 So, welcome to module one of the course of advanced geotechnical engineering and lecture number 11. In the previous lecture, we have understood about the effective stress and capillarity. In this lecture, we will try to look into some problems and also role of water played on the, particularly when you are interacting, when a water is interacting with sand. So, we have a particular angle which is actually called as angle of repose. Dry unconsolidated drains will form a pile with a slope angle determined by the angle of repose. Suppose, if you take a dry sand, when a heap is formed, when sand is completely dry, the angle subtended with the horizontal is actually called as angle of repose, that is maximum angle what the sand can make. The angle of repose is the steepest angle at which a heap or pile of unconsolidated grains remains stable and is controlled by the frictional contact between the grains. This is controlled by the frictional contact between the grains. In general, for dry materials, the angle of repose increases with increasing grain size, but usually lies between about 30 to 37 degrees. For example, if you take a sand having classified as SP, uniformly graded sand and which is having a average particle size about 0.15 to 0.2 mm, this particular sand in dry state exhibits an angle of repose of about 28 to 29 degrees. So, in general for dry materials, the angle of repose increases and increasing grain size with increasing grain size, but usually lies between 30 to 37 degrees. That means that the sand cannot actually stand vertical or steeper than this angle of repose. So, here in this slide, what you see is a pile of sand which is actually formed with a dry sand. In contrast, if you look into a micro picture here, what will actually happen is that you have the grain to grain contact between these two places. For example, if you take a magnifying view, the grain to grain frictional contact will ensure that to have a subtended angle of that, the maximum steepest angle that what we call it as the angle of repose. So, what is the role of water? Suppose if you add little amount of water, what we have discussed earlier is that it forms a thin film, makes this appear like it can take the so called steeper angles than angle of repose. This is because of the capillarity action. So, think about building a castle on the beach. If the sand is totally dry, it is impossible for you to build a pile of the sand with a steep face like a castle wall. But if you make the sand somewhat wet, however, it is possible that you can actually build a vertical wall. So if the sand is too wet again, then it flows like a fluid and cannot remain in the position as a wall. So if the sand becomes too wet, it cannot actually stand vertical. So this can be explained here, for example, if you take a particular mould and you take a shape here and in this case when you have got water in contact with sand grains and when it is actually formed like a thin film, which is that this film is actually caused because of the surface tension of the thin film of the water is actually holding the grains together. You can see here the grains are actually held together by this particular action of soil water that is solid water and air interaction. What you see is that solid, solid is nothing but the sand grains and water and air interaction. So here in this particular case is slightly wet and unconsolidated materials exhibit very high angle of repose. So slightly wet and unconsolidated grains exhibit very high angle of repose. The reason is that the surface tension between the water and the solid grains tends to hold the grains in place. So in case of dry state, the angle of repose is very less. In case of a slightly wet state, the same unconsolidated sand grains or unconsolidated materials exhibit very high angle of repose because the surface tension between the water and the solid grains tends to hold the grains in place. Now on the other hand we have discussed that if we are actually adding more amount of water than what it designed, for example, a water saturated sand it actually flows like this, water saturated sand flows like this. And here what you see is that the grains are actually floating in the water and water completely surrounds the all grains and eliminate at grain to grain contact. So whatever the frictional interaction which is actually generated because of the grain to grain contact will remain absent if you have got actually more amount of water surrounding the grains. And in addition to that the surface tension whatever which is actually accumulated that the films which are actually formed because of the solid air water interaction get washed off. So the role of water is explained here when the material becomes saturated with water the angle of repose is reduced to very small values and the material tends to flow like a fluid. Here the material tends to flow like a fluid and the grains actually float along with the water. This is because the water gets between the grains and eliminates the grain to grain frictional contact. So almost like the grain to grain frictional contact comes to zero. So in case of clays for example if you have got a clay the role of water is again peculiar. So in this particular slide you have on the left hand side unexpanded clay that particularly some expansive clays which are having man to man light when they come in contact with water they increase in volume. So when the polar water molecules are in coming contact with this platelet particles the water accumulates between the particles or platelets and there is a possibility that these this is the it will form a status like expanded clay. So this is in the dry state and this is in the wet state. Same time when this water you know evaporates because of the exposure to the temperature there is a possibility that you know the clay is subjected to shrinkage which is in terms of for this type of soils it is also called as hydro compaction. So soils containing spectites or man to man light expand when they become wet as the water enters the crystal structure and increases the volume of the mineral is increases the volume of the mineral because the water accumulates between the platelet particles and makes the particles push apart and because of that the volume of the soil mass increases. The volume of the soil mass increases means that the soil mass is subjected to an increase in the swelling potential and it is also you know when it water gets evaporated it is also subjected to the so called shrinkage. When such clays dry out the loss of water causes the volume to decrease and the clays to shrink and are compact. So the clay particles will be pulled together and this process of you know evaporation of the clay evaporation of the water out of these you know particles which are actually formed with the spectites or man to man light mineral is actually called as the process called as hydro compaction. So hydro compaction generally occurs in case of a soils having minerals which are actually have nothing but a spectites of the man to man light and they expand when they become the wet as water enters the crystal structure and increases the volume of the mineral. When such clays dry out the loss of water causes the volume to decrease and the clays to shrink or compact. So this process what we actually have discussed is called hydro compaction. So we actually have seen you know a peculiar you know role of water in case of a sandy soil when the water is less it makes the sand to have very steep angles of repose. When the water is high the angle of repose is reduced to 0 in the sense that the sand with high water content starts flowing. In contrast if you have got a higher amount of water the clay tends to expand its volume and when the water is lost out of the same clay because of the evaporation then it is actually the process which actually induces on to the soil is called the hydro compaction. So the physical examples of capillary phenomenon if you look into it this is you know very clearly at the beaches at beach which is available say for example if you have the place if you take a groundwater table the soil below the groundwater table is completely saturated that we have discussed. And here the soil above the certain portion of the soil above the close to the groundwater table depending upon the type of the soil it is 100% saturated above that certain zone there is a partially saturated and here there is a absence of capillary pressure. So if you look into here if you take the soil here it actually possess the pore strength and in this zone it actually possess the pore strength and again it possess the pore strength. So here what it actually happens is that the confining pressure results from the column of the water hanging on the different men's cave at the surface of the beach. So relative density more or less for example if you take you know near the you know situation where in the beach the relative density of a soil is more or less same that is relative density is nothing but e max minus e by e max minus e max minimum e max minus e minimum where relative density of a deposit is more or less same because the same process is actually it is getting happened. Only change is the presence of the capillary moisture or its absence. So when there is you know in the capillary zone when there is inadequate when the water is actually less let us say that you know the all the sand molecule the sand particles is actually covered with you know a thin film of water and that makes the you know the particles you know the so called which is called as a negative pore water pressure. So this negative pore water pressure pulls the particles together and makes actually you know if you look into this effective stress at this point here when the total stress is 0 and the negative pore water pressure is minus u and with that what will happen is that the total stress is nothing but sigma which is 0 minus of minus u it becomes sigma dash is equal to u that means that whatever the negative pore water pressure is there that much you know effective stress it actually generated that makes actually the soil to carry you know exhibit good strength. So this allows us to you know for riding vehicles or one can jog very close to the place where you know the wave breaking does not take place for in case if there is excess amount of water then what will happen is that the negative pore water pressure which is actually binding these particles will get diminished. So in the process what will happen is that the same soil actually sense strength reduces to 0 with that the process of what we get physically observe is that physically a sinking feeling which actually comes because of the loss of the strength which occurs in the phenomenon. So when the seawater breaks the capillary minus k which are there surrounding these particles sand particles gets washed out and temporary induced shear strength is lost. So the capillary phenomenon whether in the below the ground suppose if you even if you have got a you know the particular soil type which actually has got a capillary phenomenon capillary phenomenon what it does is that the it make because of the presence of capillary effect there is a possibility that this effective stress will be high but you know this makes if an increase of effective stress makes that you know temporarily the shear strength will be high but once this capillary phenomenon effect diminishes then there is a possibility of the loss of that effective stress that means that the temporary shear strength which actually exhibited by the soil will be lost. So hence because of the because of this nature the effect which is actually due to because of the capillary water is not really considered in the design. So when the seawater for example in this particular phenomenon what we consider when the seawater breaks the capillary means k gets washed off and temporary induced shear strength is lost. So this is an example for the observed behavior of the soil very close to the beach where there is a soil exhibits good strength that is because of the negative pore water pressure which is actually prevalent in the portion as you go away from the wet zone because of the you know partial capillarity that negative pore water pressure will not be there. So because of that you know the soil actually positions. So it is very difficult to walk in this zone but it is very easy to walk in this zone. So because of this particular region this you know this capillary phenomenon can be explained. Another physical example for the capillary phenomenon is that the honey combing particularly we have discussed that soil fabric in case of some sand particles when they are actually moist and then when there is a film which is actually surrounding the sand particles. So what will happen is that this exhibits honey comb structure can result in some granular soils or in some sandy soils because of this film which is actually surrounding the particles. So here the enlarged soil particle which is actually shown here the capillary water in wedge formed by soil particles. So the bulking structure in sand is due to you know capillary action. So for example here what does it mean is that if the particles are actually appear like large volume but in between there are you know sand particles are actually filled with air. So this is something like when you look the real you know moist sand it actually exhibits somewhat like honey combed structure that is why it is actually called as the honey combed soil fabric structure in granular soils. This is because of the capillary action. The strength grain in granular soil is due to partial saturation and surface tension is actually this particular surface tension which is actually making the particles to bind together is actually called as apparent cohesion. So this type of apparent cohesion is prevalent particularly above the groundwater table where there is you know the possibility of the evaporation and also in some ash deposits like coal ash deposits the particular type of you know Kala coal ash deposits they exhibit very high apparent cohesion. So the strength grain in the grain wars granular soil is due to partial saturation and surface tension and partial saturation and surface tension and it is termed as apparent cohesion. So this cohesion is actually a property of the soil which we will be discussing later but if you look into this here now there are two types of cohesions one is called a true cohesion which is generally referred with the or which is actually is the property of the soil which actually can get because of the presence of type of the mineral for example carbonates actually can induce some cohesion in the soils in silties type of soils. So because of that the silties type of soils can actually stand vertical to some extent where if they are actually having a prevalent carbonate deposits. So in that case that particular type of soil set to actually exhibit a true cohesion but if a granular soil when it is actually partially saturated and because of the surface tension the particular nature which actually resulted is termed as the apparent cohesion. So let us look into some example in this particular example one a soil profile which actually shown in the figure we need to draw the total stress pore water pressure and effective stress diagrams and the soil in the capillary zone capillary zone is assumed to be saturated. So here a soil profile is actually shown here and this is at elevation 0 meters that is at the ground surface so this is the ground surface and here it is minus 1 meter and this particular portion the soil is actually 0 to minus 1 meter the soil is partially saturated minus 1 to minus 2 meter by virtue of the presence of ground water table here the soil is actually capillary this is called as a capillary zone and the water column is actually maintained above the that means that up to 1 meter above this distance there is a you know the saturation is actually prevalent and minus 2 to minus 4 meter that is again it is actually having saturation. So there are two types of soils layer 1, 0 to 4 meter and 4 to 11 meters there is layer 2 that is here from that is about 7 meters. So the solution for this can be worked out like this if you look into this particular figure what we have done is that we actually have transformed the figure which is actually given like 0, 0 meters that is elevation. So this is the ground surface what we are calling this as ground surface and this is the minus 1 meter we are actually indicating each level as 0, 0 and 1, 1, 2, 2, 3, 3 and 4, 4 the 4, 4 is the place where the bottom of the strata and at 2, 2 there is a ground water table and at 3, 3 the from 3 between 3, 3 to 4, 4 the layer 2 is actually starting between level 0, 0 to level 3, 3 there is a layer 1. So if you wanted to get the total stress and pore water pressure and effective stress diagrams, so in this example we have actually taken gamma w the unit weight of water as 10 kilo Newton per meter cube. Now let us consider at minus 1 meter that is at level 11 the total stress which is nothing but 18.5 that is the bulk unit weight of the soil into 1 meter which is nothing but 18.5 kilo Pascal's at minus 2 meters that is 2 meter below the ground the total stress is 18.5 plus 19.2 into 1 so it becomes 37 at 4 meters that is at minus 4 meter level 37.7 plus 19.2 into 2 because 19.2 is nothing but the saturated unit weight of the soil. 2 meter is the vertical distance between minus 2 meter to minus 4 meter with that what I have got is that 76.1 kilo Pascal's or kilo Newton per meter square as the total stress at minus 11 meter 76.1 plus 21 the saturated unit weight of the soil is actually given as 21 kilo Newton per meter cube into 7 which comes to 223.1 kilo Pascal's. So what we have done is that at elevation minus 1 meter that is 1, 1 and at elevation 2, 2 at elevation 3, 3 and elevation 4, 4 we have actually determined the total stresses. The pore water pressure is actually obtained like this. We actually have said that between the zone 1, 1 and 2, 2 so 2, 2 is the level of the groundwater table. Now because of the capillarity effect what we have actually discussed is that in the zone of the capillarity there is a capillarity height which is actually called as H suffix C, H C. So in that case minus gamma w into 1 that is minus 10 into 1 minus 10 kilo Newton per meter square is the negative pore water pressure which is actually exhibited by the soil at level 11. So at level 11 that is elevation minus 1 meter the negative pore water pressure is minus 10 kilo Pascal's. In principle for example if there is no capillarity effect and if water table is actually not there means then there is no pore water pressure but because of the virtue of the capillarity effect the minus 10 kilo Pascal's pore water pressure is exhibited at this level. When it comes to the minus 2 meters that is the level where the groundwater table is there so here the 0 you know the pressure is actually here 0. When you go down below the groundwater table that is say 2 meter below at minus 4 meter which is nothing but level 33 what we see here is that 10 into 2 that is 20 kilo Pascal's or 20 kilo Newton per meter square. When we actually have minus 11 meter that is nothing but 20 plus 10 into 7 that is 90 kilo Pascal's or kilo Newton per meter square. So this we have actually got total stress and this we actually have got pore water pressure. Now the effective stress which is actually nothing but sigma total stress is equal to sigma dash plus u that is what actually we have actually discussed. So effective stress is equal to sigma minus u. So in this case as the at level 11 the total stress is 18.5 minus of minus 10 which comes out to be 28.5 kilo Newton per meter square or kilo Pascal's and at level 22 the pore water pressure is 0. So hence 37.7 minus 0 you will get 37.7 and at level 33 that is at the point elevation of minus 4 meter 76.1 that is total stress minus pore water pressure is positive here which is minus 20 which comes to 56.1 kilo Pascal's and in case of minus 11 meters so 223 minus 1 minus 90 is 133.1 kilo Pascal's. So we actually have done is that total stress pore water pressure and effective stress has been calculated at each levels and the diagrams are actually obtained like this. So here what we have actually indicated again the soil profile at 0 that is the ground surface. So the total stress is 0 at this point hence this ordinate is actually obtained and at this point it is 18.5. So the pressure is actually represented here and this is 37.7 and here it is ordinate is 76.1 and here it is 22.2 kilo Pascal's which is 23.1. Though the unit weights are little bit different but the minor variation will be there in the gradient and here in the case of pore water pressure for example here what we have discussed is that this is if this is subjected to completely saturated zone or this is the capillary zone. So minus 10 kilo Pascal's is obtained. So what we have discussed in the previous lecture this indicates that as the comes to the ground surface the pore water pressure reduces to 0 that means that here the soil actually tends to be in the partially saturated state that means that depending upon the degree of the saturation the soil actually has the decrease in the pore water pressure and here what we have is that 0 here and then here it is 20 and here what we have the pore water pressure is 90 kilo Pascal's. So when we take this one sigma dash that is nothing but sigma minus sigma u, sigma dash is equal to sigma minus u we actually get the effective stress diagrams. So in the given problem what actually has been asked is that for the soil profile that draw the total stress pore water pressure and effective stress diagrams. So we actually have used with the concepts what we have discussed and then we try to draw with the effect of the with the effect considering the ground water table that is which is actually having a capillarity effect. Now let us try to do one more example from the slide which is actually shown here. In this example a 3.5 meter thick silt layer underline by a 3 meter thick clay layer is shown the figure will be shown in the next slide. We need to calculate the total stress pore water pressure and effective stress at points A, B, C, D and E. The water table is located at 2.5 meters below the ground surface and the capillary rise in the silt layer is 1.5 meters. Assume that the silt layer has a degree of saturation of 60% only in the zone of capillary rise. So here we actually have the partially saturated soil with a degree of saturation of only 60%. So a 3.5 meter thick silt layer underline by a 3 meter thick clay layer is actually considered in this figure and we need to draw the total stress pore water pressure and effective stresses at points A, B, C, D and E which we are going to see in the next slide and the water table is actually located 2.5 meter below the ground surface. So the data which is actually given here is the silt layer which is actually having the specific gravity of 2.7, void ratio 0.6 and degree of saturation 60%. Degree of saturation is sorry this is degree of saturation here is 0 that means that the soil is in almost in dry state. And here the zone of the partial capillary zone wherein the degree of saturation here is 60%. The gray colored zone which actually is the partially saturated capillary zone and here below the ground water table the soil is actually having 100% saturation and degree of saturation is same, the specific gravity of the solids is same and the water table is actually located 2.5 meter below the ground surface. And here the clay layer having a specific gravity of 2.69 and void ratio of 0.807 and specific gravity of 100%. So we let us locate at this particular point and at this particular point A, B, C, D and E. So this is the partially saturated capillary zone. So with that total stress which is can be given like this based on this data one can actually obtain the gamma which based on that we will be able to get that is 716.55 kilo Newton per meter cube. So with that what we get is that this particular ordinate and by going further with degree of saturation 60% by using the void ratio we can actually get the gamma relevant to here and adding this you will able to get this ordinate as 44.75 kilo Pascal and here below which is 64.95 and at this point it is 121.89 kilo Pascal. So this we have plotted here total stress and here this is the pore water pressure diagram here at this point U here it is 0 and when it comes to this point here as the soil is actually partially saturated what we can actually write is that minus 0.6 into 1.5 into 9.81 here it is actually taken as 9.81 kilo Newton per meter cube with that this ordinate what we have written is minus 8.82 kilo Pascal and at this point it is 0 and then we have here 9.81 and then here it is 19.24 kilo Pascal. So when we take the draw the effective stress diagram here it is 0 and then when we have got at this particular point just above this we have got 16 just above above B the ordinate is 16.55 kilo Pascal just below B it is 25.35 kilo Pascal and then at this point 44.75 because this point is 0. So what we have is that the total stress minus pore water pressure it is 44.75 and 55.4 and then here it is 82.65 kilo Pascal. So in this problem what we have done is that we actually have applied whatever actually we have learnt in this module to try to calculate total stresses and effective stresses and from the by knowing the pore water pressure distribution. So in this particular module what we try to understand is that the particularly we actually have tried to understand the origin of the soils and then we actually also discussed about different types of soils and soil deposits which are actually prevalent in India and other parts of the world and then we also discussed about the soil classification particularly we have concentrated on the unified soil classification systems. And before soil classification system we have actually discussed about different weight based and volume based ratios and which are actually used for estimating the soil parameters. And then we also have discussed about soil compaction and then we have discussed about how we can actually determine the particle size distribution or how we can actually determine the different physical states of fine grained soils and we have actually given enough attention towards determining the institute densities as well as the densities in the laboratory. Thereafter we tried to discuss about the effective stress and capillarity.