 Until now we have discussed a lot of things regarding the fundamental behavior of soils and particularly you know their classification system, different types of weathering processes, how the soils are formed, how do they get deposited and how do they get, what are the transporting agencies and so on. Now today I will be discussing about the classification scheme number 2 for soils and this is what is known as the mechanical characterization of soils. Sometimes we can also call this as the classification. So, this could be either mechanical characterization or classification of soils. Now one thing you should realize here is that soils can be classified in different ways. We have talked about the geological classification scheme where the dual and weathered. We have talked about the characterization or classification of soils based on the transporting agencies and we have also talked about the classification of soils based on their constituents. Now we will be talking about how the mechanical attributes can be utilized to characterize or classify the soils. So, as far as the mechanical characterization or classification is concerned we classify soils in two forms. The first one is a coarse-grained material, coarse-grained soil and the second one is the fine-grained soils. As the name suggests, the particle size happens to be the most important thing to differentiate between the class of the soils. Mostly when we talk about the coarse-grained soils, we perform sieve analysis which you must have done in the lab. This is conventional, is the conventional way of classifying the soils as a coarse-grained material. There are different gadgets which I will be talking about in today's lecture which are say NEO. So, NEO tools or you may say gadgets. These are sophisticated instruments which are used for classification of the soils. Now fine-grained soils are normally classified based on something which is known as hydrometer analysis which you might have performed in the laboratory or we have again different type of sophisticated instruments which are used to characterize the soil. The process is simple. You take some oven-dried soil and pulverize it and dry it so that the lumps are broken and then by using a series of sieves, you can find out what is the percentage of weight which is retained on the sieves. I hope this exercise you have done in the laboratory. You have done this classification. So, I am skipping this portion. You should be conversant with the sieve analysis to read about it and perform a laboratory experiment. Similarly, hydrometer analysis also I am sure you must have performed in the laboratory. I will be talking about the philosophy of how these tests are done. What is more interesting is in today's world the results which I get from any of the mechanical characterization schemes. So, results are very precious and these results are treated as the results which a pathologist gives to the medical professional, all right. So, looking at these results, I can do a lot of diagnostics of the soils used to understand the fundamental behavior of the soils and this is an art to make out what type of soil you are dealing with. Now, one of the ways to interpret the results would be in most of the conventional schemes. When we talk about the NEO tools or the sophisticated instrument, we may get the image and we can measure the particle there itself in C2. But when you talk about the conventional systems where you are doing either sieve analysis or hydrometer analysis, normally we get what is known as particle size distribution curve. We do not use the word curve, though it is a curve, rather we writing curve we will use the word characteristics, all right. In short way we write it as PSD because lot of information can be revealed or diagnosed from the particle size distribution graph or the curves, we normally use the word characteristics. A typical particle size characteristic curve would look like this is a nomenclature, we plot as percentage finer then is written in some of the books is not a very good idea to lose the word then because it is understood that if I am considering diameter of particle, normally we write it in microns or mm micrometer. The way we define this term percentage finer than is corresponding to a diameter, we call it as dx. So, suppose if I get a graph like this, this is a typical PSD, the way you plot it is you do sieving, whatever is written on a certain sieve size you find out what is the weight fraction and then plot it over here for a given diameter of the sieve or the aperture of the sieve. So, this is how this is read, this becomes one point. So, this is how the experimental points are joined together to get a PSD characteristics. Now where is the technology part coming into the picture, this you will find any book but how a technologist will interpret the information from this graph is very, very important. So, this is a typical sieve analysis and looking at the nature of the curve alright or the characteristics I can define lot of behaviour, phenomena. This could be something like this also, I could define a curve like this also or I can get a soil where the characteristic curve would be let us say of this type alright. The red one is defined as a poorly graded material alright. Why poorly graded? Because most of the particles are falling in a certain range of particle size starting from let us say 0 to 100% and this size, this size the diameter increases. The yellow one seems to be a step graded material or let us use the word soil. However, the white one would be a uniformly graded soil. So, looking at the nature of the graph or the characteristic curve, I can understand what type of soil I am working with. What is the philosophy behind this? The philosophy behind this is at the most first of all I can have 100% of the soil mass and then the minimum would be let us say in few microns. A poorly graded material cannot be compacted. So, imagine you have all snooker balls and if you want to compress them together or bring them close to each other, it is not possible. Why? Because the sizes are so uniform that you cannot create a dense matrix out of it. So, absolutely difficult materials to compact, compaction is next to impossible is poor let us say alright. Size of the grains of the soils are uniform and hence you cannot compact them much. That means I cannot create a compact system out of it. Most of the soils which are lying in the genetic basin and which are prone to liquefaction. I think we have discussed the word liquefaction earlier loss of strength because of shaking earthquake would be mostly poorly graded soils alright. So, they cannot be compacted. You cannot use them for designing a good let us say foundation pad. However, step graded soils they look like as if they are the combination of two types of soils. So, this is soil number 1 and this is for soil number 2. So, this is step graded or sometimes we also call this as gap graded alright. As if they are the combination of two types of soils tricky materials to utilize. Now, where is the technology? The technology is tomorrow one of your customers is going to tell you give me a finished product where the particle size are going to be only in certain range and I want a certain gamma D. Now, this becomes an interesting problem where technologists have to work. Material scientists they are trying to pack the nanoparticles to a desired density for making a chip let us say. It is a difficult task. This is absolutely impossible of poor. The best material to deal with as a civil engineering material would be a well graded material. Now, this is also known as sometimes well graded. The type of book which you follow you will find these type of analogies. So, excellent materials to or soils, material means soils to compact and create a structure of your requirement alright. Now, I am sure you must realize until now everything is going very, very you know qualitative. We are saying poorly graded, well graded, step graded, gap graded everything is qualitative. There is no quantification of the phenomena which we have done until now. So, what we do is as far as the coarse grain materials are concerned we try to quantify them by using DX which are D15. Now, how would you read this D15 is the diameter of the particle which is 15% finer than the entire particles. Is this part okay? So, D15 is the diameter of the particle which is 15% finer than the entire mass. So, in this type of a soil you will have certain value of D15. We use another term as D30, 30% finer than diameter. Then we use the term D45 sometimes we use the term D60 sometimes we use the term D85 also nomenclature. And remember D is the diameter in millimeters. So, one of the ways to read this graph is on x-axis from left to right the particle diameter increases alright. You should never plot it reverse then the whole philosophy will be changed. So, the nomenclature is you plot the diameter on the x-axis which is increasing in size. So, normally from micron range to millimeter range and this is from 0 to 100% this is okay. So, when you do the laboratory experiment please try to plot these graphs and interpret. Now, the interpretation number one is about the particle sizes. I hope you will realize we are talking about the mechanical characterization of soils. So, no chemical attributes are coming in the picture. No mineralogical attributes are coming in the picture. It is only the attribute size and based on size we define clay fraction, silt fraction, sand fraction, gravel fraction, cobble fraction, stone fraction, boulder fraction. Is this funda clear? So, we are not using here word the clay as the mineral. We are using here the clay as clay sized, silt sized alright gravel sized and so on. So, these are all sized we define this as y sized, y could be clay, y could be silt, y could be sand, y could be what it could be. See coarse sand fine sand then comes your gravels then comes the cobbles and then comes the boulders. So, the way we read it is clay sized, silt sized, sand sized in sand coarse fraction of the sand fine fraction of the sand gravel sized cobble sized I will remove s boulder sized. One of the guidelines says that clay size is less than 2 microns, silt is less than 75 micron. This you have to remember alright. This part you should remember sand is normally 4.75 micron first of all less than 4.75 micron gravel is less than 75 micron no 75 mm cobbles are less than 200 mm and boulders are greater than 200 mm. This is the classification system which is normally used as per BS, British standards. There is a small deviation as compared to other classification schemes I will not go into those details. As far as the fine sand is concerned the fine sand is normally less than 0.2 mm and coarse sand is less than 2 mm. This is as per the International Society for Soil Science. So, there are standard yes please this is 4.75 less than 4.7. So, I understand your point. So, this is less than that is all I said there is some discrepancy. So, the more and more which one 4.75 micrometer yes sands no this is micrometer. So, sand is 4.750 this is okay mm yeah. So, 4.75 mm yes and then you have less than 2 mm 0.25 mm 75 yeah now it is alright. So, there could be a discrepancy in some of the particle sizes depending upon the type of course which you are following but try to remember at least British standards and this is what is going to help you. So, when you analyze these graphs you plot these numbers over here and read out what is the fraction which is finer than is this okay this I am sure you must have done in the laboratory. Now, one step ahead of this would be there are few numbers which we define for coarse grain materials based on the sieve analysis utilizing this concept where we define a term which is known as Cu this is known as a coefficient of uniformity and there is something known as Cc we define this as coefficient of curvature sometimes we also call it as gradation coefficient of gradation alright. Now, what Cu and Cc are so Cu is d 60 by d 10 this is correct is it and this is d 30 square upon d 60 into d 10 this is part okay as far as coarse grain materials are concerned the classification is done. So, you take coarse grain soils texture would be very sandy material gravely sandy material sieve them through a stack of sieves find out the percentage which gets retained on the sieves compute the percentage finer than that aperture and plotted with respect to diameter plot this graph from this graph get the dx values classify the soil based on this nomenclature compute Cu and Cc term alright and there are some standard numbers which are assigned to this we will talk about that. Now, what is the application of the whole process as a technologist just try to remember this series nothing more than that I think you have understood those of you will get a chance to work in the design of filters and this is where chemical engineering becomes very close to geotechnical engineering soil mechanics alright when you design different type of filters different type of filter media or when you design different type of filter or seepage control talking about the design of dams. Dams are the ones which are most neglected objects in our society and I hope you have realized that if you are not giving them due consideration what is going to happen hope you are realizing last one month whatever has happened in the country is this correct you must be reading newspapers and all. So, this is going to be an interesting subject to discuss we will be discussing quite in details one of the components of the other dam is filters and filters are nothing but the assembly of coarse-grained material alright. So, when I say coarse-grained soils you will be utilizing different components fractions in such a way that you can form a good filter media swimming pools have normally granular filter beds alright with the water trickles and these granular material are quite prone to give shelter to the bacterial activity they get converted into bio filters and through which I can pass the sewage and the sewage can be treated. So, those of you are interested learn this more and more when you design filters the criteria is do not try to mug this up it is all available in the courts so as a designer you will be getting quotes which you can use upon D85 this is just to showcase to you what is the application of the particle size characteristic curve D15 of filter divided by D815 of soil one of the guidelines to design the filters. The second guideline is the particle size distribution curve of the filter soil or the filter material should resemble the particle size distribution of the soil. Now, let me ask you a question suppose if I have you know PSD now I will not be drawing xy axis all the time and suppose if I say this is the soil why are you designing filters first application is which I said that you want to allow the sewage or the wastewater to trickle through it and get purified apart from this the filter could be designed to stop erosion of the soil fine so that the particles of the soil get trapped in the pore space which has been created because of the grains. So, a typical conceptual model for a coarse grained filter material would be like this, this is the soil or the grains of the soil and the finer particles this would not be the grains of the soil this would be a filter media so this would be a filter media and the soils would come and sit somewhere here soil particles will come and get mechanically log over here. So, this would be a soil grain I hope you are understanding what I am trying to depict the filter particles are acting as a sieve and they will not let the fine grained material to pass through the voids this is okay. So, this is what becomes a good filter media so now if I extend this analysis over here and if I ask you a question where the filter media should be sitting what would be your answer so this subject requires a lot of intuitive thinking and mugging is not going to help you it requires dedicated understanding of the concepts I am sure you must be realizing a lot of concepts I keep on asking why when where how this is what I expect from you that you should be aware of this for this you have to go back read some literature apply some mind though I give a lot of hints over here. So, anybody who can answer this question if the soils are here where the filter should be on the left hand side or right hand side the soil particle have to be finer than the filter media so this answer is wrong why there is no fun in providing a filter media which is finer than soils agreed because soils are soils have to be protected so this is what we have learned today correct is interesting apply logic believe me you need not to mug up anything so this is a filter media okay this fulfills this condition of remember this side the particle size is increasing this size the first percentage fraction is increasing and this is the condition why I wanted to design filters so that the fine particles of the soil get trapped and they do not come out of the matrix to stop erosion process alright this is one constraint the second constraint is so this is what the first condition would be what is the second condition soil is a very intelligent material remember the moment you include something into it it has a tendency to reject that inclusion unless the system is identical to it among all the construction materials which will come across in the history of mankind or evolution you will realize that the soil is the most you know intelligent material so intentionally I have drawn both the curves quite similar to each other clear so another requirement is the PSD characteristic shape should be identical to the type of soil which you are trying to protect alright they should be similar as if they are slightly shifted on the right hand side now if your material happens to be let us say a poorly graded soil which is which are the chances in the material sands you cannot have several sizes available in the system the question would be I cannot achieve the density because I have written there you cannot compact it you cannot create a compacted bed out of it and if you really want to compact a material this has to be a material where most of the particles of different sizes are available in it alright then only the materials can be compacted what is the theory behind this the theory behind this is uniformly graded soil well graded material the first layer of the particles would be bigger the second layer of the particles would not layer I should use the second types of particles which are available in the soil mass would be this alright the third types of soils would be finer than this and so on so larger the variety of the particles which you have in the soil system the chances of compacting it would be better and this we will prove later on with the help of theory of compaction is this okay now those of you who will be working in let us say interdisciplinary areas like growing grass on the pitches of the sporting fields whatever pitches or courts of different type of sports what is expected it is expected that you create this matrix first number 2 grow the vegetation so the roots of the vegetation should pass through the pores which are available in the system and they should go and hold the bottom layers of the pitch or the coat agreed and then comes the microbial unit so microbes will harp on these available spaces they will grow over there and they will form a strong system of soil root bacteria environment water interaction now this is a hot subject on which people are working is this part here diameter of the particle increases the percentage of its fineness should decrease very good question remember this graph has been obtained by sieving you must have done sieve analysis in the lab so you must have seen the apertures on the sieve clear so the top most sieve is a big aperture or the small aperture sieve because how to read this is good that you have asked this question so the biggest particle everything is far finer than this everything passes through this agreed the second sieve size is lesser than the first one less particle size 80 percent finer than this agreed and so so it is good that you have asked this question for the sake of everybody percentage finer is also same as the percentage passing anything which is finer than that particular aperture is going to pass through that sieve and hence it is finer but it is passing also it depends upon what you are using anything else yes the filter which we use for water purification if once the dust or the dirtiness is trapped in the filter so is any process to remove the dirt or just it where the filter is got wasted very good so excellent question when I am teaching seepage analysis if I do backwash all right so what I am going to do if I apply backwash if I if I pump let us say some fluid inside the filter and if I force these finer particles come out of the matrix it is a sort of a washing clear so by applying back pressures or by applying back washing I can clean up the filters so you can rejuvenate them read more on the net about this so in most of the environmental engineering related problem the biggest issue is you may design a filter and the filter stops working after it has lived its life agreed so what I am supposed to do I am supposed to throw it and the moment I throw it this becomes a secondary source of contamination and imagine a mattress which has lot of concentration of chemicals so where are you going to throw it big question how we lifted another question so better what you should do is keep on cleaning frequently all right okay now coming back to your another question regarding the cleaning up of the water which you are using in the candles of water purification system their pores are going to be extremely small so they are made up of zeolitic material I can create a mechanical sieve read more this more about this this is a mechanical trapping I have created all right based on the particle size I am trapping the small particle clear I can design a system of filters which could be a molecular filter so what is going to happen now all these sieves all these systems which are going to be in a in a matrix will trap cations and the molecules plasma trans plasma treatment of different types different types of silica transplantation different types of chemical processes which are taking place in the industry he making particularly vegetable oils different type of medicines which you are doing are all based on sieves blood transfusion is another good example of how you would filter out the bad blood from the from the good blood good example of molecules it would be kidney of the human body so read about all this okay is the concept clear so here we have gone from mechanical to molecular system is a different aspect altogether so in the candles which you are designing all the cations will get held up and hence the water gets purified currently there is not any technology for RO purifier to clean its filter we are just throwing all the filter of RO purifier I think you know that RO is a obsolete idea and people are again coming back to the point that RO should not be used obvious reasons all your calcium sodium magnesium has gone out of water and that is what you are drinking and people are saying that your vitamin deficiency is because of RO water and canned and watered water you read lot of discussion is going on so what they are doing again after doing RO they are doing mineralization of water dystopianity let us move on to now I will show you what is the state of the art in classification or characterization of coarse-grain material remember we are still talking about the coarse-grain materials so when we do when we deal with the coarse-grain materials all this is conventional which has been done since 1930 40 you know not much of fun here but these two concepts confocal micrography and optical micrography you know people are using to study the particles in a better way so those of you might have heard about neoprene bearings clear so bearing B E A R I N E bearings like you have ball bearings so neoprene bearings you know people tried to dose steel with some sort of additives it could be carbon it could be carbon black twist very high speed carbon they add into it so when you do doping of the steel it becomes very high strength and you know it resilience modulus and other modulus are extremely high so when you are doing this type of research or application then this type of studies become very important I want to see the whole morphology of the particle so 2d and 3d types of analysis is done this is a peculiar standard sands which I was talking about that as per Indian standard this is supposed to be a spherical system of sands which is not true these are the thin sections which have we have taken and we have done the analysis in 3d the standard sand looks like this highly irregular shapes these are the glass beads which are made up of glass manufactured by industries and this is how the complete modelling of grains is done in today's world so you take the photographs of the each grain sit down in your lab maybe 3000 4000 grains you take photographs and then you try to inscribe ascribed as many circles as you can so this is a grain of the sand one of the grains and then try to fit in as many circles as you can fit in inside the grain boundary and one which is you know subscribing the entire thing and then you take their ratios to define the sphericity roundness and regularity those of you who might get a chance to work in earthquake engineering soil dynamics particularly for them this becomes very very important so how spherical a system is how rounded a material is how regular a material is and then by defining these indices we can go ahead with this those of you are interested in reading much about it read the papers which have been published by Prasad Bhattake and myself long long back and then we have correlated the particle morphology with the shear wave velocities which are required to cause liquefaction of the soils another interesting thing this is what is known as image analysis system this is the pristine historic you know laser part in the scanner on which we used to work maybe 15-20 years back but now the world has become quite technologically advanced so just to avoid any copyright and unnecessary canvassing in the classroom I have not included any particular website but what you can do is whenever you get time please go through all these websites where different vendors have come out with very sophisticated particle analyzers so gone are the days when people used to do all these things manually or sieve analysis becoming obsolete the reason is simple if I am dealing with the sands which have lot of carbonate on them or if I am having sands which might be having some sort of a alteration of the properties by any chemical process just now I was talking about a chemical alteration of the sand into you know mineralogical alteration which I discussed long back so people like to see the real life situation rather than breaking the bond and breaking the you know carbonate adhesion between the grains and so on. So one of the systems is known as image analyzer which we have in IIT I think most of the departments would be having malvern and just go and check out the video which would give you enough idea about how this particle analysis is done for the coarse grain materials and everything is computerized for that matter and you can get results quickly. Fine then sieves which you might be using in the laboratory but these are slightly sophisticated sieves which we have in our laboratory and these are laser cut sieves and we can go up to 2 micron dry but this is an art and there is a paper which we have written in ASC American Society of Soul Engineers where we have shown that why all this should not be studied anymore but coming back to the third year classroom I have to talk about all these things. So this is advanced research and there I am trying to show that none of this works if you have time if you have talent and idea go through this alright this work was done by Shanta Kumar and myself in 2013-14 I do not know as Shanta Kumar. So these are the sieves which are used for dry sieving up to 20 microns, 22 microns, 20 microns and these are known as ultra sieves. The results of soft imaging are this earlier days my students used to work on this type of histograms you know 4500 particles have been counted you will not believe but this is what has been done and then we used to draw a particle as distribution. Now life has become simple we have different type of gadgets where you can do analysis quickly. Now just to show you something interesting different type of materials and their specific surface area and this is silica fume. You remember we have been talking about 20 meter square per gram is the surface area of the silica fumes and this is how the statistics used to be done number of particles they are falling in which range and based on that you see the predominance of the particles. So there are many research papers which are available where people would like to withdraw certain part of the particle size distribution curve and that becomes a synthetic soil. So suppose somebody orders for a specific purpose I need this type of a soil clear how would you create it. So this becomes an art so from this I would like to take out few fractions by sieving them and then this becomes my synthetic soil and then how to manipulate this is a interesting idea. Now let me start discussing about now the fine-grained soils. I am sure you must have dealt with fine-grained materials like silty clay sandy soils in your laboratory experiments. It becomes difficult if you are dealing with the fine-grained materials. So one of the ways to find out their particle size distribution characteristics would be hydrometer analysis. This is also known as sedimentation analysis. How many of you remember Stokes law? How many of you remember terminal velocity, critical velocity you remember very good. So when you are studying 10 plus 2 physics you never thought that where it will be utilized. The complete geomechanics of fine-grained soils is based on the Stokes law which is nothing but the sedimentation analysis where we will be using the concept of terminal velocity. Sometimes this is also known as critical velocity but try not to use critical velocity term. Let it be terminal velocity. A good example is drops of the rain alright when they fall and when they come on the when they hit the earth they normally hit at terminal velocity correct. As I said these are tricky materials to handle and hence nowadays people are taking use of laser particle scanning, laser diffractometers they are using. Sometimes they use SEM though it is difficult I think we have discussed about this and sometimes they use what CT scanning that will not give you particle size fine-grained material SEM of different types. So let us go back to the conventional concept. Fine-grained soils when you are dealing with the moment you put them in oven at high temperature their activity is lost. So you should not have done this mistake air dried. So we will put a condition over here remember in coarse-grained material we said take the soil pulverize it and put it in the oven in the coarse-grained material. In fine-grained material we should not do oven dry. We should do air dry remove the clots fine-grained materials are very notorious you know what happens because of the surface chart which we have talked about double layer theory and all those things the moment hygroscopic moisture is available they form clots. So several particles will come together and they will form a clot clot is a sort of a agglomeration of the particles alright. So you can just break them by using a light tamp normally we use wooden mallet we do not use a heavy tamp also having done this try to get rid of all sorts of unwanted materials what are these unwanted materials number one organic matter. So what do they do they will allow the interaction of the soil with H2O2 hydrogen peroxide it oxidizes the organic matter which is present in the system fine. We use some deflaculating agent what these deflaculating agents do they disperse the fine-grained material sodium hexametaphosphate is a good example of this yes it directs the bonding particularly the hydrogen bond H2O and that is it. So when you say it is the water hygroscopic moisture which is binding all the particles forming the clout when you add these type of system they reduce surface tension number one and number two they break the hydrogen bonds between the different clay particles. So this is what is added to disperse the fine-grained materials so that each particle becomes an individual entity just take it out the give me the correct formula to create an individual particle which would fall in a column of water sometimes what we do is we heat it also to get rid of the compounds of Fe2O3 which are mostly present in the soil and Al2O3. I hope you can realize it is a sort of a manipulation which you are doing with the material to change the basic characteristics and then you are dealing with it. So there are a lot of limitations of the material normally sodium hexametaphosphate is less than 4% by weight let us talk about the principle of sedimentation see those of you are preparing for competitive exams you have to remember these things because there is no other way this is meant for mostly silty and clay soils first the concepts of the analysis and then I will write down in a typical bookish manner which you have to mug up. Normally we consider a jar or a volume which is quite big so this is the volume of water we fill it up with water the solution of the soil in which all this has been done you have treated the soil with H2O2 organic matter is there you have added sodium hexametaphosphate to get rid of the flocculation making it defloculated you have heated it with Fe2O3 Al2O3 to get rid of alright take W of this soil and dissolve it in V volume of the fluid water. So this is the V of water in which you have dissolved this and then mix it thoroughly I hope you must have done this alright so once it become a slurry of good consistency I hope you can realize why we are not using sieve analysis sorry we are not using sedimentation analysis for coarse grain material because if coarse grain materials are there in the process of making a slurry half of the particles will settle down so this becomes a heterogeneous mix and hence we never use coarse grain material we filter it out and from the soil after filtration of the fine grains that fraction only is used for this analysis. So W is the weight of the solids which you have taken dissolved in V of water to make a slurry and this slurry is transferred into the jar so this becomes your slurry in the jar I am sure you must have used the hydrometer so hydrometers are used to measure the specific gravity of the solids in a slurry a good example of hydrometer which is used for finding out the quality of the milk would be electrometer I can measure the specific gravity of the fluid and then I can know whether this is adulterated or not so as far as the mechanism is concerned if I consider a particle of a fine grain material which is falling freely in the system and if I zoom it this is how it would look like a poor assumption is that even the fine grain soils are spherical in nature is an assumption the Stokes law limitation is it is valid only for circular particles. So if G is the diameter of this grain can you draw the free body diagram what is the third force which has to act any idea no you are doing fluid mechanics surface viscous force you are right what is that viscous force known as drag very good so if this particle is dropping down in an infinite column of fluid clear why infinite because this V is much, much, much larger than volume of this file grain this is okay. So if it is going down there will be a drag force what is the magnitude of this force anybody remembers very good yes yeah you are right so this is 6 pi I define as a mu theta is what your viscosity okay alright so you are convenient with eta is porosity if you remember so notations have to be carefully chosen otherwise chances are when you will be dealing with the problems later on in the porous media when the fluid is flowing you will goof it up fine. So 6 pi mu r is the radius into very good so this is 6 pi mu d by 2 into V rest is simple so this is the gravity so 4 by 3 pi r cube into what will be this component gravity component very good no no no no no gamma d gamma d is the matrix it cannot be only gamma so when I said hydrometers measure what specific gravity clear so this is going to be the unit weight of the grain this is okay so this becomes your volume into density mass multiplied by g will be taken care of clear is this okay and then you have another force acting what is that force buoyancy very nice so this becomes 4 by 3 pi d by 2 cube into now tell me what this would be gamma very good and that is your equilibrium this gamma s has to be substituted in the form of yes first you understand this thing that your this has to be in the form of g is this okay why because you have to hydrometer analysis so you should be lowering a hydrometer over here this is how the hydrometer looks like this is a CG of the hydrometer those of you have done this experiment you have done very good so what type of corrections you applied those three corrections the first one is temperature why normally hydrometers are designed for 20 degree centigrade so when you are working at room temperature 27 28 degree you have to apply this expansion of the hydrometer normally this is filled up with what you call it is as lead so the first temperature correction has to be applied number 2 meniscus mostly soils when they are in the slurry form what happens you know the meniscus is getting formed like this this is a meniscus so when you look at the materials which are not transparent you have to read at this surface and not at the bottom of the meniscus so you have to add this much of the correction which is known as meniscus correction in the hydrometer reading sure you must have observed that hydrometer readings would be increasing from top to bottom is it not so if I say that this is r value it is understood that if r is known g will be equal to 1 plus r and normally r is up to third decimal place this is okay so you apply the temperature correction meniscus correction number 3 is whatever additives you have added over here because of their addition what has happened the gamma s of the slurry has got changed so this is the additives mostly dispersive agents so I will give you the correct answer of what these functions are write down these expressions and try to prove it of course there is nothing much to be proved d square upon 18 rho s minus rho w upon mu into g try to prove this rho s into g is gamma s which is the density of the slurry rho w into g is gamma w which is the unit weight of the water now try to reverse this function and write d square as a function of v and this is what is known as I have to be careful this has to be a small v because capital V I am using for volume so please be careful this is small v small v so this will become 18 into v into mu upon rho s minus rho w into g in other words d would be under root of the so what it indicates is d is a function of root of v I think this is simple you can just sort it out what is the interpretation of the whole thing the first one is this is valid only for particle size less than 2 micron which is a typical clay size fraction that is a big thing number 2 is particle is the spherical particle which you are assuming though clay particles are plate plates and they are not spherical number 3 the volume of the jar in which the suspension is taking place much much larger than the volume of the particle all right Brownian motion so less than 2 micron is for not considering the Brownian motion less than 2 micron the Brownian motion will start and hence we cannot do that yes turbulence is not yeah so turbulence in the sense when you are dipping it in the soil then you are disturbing it that is not a limitation of the Stokes law let us consider this is the jar and at this point I am measuring the density of the soil unit rate of the soil all right and this point is matching with this point the one of the questions is how would you get the v value one of the assumptions could be that velocity is equal to L by T where L is the distance which the particle has travelled from one point to another point during sedimentation process extremely difficult to obtain but the classical geomechanics talks about this so imagine if I have laser obscuration method those of you are interested read about this allotm in our department we have this machine so this is basically a sort of a laser obscuration transformation method obscuration time sorry laser obscuration time method yes so what it does is when a particle is falling from a particular distance let us say point number A to point number B I can capture this by using a laser beam and hence I can obtain the L and I can notice the time this type of device is used to understand how the rotation and the dynamics of the particle is taking place about its axis and so on you can do the shape analysis also this is one concept in conventional geomechanics when we are dealing with hydrometer we are not going to use this concept much unless somebody measures in how much time a particular particle during settling is falling from one place to another place sometimes it might be visible you are dealing with the soil you must have noticed once you keep it on a flat bed the particles start settling down and the topmost water becomes clear and you will be having sediments getting deposited over here now this logic tells me bigger the diameter the velocity is going to be more so all big particles are going to sit here and as you go up the particle size would be decreasing is this okay is this part clear now if I assume that there is a hypothetical plane at this point and the thickness of this plane is let us say dz and n is the fraction of the particles which are available in the system which are finer than this diameter of particle d so it is a sedimentation column where the sedimentation is occurring I have taken a hypothetical plane in the system of thickness dz and I am assuming at a given time all the particles which are greater than diameter d I have settled down and whatever is remaining the system are n percent finer than clear this analysis will have to do later on related with g related with d related with the velocity d yeah you are right very good say gamma s so if you see here this is the density of the suspension or the slurry so this has to be greater than as gamma w correct you are right otherwise sedimentation will not occur so the soils which might be having components lighter than water this is another another limitation he is forcing us to create now in this series if the soils are organic in nature they cannot be used and hence you get rid of them because they will be floating only on the water surface and they will not settle and hence this analysis cannot be done there is another limitation