where higher the specific surface area and
low is the permeability. That means depending upon the type of mineral
for example kaolinite, Montmorillonite and elite. The kaolinite has got lower specific
surface area compared to Montmorillonite. So that means the soils which are having Montmorillonite
can have low permeability compared to soils which are having kaolinite. Similarly the
quartz which is having very low specific surface area exhibits very high permeability with
this particular relationship. So based on the discussion what we had, we
can classify the soils according to their coefficient of permeability. The degree of
permeability high, medium, low, very low or practically impervious can be said like this.
High we can say that if the permeability is 10 to the power of minus 3 meter per second.
Practically impervious if it is less than 10 to the power of minus 9 meter per second,
low is 10 to the power of minus 5 to 10 to the power of minus 7 meter per second. So in this lecture what we tried to understand
is that the methods for measuring the permeability in the laboratory and different factors affecting
the permeability, especially the compaction effort or type of the soil structure and soil
type that is where we have discussed about the flow of water through conduit. And we
said that k of the coarse-grained soil is more than k of the fine grained soil, though
the void ratio for the fine grained soils is more than coarse grained soils.

## One thought on “Lecture – 23 Flow of water through soils – IV”

1. Bhupendra Singh says:

Nice