Continue with the first concrete in this lecture. Today we shall look into role of mix parameters.
What are the mix parameters? First is the paste and water. Then, next we will look into
role of aggregates. And in aggregates we have grading. We will also look into effect of
maximum size of aggregate and their shapes. Also we will look into how to increase workability,
how 1 goes for any increasing workability. So, this will be the general outline. So,
let us start with role of paste.
When we add water to the cement it becomes plastic, otherwise cement is a solid which
is in a dry condition; it is not moldable it will not deform low just like that. So,
to make it plastic what we do; we add water. And as progressively we go on adding water,
originally dry cement particles are air filled. The voids or interstitial void space between
cement particles will be filled with air. And this air filled now spaces are now gets
filled by water. And as they get filled by water, gradually you know a stage comes initially
all the surfaces of the cement particles would be dry, as you add water some surfaces will
tend to become wet. Air of course, initially forms a kind of open
continuous channel or connected air filled system. As you add water this connection gets
disrupted, because water fills up and air filled voids tends to become isolated. And
a stage comes when all the open air voids are isolated by water and they become air bubbles. This water
corresponding to and the corresponding consistency is something close to normal consistency.
So, normal consistency we have defined in case of cements. And this corresponds to the
state where, water has been is just sufficient to isolate the air bubbles. In fact, it is
not totally air free; the voids will still contain air bubbles and they will be isolated,
they are independent closed pores where air bubbles are filled. And the ratio of air to
water at this stage is about 1 to 7 and this is called basic water or the water corresponding
to normal consistency or this corresponds to normal consistency that has been defined.
Now if you add more water to it, it makes the paste softer rapidly and generally disruption
of the cement particle takes place. So, that is the mechanism when you add water to the
cement and progressively go on increasing the water content. Now let us see what happens
to rheology of fresh concrete.
We have discussed earlier the rheological parameters and the yield shear stress and
the viscosity. So, we can look into the viscosity; nu is the viscosity, delta is a parameter
which defines particle dispersion, it defines parameter representing particle dispersion,
as we can see now delta is a parameter representing distance between particle. So, as I add water,
distance between particle will go on increasing. And as this delta increases from this equation;
this is viscosity you can see that as delta increases viscosity will reduce, because delta
to the power minus 0.6. So, if I increase delta nu will reduce and it reduces till possibly
a distance between the cement particle becomes 5 micron. Any distance beyond this any addition
of water and further dispersion beyond this of course, does not cause further change in
the viscosity. So, we can see that viscosity reduces. Therefore,
flow will increase, flow will improve, this is of course, nu in centipoise nu the viscosity
in centipoid and this comes here in 1 of those equations nu 0 is the viscosity of water.
Similarly, you can see that this nu increases with and decreases with water cement ratio.
As I increase the water cement ratio, this is exponentially related to nu. Higher the
water cement ratio since this is e to the power b, b is an empirical constant into w
by c. So, if I go on increasing w by c, nu will reduce right and exponentially it will
it will reduce exponentially. So, higher water to cement ratio in case of
paste causes; whether dispersion, more dispersion and also it causes reduction in the viscosity.
So, water cement ratio is a factor in case of paste, which causes reduction in viscosity
therefore, improves the flow ability. This is even from common sense this is understandable.
The other important factor is the surface area or particle size distribution of the
cement particle. s stands for Blains fineness we can see that s stands for Blains fineness
which means; is the specific surface defined in terms of earlier we defined in connection
with cement, this is centimeter square per gram it is the specific surface.
So, as the specific surface increases the fineness of the cement increases, specific
area is what it is the surface area per unit mass. So, if the surface area per unit mass
increases; that means, it is finer the finer particle has more surface area compared to
course particle area. So, as the surface area increases, the finer particle sizes are finer
and finer, then this viscosity will have a tendency to increase the viscosity will increase,
this increases the viscosity increases and this has got some relationship with water
cement ratio also. This is the water cement ratio for normal
consistency. If you have more water cement ratio then normal consistency, you can see
that the viscosity will reduce. So, this is a more generalized equation, relating both
water and cement ratio and the fineness of the cement. So, higher the water cement ratio
with reference to the normal consistency, because if you have normal consistency water
this would be very, very you know this term would be 0, this term would be 0 and this
is actually very large. So, therefore, viscosity reduces as I increase
the water cement ratio beyond the normal consistency and it increases with fineness of the cement.
So, it increases with fineness of the cement and reduces with increase with water cement.
So, flow ability would be better for higher water cement ratio and also for coarser cement
range, final cement will require more water to become plastic actually. So, that is the
idea. So, that is what it is alright. So, this factors actually governs the rheology
of fresh paste. So, water cement ratio is the main aspect
and of course, the fineness of the cement plays a role in the flow ability of the cement
paste. Paste itself must be flowable, because if you see all other materials are you know
coarse aggregates and fine aggregates; they are dry materials and on their own they will
not be have much mobility. It is the paste which should be there. So, what does actually
If you see the role of the paste in case of concrete paste of course, it will have a little
bit of air in it, forms a matrix I may call it as a matrix in which the coarse or fine
aggregate are the inclusion. So, this forms a matrix where aggregates are dispersed; they
are the inclusion and they are dispersed. The matrix separates the aggregates and also
holds them together. So, this aggregates are separated from 1 another by this paste which
is inside in between and it holds them together also, it binds them together, even in fresh
state it holds them together and acts as a lubricating material enabling plastic deformation.
So, therefore, paste is a main; is most important part as per as workability or you know deformability
and mobility of concrete is concerned paste is the most important part. It is the 1 which
holds the aggregate together, it disperses them together and then gives you a lubricating
material enabling plastic deformation. This degree of dispersion of course, is not very
large never more than 3 to 10 percent; that means, you know the volume find out the distance
between aggregates before paste was added and after paste was added, this increases
in the distance from original distance; mean distance to the increased distance is not
more than 3 to 10 percent. So, dispersion is not more than 3 to 10 percent
and therefore, this is important, but the paste you know is important to have paste
and sufficient paste so that, it can take care of the dispersion also. So, if you decrease
the volume of matrix that is the paste, dispersion you know it reduces the dispersion and it
will increase the particle interference resulting in stiffening of the concrete.
So, matrix must be sufficient. That is what we understand that, matrix must be sufficient
to hold the aggregates together and also ensure dispersion of this aggregates together. Now,
matrix itself must be capable of flowing itself, it should have low viscosity so that it can
move. So, that is the first fundamental; matrix must be of low viscosity; it should be able
to move itself, deform itself, should be capable of plastic deformation and for that you need
a water cement ratio more than the consistency situation. And it should be sufficient to
hold the aggregates and also cause their dispersion so that, there is an ability for the concrete
to undergo plastic deformation. So, that is the role of the paste.
Continue with the role of the paste; if we lower below a level the paste content, if
you lower the paste content below a lower level, if you lower the volume of the matrix
it results in harsh and segregating concrete, because if you have too much of if you have
low paste the aggregates will be left alone, they will not be held together. So, they can
segregate very easily. So, and that is the point actually.
So, this is the next stage; increasing volume matrix on the other improves concrete consistency
and matrix itself must be, that is what I was mentioning that, if you increase the matrix
volume, it will improve the matrix consistency I mean the concrete consistency or workability,
but at the same time matrix itself must be adequately consistent.
Low water cement ratio matrix may cause dispersion, but cannot hold the aggregate together. So,
if you have low water cement ratio, you know water to cement ratio; that means, the matrix
is dry, it may cause dispersion. If you put sufficient quantity it will push the aggregates
apart, but will not hold the aggregate together, because it itself is also dry. And therefore,
it will stiffen. Too high water cement ratio on the other hand; the matrix becomes too
thin, it is flowing very thin and not enough to hold the segregation is there. So, there
will be segregation and could be form of bleeding and no dispersion is and you know and low
holding capacity. So, it cannot hold and therefore, there is a possibility of dispersion. So,
low water cement ratio is a problem, high water cement ratio, very high water cement
ratio is also a problem.
Continue with the role of paste incidentally normal consistency corresponds to around water
cement ratio of 26 to 0.26 to 0.33. And you know in normal strength concrete, as sometime
we might have define characteristics of concrete structures grade of concrete starting from
20 m p or M 20 to around 40 or say 50 or so on. The water cement ratio is usually more
than this 0.26 usually it is more than this value. So, normal concrete normal strength
concrete not very high strength, we are talking of normal strength concrete. The water cement
ratio is usually higher than this value. So, this is generally you will have adequate
consistency. Well, paste content should be adequate. This is clear that paste content
shall be adequate; this should be adequate paste content; that means; matrix must be
sufficient now you understood. So, it should be sufficient to fill in all the voids in
the aggregate system, but also more than that for proper dispersion. So, it should be more
than what is required to fill in the dry volume, you know interstitial space between aggregate
when they are compacted alone. So, it is the amount of paste required is
more than that is required to fill the interstitial space of the aggregate, when they are compacted
alone. So, you need more, because there will be dispersion as you introduce space into
the concrete you know. So, they will cause dispersion of the aggregate particle and therefore,
you need more right you need more. But for reasons of economy and of course, factors
like shrinkage etc, we cannot have too much of paste content to have high paste content
is good, because it will give me workable system. But we cannot have too much of paste,
because cement is the costliest material in normal strength concrete compared to let us
say aggregate, you know coarse aggregate as well as fine aggregate and water.
So, therefore, if I make if I make if you use more paste more cement will be going into
it, for a given water cement ratio more cement will go to it and therefore, it will be costly.
So, I really cannot increase the space content in normal strength concrete very, very high,
I have to control it. So, therefore, from point of economy and also it can cost shrinkage
and other secondary effects. So, therefore, we do not want too much of paste in the or
cement in the system and therefore, normal concrete the paste content ranges from 28
to 32 percent. Higher paste content will improve the workability, but we do not do that because
as I said the economy will forbid as doing that.
But in certain special concrete it will do, example very, very high strength matrices
very, very high strength matrices not of 20 30 order of 800 or 250 more than 200 you know
the reactive powder concrete; there the paste content of course is relatively much higher,
but that is a separate issue. But also in self compacting concrete the paste content
is much higher where I need lot of flow, but then paste does not consist of cement alone
it consists of cement and other cementitious material. Therefore, both economy and other
secondary effects all are taken care of when we are we use high amount of paste content.
But in normal concrete what we were discussing at the moment; this is about 28 to 32 percent
and we do not use too large paste content. This you will recall that we said that aggregate
constitute about 70 percent of the concrete system, in the beginning when we define concrete
right. So, that is the role of paste. Now let us look into the role of aggregate.
Well aggregates are inert material. They should not react, they usually they do not react
with you know take part in hydration process and should remain inert even in the future
life, otherwise durability could be a problem. So, generally inert material bulk of this
material that forms a concrete and provide a strength and stability to the concrete system
as we have mentioned earlier. So, they are inert material and they form generally skeleton
of the concrete if I may say so. And for economy normal concrete, 1 would like to minimize
the volume of paste; that is what I mentioned and maximize the aggregate volume fraction.
So, that is what it is 1 would like to do that.
Now, interstitial void space in the dry aggregate system is altered when paste is introduced,
we said that this happens, because you know is because of particle interference. Or if
you introduce a new material into the pore space or interstitial pore space of larger
size particle, a point comes when they start pushing the larger size particle itself; it
is called interference particle interference. So, paste also causes some sort of interference
and therefore, this void system space in the dry aggregate system is altered, it is actually
increased. And then paste required to ensure dispersion of aggregates is higher than the
interstitial porosity of the aggregate; that is what I mentioned. So, what I need; I need
the paste which should be more than that existing into the aggregate system alone when packed.
So, if; that means, minimum level is a void content of the paste itself. I mean aggregate
itself aggregate system, itself it will be more than that.
So, if I reduce down the void content of the aggregate themselves, then the paste content
I can reduce. So, to reduce the because for reasons of economy we would like to keep it
as low as possible, with adequate workability. We would like to keep it as low as possible
for adequate workability. You know just the maximum level is that required for workability.
So, but I would like to keep it as low as possible for a given workability. So, I must
have a good packing of the aggregate system such that, its voids are minimal so that,
you know aggregate porosity; interstitial porosity is minimal and that is what we like
to do. So, aggregate porosity should be minimum.
So, aggregate should pack very well. And this can be this can be expressed in terms of what
is known as packing density. This is this can be expressed in terms of what is known
as packing density. Packing density is nothing, but it is the volume of solids in unit bulk
volume. Total volume if it you know unit total volume of the solids; that called packing
density and it is nothing, but 1 minus p where p is the porosity, you know p is the porosity
interstitial porosity of the aggregate. So, 1 minus interstitial porosity porosity is
the packing density. So, we would like to maximize the packing
density so that, p is minimized. And if p is minimized I need p plus something amount
of paste. So, if have minimized if I reduce the p therefore, paste requirement will also
will reduce for a given workability. So, role of aggregate is therefore, to provide a skeleton
system which gets dispersed into the matrix, but should have a low porosity, should have
a high packing density. How do we achieve that?
If we look at packing density of single size particle, you know if we look at packing density
of single sized particle, say just 1 unit size say spheres, then they would pack to
you know single sized particle, they would simply pack to a relatively low packing density,
even if it is sphere then relatively low packing density. And it depends upon its packing arrangement.
For example, this is a simple cubic arrangement it will have a characteristics porosity of
about 48 percent. In other words the packing density of about 0.52, we shall see that,
so simple arrangement. But supposing I have better; let us say body
centered cubic arrangement or face centered cubic arrangement, then I have better packing
density. So, but, you see this there is a limitation, I cannot go beyond with single
sized particle the porosity which is nothing, but the volume of voids present you know here
divided by the total bulk volume; that is ratio actually and that ratio is for a given
single sized particle is relatively quite high, the porosity is quite high you cannot
reduce it. Whatever may be the size of this particle, irrespective of the size of the
particle porosity remains same, because you can make size finer or coarser because it
will remain same, because relative volume relative total volume you know relative volume
of the pores divided by the relative total volume I am interested in.
So, relative volume of this volume divided by this volume, similarly in another case
if I have smaller particles, in that case the pores are here this relative volume or
I may use another color, relative volume you know relative volume of pore to the total
volume or porosity; they would remain same, irrespective of the size of the particle.
So, that is important. If you have single sized particle, you will have porosity similar
irrespective of the size of the particle, it will depend only on packing. As I mentioned
in the packing density of simple cubic, body centered cubic and face centered cubic arrangements
are 0.52 0.68 or 0.74. 1 can theoretically calculate this.
If you are looked into crystal structure you know school days you know arrangement of crystals
this is also there in those case. So, we can see that if I have you know if I have a simple
cubic arrangement, irrespective of the particle size, irrespective of the size of the particle
the packing density is 0.52, irrespective of the particle size it is point 0.68 for
body centered cubic and for face centered cubic this is 0.74. So, particle single particle
size will always give this. So, it is not single particle size definitely,
not a very efficient thing to do. Actual packing density of course, in case of sphere of single
size lies somewhere between 0.5264 and 0.74 0.2568 and so depending upon what is the arrangement.
So, you cannot feel improving it very much, because 0.74 is a specific type of arrangement
which you never get. You can get actually theoretically it is possible, but actually
that is the maximum theoretically maximum, but you get it much less packing density with
But supposing I add another size to the same single sized particulate system, this will
improve the packing density, because the finer size say original was larger size, now I put
a finer size; the finer size will go into the interstitial pores of the original coarse
size and resulting in reduction in the voids paste right. So, if you want to get higher
packing density, then we should actually use aggregate of different sizes. If you want
to get higher packing density we should use aggregates of different particle sizes and
that is what we actually do in practice. The proportions of this different proportions
of this different size fractions shall be appropriate, because we just cannot add anything
to anything any proportion and you will get improve it, now there is a you know inside
an sudden rules you must do according to sudden rules and that is how you can maximize the
packing density. Now we will look into the case of a binary mixture and we shall see
how this packing density increases. We will see the binary mixture and we will see how
this increases. So, we will go to the binary mixture and we
will see how this increases. So, we will, this degree of improvement also depends upon
the size ratio. So, you go to the binary mixture and see how this packing density increases
with another sized material and degree of improvement of course, depends on the size
ratio. We shall see that next.
Consider this case: supposing I have got a singled sized particle as shown here, single
sized particle you know it is all same sized spheres. Let me say nearly rounded all aggregate.
Now, I add to this fine particles. So, where it will go; just little bit very small amount,
then it will go into the interstitial pore space. You know this red ones are the fine
particles that I have added into the system. So, they will go into the pore space interstitial
pore space of the large particulate system. If I go on adding further then of course,
they will go on filling and it will sink down the voids, because they are going into the
interstitial pore spaces. But time will come that the original packing of the large size
aggregate will be disturbed and that time they would get separated further, because
this fine particles have come and they are trying to occupy the space within that. So,
this is called particle interference. So, the rate at which the voids are reducing will
now diminish. Let me repeat; first of all we have got all large size particle, you put
very small amount of fine size particle. It will go into the interstitial space you know
pore space of the large particle, without disturbing the large size particle. So, voids
will reduce. Now, next what will happen; it you know next
actually if you go on increasing it further, it will the finer particles they will tempt
to go into the pore space between the larger particle, but they will try to push this larger
particle apart. So, this is called particle interference. So, rate at which voids would
be reducing would get now reduced. Initially it will reduce the voids, voids would reduce
at a higher rate with increase in the finer particle, but if you go on further finer and
finer particle you will not get reduction of voids at the same rate.
But, when you are adding too much quantity of this fine particles, then fine particles
will start dominating and actually pores, because if they are more than this voids space
available, then they will be separately as an separate material. So, void space within
the fine particles will now add to the voids. So, in other words if you look at packing
density; packing density will initially decrease, but its rate of decrease you know rate of
decrement would reduce. There will be a maximum and then it will start increasing. We can
see that, let us see we can see that how it occurs.
See supposing I have got from the reverse side, when too much of fines are there, I
have a situation like this too much of fine and I add too much of fine it was full and
I will just add this material here 1, you know remove some of this and put a large size
particle as this. So, in such situation when too much of fine is there; little bit large
sized particle 1 just for large sized particle I have added. This volume is of pure solid
volume. So, it will reduce down the voids. In other words, packing density would increase.
So, when I start from I started earlier from I started earlier from coarse side particle
added fine particle. Supposing I have large fine particle from
the other side and I just remove some amount of fine particle put across particle, void
will again reduce packing density will increase. I go on doing this, this will occur in the
same manner, but after some time the packing occurs the fine particle will be disturbed
by the larger particle. The result is something like this. The packing density versus fraction
curves would be something of this kind, you know supposing A and B; this is larger 1 is
let us say A say this is A and this red ones are B. So, A; I increase go on you know B
was 100 percent here I go on increasing A. So, the packing density will initially increase,
but the rate of increase is not linear, it goes on reducing down the peak is reached
and it follows like this. Similarly, if I start from this side I have
got all large particle, then the small particle I go on adding a little bit, packing density
will increase they will be maxima and there will be a reduction. So, what we observed
from this is; packing density increases linearly with addition of second size, but increases
less than proportionally there after due to particle interference and you know there after
it increases. So, there is a maximum point of packing density. And at particular proportion,
we will get maximum and by adding 2 particle size you can reduce increase the packing density.
If you go back again to the earlier 1 if you go back to the earlier 1 again will see that
packing density of B was here, will see that packing density of B was here actually you
know packing density of B was here and packing density of A was here. So, as you combine
2 materials packing density is actually improves, it is much higher than both of them you know,
it is much beyond much higher than both of them. So, by adding 2 different particle size,
we can actually improve the packing density.
If you repeat this for many particle sizes the packing density you can maximize. So,
you can increase the packing density from binary mixture to trinary mixture packing
density will still increase and if you multinary mixture the packing density will increase
in a significant manner. So, each subsequent addition of sizes actually will increase the
packing density. So, that is the idea. So, therefore, you should have large.
So, that is why we use several sizes of aggregates in concrete to reduce down the packing density
so that, our paste content required for a given volume is less. We can identify the
optimal fraction as we have seen, by some simple equations 1 can identify, but overall
if you have a multinary system it becomes a complex thing, requires certain experimental
factors experimental determination of certain factors. We can identify, but we do not do
that actually, because this theories we have not really clearly developed, of late only
there are certain models available on packing density.
So, what we do is; we use what is known as practical grading. So, practical gradings
we use actually instead of using. So, this we said that we can do it, but theoretically
we do not do it to ensure dispersion and to take care of particle interference etcetera.
This is another issue; the mortar used should be more than little more than the voids corresponding
to the coarse or aggregate, maximum density of coarse or aggregate. Paste should be more
than the void space in the all total aggregate and the paste and sand that makes the mortar,
mortar should be more slightly more. In mortar actually the coarse or aggregate gets dispersed
therefore, mortar should be slightly more than that of the voids in the course or aggregate
system. So, in case as I said in normal concrete what
I do is; we use practical gradings, you know these are proposed and practical gradings
which are proposed in codes and for basically we cannot model it for packing density etcetera,
it is there are lot of you know lot of complexity involved varies from place to place. So, at
the moment the practice is to use practical grading curves for normal grade of concrete,
although there are mix designs based on packing density as well.
Now, we are available in literature, but common practice is to ensure that your aggregate
falls into a right kind of particle distribution, because that would give you good kind of packing.
So, the ranges of particle size distribution that is proposed and this we call aggregate
grading. So, range of sieve fraction of overall aggregate system is proposed.
For example, IS 383 is the code Indian standard code is IS 383 and there this is for all in
aggregate. When your sand and aggregate combined, this is a kind of grading suggested whereas,
say for grading suggested for 40 mm maximum sized aggregate m s a stands for maximum size
aggregate. 20 mm maximum size aggregate. So, it should pass through 80 mm sleve 100 percent
40 mm etc.So, it tells you that, it must by sleve analysis actually you do it,
you do it by sleve analysis, we have nominal sleve size square sleve size and 90 to 100
percent should pass through 80 millimeter 80 mm square sleves. So, you know and because
they are not the spherical particles, they are any can be irregular crust etcetera.
So, this through this sleve analysis results gradings are confirmed right and this is the
suggested grading that should proposed grading, one should follow in case of all in aggregate
as per IS code.
Similar grading curves are available for coarse aggregate alone or sands, you know these are
given in the same code, it is given. I just picked up 1 to show you the as an example
to give the grading and, but details are available in the same code right. Now for fine aggregates,
the code defines for grading zone. You know finest is zone 4 and zone 1 is the coarsest.
So, you defines it defines actually 4 zones, zone 4 and zone 1 2 3 4, 4 is the finest maximum
fine particle and 1 is the coarsest. So, fine aggregates that is usually sand or
crust sand or whatever it is river sand or land sand, this gradings are defined. The
1 table I showed corresponds to combined aggregate, but you cannot separate. In some places you
might come across what is known as fineness modulus of sand, because fineness modulus
also defines like, like the zone defines the sizes of the sand fineness modulus also defines
the average size of the sand, average sieve of the fine aggregate, in terms of sieve number
average sieve number. So, it is that is how we define. Just let us look into the fineness
Fineness modulus of ith size starting from 75 micron, size is given as 3.73that is an
expression very simple expression. And if you put d i is equal to 75 micron here, here
d 1 you know you will find this value equals to 0. If you put 150 micron because our sieve
coefficient is 275, then 150 micron is coefficient this is called coefficient, multiply by 2
you get the next sieve size 150, multiply by another 2; 300 600 120 1.25 1.18 millimeter
that is and 2.36 nearly above 2 and so on, because they got change from the British unit
to the SI or you know what you call MKS or CGS unit. So, therefore, there are slight
differences, but usually nearly about 2. So, sieve coefficient is 2 and log 2 you know
is 0.3010 multiplied by 0.322 will give you 1. So, d is as this is 75 this is equal to
0, if it is 150 this will be equals to 1, if it is 250 300 this will be equals to 2
and so on. So, as the sieve size increases, nominal sieve size increases you know the
fineness modulus increases by 1, 2, 3 etcetera. For example for 75 micron fineness modulus
is 0 for 150 micron fineness modulus is 1 and for 300 micron it will be 2, for 600 micron
it will be 3 etcetera. So, in a way fineness modulus for individual
sieve size; it corresponds to the sieve numbers, starting from the bottom most sieve right,
which is 0. FM for combined aggregate that is for sand which has got all or sand or even
for total aggregate you can use for any combined aggregate, this is given as a weighted average
size. For example, it is given as p 1 2 p 2 3 p 3 etcetera, where p 1 and p 1 p 2 p
3 etcetera this ones are the mass fractions of particles in 150 300 600 micron sizes.
So, p 1 means the particle fraction in 150 micron passing to 300 retain in 150, I mean
passing to 100 retained and passing to 300and similarly p 2 is passing through 600 retained
300 etcetera. And if you some this up this will give you p 1 2 p 2 3 p 3 etcetera that
will give you the overall fineness modulus of the overall fineness modulus of the aggregate
system. Well, by algebraic 1 can show that fineness modulus, same thing can be calculated
as cumulative percentage retained. Sum of cumulative percentage retained in each sieve
divided by 100. You know if you cumulate total sum of cumulative percentage retained in each
sieve. So, you know the cumulative percentage retained
in number 1 sieve, number 2 sieve from the top largest size, the next sieve the cumulative
percentage retained with that retained in the previous sieve and this sieve and so on.
So, if you sum all of them up and divide by 100 you get FM, because this will algebraically
will be same to this. So, this is the measure of average size in terms of average sieve
number. So, that is what is fineness modulus, sometimes this is used to denote the fineness
of the aggregate like zone 1, zone 2, zone 3, zone 4.
So, we have seen that grading of aggregate is important, because if you have different
sizes in the right combination, then you can reduce some of the packing density. So, and
we do control it through grading.
Next aspects about the aggregate role of aggregate is the size of aggregate. Lower size of fine
aggregate is 75 micron. So, least size is 75 micron, I do not have anything lower than
that then I will go to cement or cementitious sizes. So, 75 micron is the lowest size of
aggregate. So, if I want to increase the aggregate packing density, I will have nothing lower,
but if I know that if I make this aggregate from binary to trinary, trinary to protonary
etc., and increase the number of sizes, then packing density improves. So, if I increase
the maximum size of aggregates of the higher side, I am now increasing 1 more size. Therefore
packing density will increase. So, maximum size of aggregate if I increase
packing density will increase. So, nominal maximum size of you know aggregate implies
that, increasing number of size sieve size number of size from you know from 20 to 40
millimeter means addition of 1 more size. Therefore, what will happen this will ensure
that my packing density has increased. So, increasing maximum size ensures that, I increase
my packing density. So, overall voids in the aggregate would thus reduce by increasing
m s a. The paste required would be less. That is the idea. The paste required would be less.
So, that is the role of m s a. So, 2 things we have seen so far; 1 the grading
of aggregate, that is, you know proportions of various size fraction and they are important,
also maximum size of aggregate that is number of size fraction that is important. So, maximum
size of aggregate actually improves the number of size fractions.
Aggregate shape is a next issue.
This must be understood very well, because there can be little bit of confusion sometime.
Spherical particles packs higher packs to higher packing density compared to irregular
shaped particles, this is important. Irregular shaped particles do not pack to good density;
spheres would pack to good packing density higher packing density. If you have also say
irregular they will have lot of voids within in the interstitial voids within them. Natural
aggregates are of course, thought spheres definitely, but they can be classified as
rounded you know rounded gravels natural gravels of course, will be rounded. If you get it
from river bed they will be all rounded, because of abrasion that has gone in natural abrasion
that it would have gone in. So, that will be rounded because through abrasion.
So, natural stones you know gravels if you collect them they will be rounded. So, rounded
aggregates are natural like that. Same, similarly river sand would be rounded, even land cored
sand would be rounded sought of natural ones would be rounded. But if you have crushed,
they are unlikely to be rounded, because they will you know crossed means they are failed
in the frailer plane in the weaker slain and the crushed ones are not rounded. There can
be regular shapes in between somewhere. So, basically we will classify generally for
all our purpose rounded and crushed later on sometime, but it could be rounded, irregular
or crushed. So, 1 can define them as rounded, irregular or crushed. 1 of the ways there
are several ways of if you trying to define the people have tried to define the shapes
in several ways, various indexes has been used. But 1 of the ways that I would like
to introduce here is say in terms of what is called angularity factor, generally given
by Loudon somewhere in 1950s. Now, this he defined as a ratio of specific
surface of size group to that of spheres having nominal volume diameter, means the sieve opening.
Let me repeat; first you find out you do sieve analysis and by permeability test you measure
the specific surface of that particular size group. You know the sieve size, so you find
out the specific surface, that is centimeter square per gram or you know equivalent unit
in square per pound or whatever it is. And also from that you find out what is the equivalent
diameter, divide this by the nominal sieve diameter.
Now, this is a measure of the angularity, this is a measure of the angularity. Higher
this value it means your surface area is large compared to the volume. For spheres this equals
to 1, because surface area is you know to volume diameter they will give you same identical.
Now here you calculate out the surface area and then try to find out the diameter of equivalent
sphere, this diameter will tend to be large as you will have large surface area, you know
surface area per unit volume and then try to find out the equivalent diameter.
So, for irregular shape surface area is more therefore, corresponding diameter will be
more. So, angularity factor is defined in terms of the specific surface of the actual
aggregate divided by the nominal sieve size and that is higher value means it is angular,
higher value means it is angular higher value means it is you know less spherical. So, that
is what 1 would say.
So, for example, you can see the values are 1.1 1.4 and 1.7 for you know for 1.1 1.4 and
1.7 for rounded, irregular and crushed aggregate respectively, it is from measurement at some
sizes there could be slight difference, but it should be understood that for rounded aggregate
this value is less, for crushed this value is much higher the angularity factor is much
higher. So, that is the idea. And if we now look at the void content of the aggregate,
people have measured this void content with this angularity factor and they observed that,
we say linear relationship this we say linear relationship. So, this side if I plot void
content, if I plot void content along this side say 0.3 to 0.7 angularity factor increasing
along this direction. So, for 1 which is in perfectly sphere and some datas are here.
So, you will see that as my void content you know angularity factor increases void content
increases. So, rounded aggregate packs better, crushed
aggregate will pack to lower packing density. Therefore, you need possibly more paste content
rounded aggregates require less paste content. So, rounded aggregates will require less paste
whereas, crushed aggregate will require more paste. In other words, you know workability
associated with the rounded aggregate would be better, it would require possibly less
water in concrete as we will see some time later on in the context of mix design. So,
aggregate shape is an important issue. So, 3 aspects we have seen; 1 the grading,
you know fractions of different sizes. Second issue is the maximum size of the aggregate,
that is, number; number of size that is involved. So, that is m s a and third we have seen the
shape. So, this 3 are the major factor and they govern the paste content and therefore,
they govern that is the role of the in workability or consistency of concrete. Higher, higher,
more number of sizes and higher m s a right kind of grading proportions of each size is
proper and rounded shape will give you better workability.
So, we can now look into how do we change concrete workability, this so far we have
talked about only normal strength concrete and we have not talked about concrete with
what is known as admixtures special additives, which you can add to improve the workability
etc.,. So, normal concrete the 4 ingredients concrete; that is the cement, the water, a
fine aggregate fraction and coarse aggregate fraction. So, with this concrete, if I have
seen what is the role of the paste water and water to cement ratio and the paste and then
we have looked into role of various aggregates. So, we have looked in the role of component,
we have not looked into anything, where by adding some additives we can improve the workability
etcetera. So, let us look at how do we change the workability if I do not have any admixtures
right. Plastic deformations in fresh concrete, is possible only when there is enough paste.
This must be understood. By this time it must be clear that there must be enough paste in
the concrete and the paste itself must be consistent, at least must have enough water
that is initial basic water, you can have higher water that is fine. So, this basic
water that is corresponding to the normal consistency nearly same has been observed.
So, this you know this should be there. Now, normal that would give you the normal
consistent paste and normal consistent concrete normal consistent concrete has slump of 20
to 50 millimeter. So, normal consistent concrete will have a slump of which has sufficient
amount of paste into it and paste itself is sufficiently consistent, that sought of the
concrete will have 20 to 50 millimeter slump. Let me just point out here, you know in the
context of concrete we shall see in terms of when you do mix design, that in mix design
process we initially determine the water to cement ratio from strength criteria. When
we discuss further about the strength, we will see that strength is mainly governed
by water to cement ratio. So, you fix the water to cement ratio from
strength criteria. Then from workability criteria fix the water content. The idea is very simple;
for given water to cement ratio if I increase the water content I am actually increasing
the paste content. By increasing the water content as well as by increasing cement, because
water to cement ratio is to maintained constant, that I cannot change. If I increase simply
water my paste will increase, but strength may reduce. So, I keep the water to cement
ratio constant and you know water to cement ratio constant and then increase the water.
So, quite often we understand in mix design that, water content governs the workability
of concrete, but that is for a constant water to cement ratio. The water to cement ratio
has to be fixed, then water content has a big role, because you cannot increase the
cement, then if you increase the cement consistency of the cement paste alone, consistency of
the cement paste itself will go down. So, if you increase the water, maintain the water
cement ratio, both water will increase cement will increase and in the process actually
workability will increase strength will remain same. So, this is important issue
So, to change actually to change what I should do; I should actually increase the paste and
I also already mentioned that, volume of air filled to water filled void in case of a consistent
mix in case of consistent cement paste is 1 is to 7. I just mentioned again repeatedly,
because consistent cement has to be there. To increase the workability paste content
has to be increased for same water cement ratio, as strength has to be maintained same
right and this can be done by increasing water content. And that is what we do in case of
For water cement ratio to be constant right, by keeping water cement ratio constant, increase
the water content water workability increases as paste content increases. That is what I
mentioned. Therefore, how do we do; what we see is supposing I have I increase delta w
increase the water, I said that I can increase my water content say by delta w. I must keep
my water to cement ratio constant, otherwise my strength will be disturbed. So, supposing
I have added delta w amount of water, my water to cement ratio is to be constant. So, w divided
b delta w divided by c plus delta c, this must be equal to w by c. So, c delta c also
there will be an increase in cement content also.
So, I must increase my cement content and because I must increase my cement content
you know. So, I must increase my cement content w plus delta w divided by c plus delta c should
be equals to w by c if, I have to maintain water cement ratio. And using this algebraic,
if I try to calculate out what will be the increase in the paste volume, the formula
will give me this. The formula will give me this because; delta c can be replaced in terms
of w by c and delta w. And if I you know use just a little bit of arithmetic I will see
the volume fraction of increase in paste will be given by this 0.32 c divided by w, where
0.32 c is the specific volume of cement, because we know specific gravity of cement is 3.15.
So, 1 by 3.15 is this into c by w plus 1 delta w into 10 to the power of minus 3.
So, if I add a little bit of water, I actually increase the paste content by this much fraction
you know volume of fractional increase in the paste content is given like this. So,
that is what we actually do in practice. A simple equation has been proposed for increasing
the workability for increasing the workability. This is called a k factor method does not
matter, but let me explain this equation. This is this can be used supposing w 2 is
the slump or any other consistency measure, usually slump will be etc, w 2 is the
water content for the slump of y 2. So, y 2 is the consistency measure, w 1 w is the
water corresponding water. So, w 2 is the water content for w 2 is the water content
for y 2 slump, w 1 is the water content for y 1 slump.
Then w 2 by w 1 is equals to y 2 by y 1 divided by 1 over i, where i is an index depends upon
the method of measurement of consistency of concrete, say slump could be 1 of them Ve
be etcetera. So, i for slum p is 10, i for slump is 10 for Ve be it is different, compaction
factor the equation becomes slightly different and so on for each you can 1 can define, but
I have just taken in case of slump. This is a simple equation through which you can find
out how much water should be there. Supposing you know w 1 is the water for your y 1, that
is, slump equals to 50 millimeter. Now you have to find out the slump for 100 millimeter,
so this is 100 and what should be the water that you can find out from this formula, i
for slump is 10. So, using this kind of relationship actually 1 can find out what is the water
requirement. We might discuss this a little bit more in connection with mixed design.
So, therefore, we will summarize our discussion. What we have discussed is so far is the role
of paste. The role of paste we have understood the role of paste. We have understood the
role of paste. We have understood the role of aggregates and how workability is increased.
So, we have understood the role of paste, role of aggregate and how workability is increased.
This we will use again in context of mixed design. I think that would summarize all our
discussion and end our discussion. Thank you for hearing.