 Now, what you are talking about is what we do is we benchmark our compaction effort by drawing a line this is what is known as 0 air void line. We normally define this as AV equal to 0. This is the place at which SR is equal to 1 hypothetical situation. You must have noticed we have been talking about the situations for the soils which are non clay soils. All the results are valid for non-clays and I said the moment you achieve optimal and the moment you add moisture and compact it water comes out of the soil clear. So, SR equal to 1 this is also known as saturation line. So, if this line is the saturation line let us say 1 1 0 air voids would be AV equal to 0 is this ok? Did you get the answer to your question? So, saturation is somewhere here. If I draw a line which is like this there is these are the contours of saturation. You know the relationship gamma D is equal to G into gamma W over 1 plus E is of not going to be much used to me if I try to interpret the results by using this equation. Why? Because there is a foreign sitting over here is in the form of E. So, I have to get rid of this E. How can I get rid of this E? Is this ok? You got it? So, what I have done? I am plotting the complexion characteristics on a two dimensional plane gamma D and W and the contours are of S. So, this is your SR that means the equation for a saturation line would be gamma D equal to G gamma W over 1 plus G W over SR this is fine. So, the moment S is equal to 1 this is a normal equation G gamma W over 1 plus G W. So, G is very important to be determined for the soil remember any mistake which you are going to do over here would get reflected in this. Is this part ok? Have you understood this saturation thing? So, these are the contours. What it indicates? At this point the saturation of the sample is equal to this which I can compute from here because gamma D is known, W is known clear? G is known SR can be obtained clear? So, very intelligently we are plotting 3 characteristics on a two dimensional plane density of the matrix for a given moisture content and what type of saturation you have achieved? I am sure you will realize that A v is nothing can you tell me what will be the value of A v in terms of porosity and saturation quick you need not to spend much time. So, if I say porosity of the system is known what will be the A v value? How many of you agree with this? 1 minus SR is what? What is SR? Saturation 1 minus SR is unsaturated state of the material this is the porosity volume of voids divided by total volume clear? So, what you get is the A v value fine? Now what you try to do is you should prove that gamma D equal to G gamma W 1 minus A v over 1 plus E. Now this is a very interesting equation philosophically what you are doing is you are applying a correction factor of 1 minus A v to the density of the dried material. This is the way to remember this 1 minus A v is a sort of a saturation value for the state of saturation which is not 100 percent try to prove this. See the point is you cannot compact a material with the same energy. So, this curve is energy specific clear? So, here what has happened? In this direction the energy increases fine, but saturation line remains constant why? Because this is material specific remember depending upon the material which you are compacting this G remains constant and hence the saturation line is material dependent it will not shift. A compaction curve has a peculiar bell shaped characteristic nobody asked this question that for a given gamma D there are two values of the moisture this nobody asked. So, we have 0.1 we have 0.2 and there must be a reason for this. The reason is if you look into the microstructure which we have talked about the grain structure of the soils. This side is flocculated system. However, as you keep on imparting more and more energy in the form by adding more moisture what happens is this flocculated system gets converted to dispersed state we have talked about the grain structure of the soil. From a disorderly state of the grains the grains have become ordered by adding more moisture. So, what moisture does to the soil it acts as a lubricant fine. So, the more and more moisture you add the particles the grains start slipping over each other they become more ordered you are compacting them. So, they have got aligned like a ferromagnetic material where the ferromagnetism takes care of the alignment of the magnetic poles which get created in the system. So, truly speaking 1 and 2 are very interesting parameters or state of the material for the same gamma D for a person who is into construction industry. One of the interpretations would be if I plot gamma D sorry if I plot hydraulic conductivity as a function of moisture content please excuse me because I have not discussed about hydraulic conductivity in the class, but you will not have much difficulty in understanding this. It is a beautiful example of how two types of mechanisms can be superimposed on the compaction characteristics. You remember when we are talking about the flocculated soil structure I had used the word that this is going to be more porous as compared to the one which is more dispersed. So, that means the hydraulic conductivity is going to be dropping very significantly and this is how the curve looks like. So, in the flocculated state of the material you have high permeabilities at OMC this is the minimum k minimum and beyond OMC it picks up a bit why because look at the graph your gamma T is decreasing in this region is it not. In this region the gamma T picks up. So, this is where the system is becoming denser and this is where the system is becoming less denser. So, less density because of dispersed state is going to create lower permeability. This type of arrangement of the grains is going to restrict the movement of any type of fluid through this. So, if I was a petroleum geophysicist and if I do an exploration in the middle of the sea and if I get the samples of the soils which are totally dispersed I have wasted my money in exploration and this is how most of the wells are discarded because a dispersed structure because of the its structure is not going to allow the permeation of the fluid so easily. It is going to be very zigzag there is a lot of hindrance with the particles are going to create for the movement of the fluid as compared to this system where the fluid movement could be easier. So, this is one of the ways to match hydraulic conductivity moisture content variation with gamma D moisture content variation on the compaction curve. This point still remains partially unanswered that what is the difference between 1 and 2 when the gamma D is same. Now this is what is known as the dry state of the material in terms of gamma D and this is what is known as the wet state of the material. The compressibilities of the system are going to be totally different when you compare 1 and 2. So, what is the difference between 1 and 2? The compressibility is going to be different. So, if you are making a cricket pitch or if you are making an embankment or you are making a airstrip or if you are making a earthen dam or you are making a foundation system you have to be very careful about where you are going to compact and what point you are going to select for constructing the structure whether the wet of optimum or dry of optimum. Now the logic says wherever the water logging is going to take place like earthen dams where you do not want water to percolate through the compacted soil mass easily because that is the whole idea. I should be compacting the material at gamma D wet. Why? Because the hydraulic conductivity is less. You got the answer? However when you are creating an embankment for the traffic or runway where you want cross drainage to occur it will be a good idea to talk about the gamma D which is on the dry side because this system shows more strength as compared to this system. The flocculator structure is much more capable of taking higher loads as compared to the dispersed load. In dispersed load if you remember the settlements are going to be a big issue. So, these type of information can be deciphered from a simple test which is known as complexion test clear. And that is why I was saying let us use the word compaction characteristics and not only the compaction curve. Characteristics are much more broader and they connote a lot of information about the material as compared to the curves. Now we have been talking a lot about the fine grain materials. What about the coarse grain materials? There is a phenomena which is associated with the sands. If you try to compact them this is what is known as bulking of sands. So, what happens here is when you talk about the bulking of sands you know it is a very funny material. What is observed is that initially the gamma D decreases when you add the moisture into sands or sandy soils attains a minimum value of gamma D and then it rises. This behavior is known as bulking. We will be analyzing this behavior based on the shear strength theory in the second course which is going to be more rigorous than the first course. This is an introduction to the subject. What is the interpretation? When you add moisture to sands, fine sands the density drop is because of the surface tension clear. So, this is the process in which the surface tension is resisting you know the compression of the particles. You keep on adding more and more moisture, surface tension gets dissolved. This is the wrong word, dissolved. But what I am trying to indicate is it disappears. So, by adding more and more water this is approximately at 2 to 3 percent by weight. So, bulking moisture content is 2 to 3 percent by weight beyond which the capillarity is lost. The more and more water you add the air gets expelled the density increases. Now, this whole process is known as bulking of sand and this is where you get 20 to 30 percent of gamma D. So, if I say this is gamma D initial, this would be gamma D final which will be an enhancement of 20 to 30 percent. This is okay. If I further play with this graph, in the previous lecture we have been talking about effective stresses and the suction and the pore over pressures. So, I would like to complete the series. So, if I define UW with respect to moisture content and this is the OMC what will happen? The more and more you compact the soil you are expelling the moisture clear. So, the pore water pressures are going to be not pore water pressure. Let us use the word suction negative pressures pore pressures. So, what is happening is the more and more you compact the more and more air gets expelled out the suction increases. OMC this is a maximum possible moisture which the system is having but just to left hand side of this the system has maximum possible suction in it. These type of situations are going to be extremely problematic. You imagine every year in Bombay city the tracks get flooded during rains alright. So, imagine that you have created an embankment rains come water logging takes place and close to OMC you have maximum suction which is getting developed in the system. Given a chance because of this suction the tendency of the material would be to suck most of the moisture which is available freely and hence the soil mass beneath the track becomes wet. Are you realizing this? So, next time when the trains move what is going to happen? These equal amount of the pore water pressure is going to get developed and hence our effective stresses are going to decrease. So, it becomes very tricky to operate trains or the infrastructure vehicular traffic if you are not taking care of how to compact the soils clear. So, the best way would be go to the wet of optimum. There is no suction getting developed the volumetric deformations are going to be extremely less when you are dealing with the wet state of the material. So, core of the dams are mostly compacted at the wet of the moisture content for the same gamma D. This is okay. Two advantages I am getting first thing is the permeabilities are going to be low as compared to the dry state of the same gamma D and second is the settlements and the lateral deformations are not lateral deformations are going to be extremely less when I compact the material at the wet of the OMC clear. So, I was talking about the compressibility here. Normally compressibility is a function of range of stress. Sometimes we define things as a low stress and sometimes we define this as the high stress. So, suppose if I plot wide ratio as a function of stress I will use that term as stress for the time being when we are dealing with the low stresses in ranges of kilopascals. This is the response of the soil on the dry of optimum and wet of optimum. What I am trying to show here is wet of optimum for low stresses in the kilopascal range the volumetric deformations are going to be more as compared to dry of optimum clear. This graph continues as if I have broken the axis and if I am dealing with the very high stresses it has to be plotted on a log scale. We normally do not take the log of the number. We plot it on a log scale that means this has shifted from kilopascal to megapascals. So, then you are plotting it on a log scale clear. What is the interpretation? This remains the dry of optimum and this becomes the wet of optimum. On the wet of optimum the volumetric reductions are going to be less for higher stresses as compared to dry of optimum. I repeat when I was talking about creating the core of the dams, the dam sites are approximately few hundreds of meters or maybe few tens of meters depending upon the type of dam you are constructing. So, the chances are you are going to work in the log of stress ranges. When you are compacting the soil at wet of optimum the volumetric deformations are going to be less clear as compared to dry of optimum. So, this point becomes an obvious choice. When you are dealing with the low stresses there will be tracks, transportation systems like pavements, low stresses, the philosophy is different. The dry of optimum deformations are going to be lesser than wet of optimum. You know we were doing in the previous lecture the state of stress and I had given you some idea about the compacted state of the material. If you remember since my fourth, fifth lecture I am talking about variably saturated soil mass. So, say water table is here and I had put a condition that if I compact this soil mass all year heavily and if this happens to be fine grain material let us say what is going to happen? This analysis you should be doing yourself. I will give you some steps which you can follow. So, first thing is because of the capillarity associated with the compacted material which is of fine grain type. If I consider a point over here at a depth of let us say z and the thickness of this layer is z1 and if I consider a point over here let us say point p and this is z2. If I ask you to compute at point p what is state of stress? Sigma p over water pressure at p and the effective stress at p. So, this becomes an interesting case. It is not difficult. I hope you can solve it still. You remember the concepts of finding out the pore water pressure here. If this is a capillary zone you will have to put a tensiometer here. You can compute the uw value. What will the value of uw? At this point you are trying to find out this is the capillary zone. This is the peak of the capillary zone. Boss, you should remember this is the capillarity. You will get a state of a zero. Apply mind before you are writing something on the piece of paper. See practice of engineering is nowadays you know legal. Are you aware of this? Whatever you write and sign is a legal document. You can be pulled up in any code of law. Remember and then the damages are extremely high both ends. You get lot of money definitely, but if you are in trouble then you might have to pay from the nose. So, this is the maximum value of hello is the maximum value of the capillarity remember clear. So, it happens do not worry. I also did similar mistakes. So, this is going to be gamma w and what is the funda? You have to put the tensiometer over here and then find out what is the drop in the water head. So, this is z 1 minus z and negative value. Is this okay? Finished. At this point is simple. You put a piezometer. So, this becomes your z 2. So, at this point I know the value of u w. I know the value of sigma. Sigma is going to be tricky. Why? This is the saturated system. This is saturated. This is dry depending upon the material property. So, you have to be careful. This problem is a real life problem which if you solve would teach you a very interesting lesson that why we should not use fine grain materials in retaining wall or for back filling for that matter. Because you should prove this. This whole layer acts as a surcharge. What is surcharge? In your engine mechanics course you must have done these problems. There is a container which is filled up with some fluid, say water and then you are pressurizing this by injecting a gas into it. And if I say that the gas pressure is P and if I ask you to find out the pressure at this point at a depth of z over here, you can solve this easily. You must have done this in your 10 plus 2 and afterwards. So, this is the P pressure which is acting constant. And this will get added up to, so this is P which I can show like this also uniformly distributed load. You must be doing a structure analysis plus this is the hydrostatic pressure. So, when you have the fine and material which is heavily compacted this becomes a sort of a surcharge which is equivalent to P and hence later on we will study in the second course, is it not earth pressure theory will be in the second course. Yes, that because of these surcharges the earth pressures which are coming acting on the retaining system will go up and that becomes a big issue. So, I have talked about compaction process today. Compaction characteristics, how to interpret the compaction curves, how to use these compaction characteristics in designing different structures and the most critical one is the beautiful example of compacted fine-grained material how it acts on the stability of the systems which we will be analyzing in the next course.