 So granularity always has attributes like angularity, roundness, sphericity see suppose this is a particle perfect sphere correct and we started shearing it under compression so what is going to happen it will tolerate up to certain point elastic range. Now there might be a breakage crushing which might occur the moment crushing occurs what happens the system becomes slightly less rounded sphericity is changing the more and more system becomes flaky irregular interlocking effect comes correct that you have to take into account which one is easy to compact this or a irregular system or a fine material you have to decide which one is easy to compact yes so that means here the densities cannot be achieved very high there is a limitation of this. So even if it gets converted to a rhomboidal structure the densities you are going to achieve much but once we start shearing the whole thing is again back to this discussion. So in my opinion more cohesion will get mobilized so if you remember in the last lecture what we discussed is the more and more the system is irregular alright what is going to happen the better interlocking effect is going to happen and better interlocking is going to give more cohesive nature to the soils keeping the density constant. So all these graphs are going to be density dependent please remember fine that is what I said so shear strength is increasing the form of the cohesion not the friction. So you just imagine the strength comes out of the dew component and say interplay between the two components here so for general soils this could be any situation depending upon this stress now you cannot say sands will show only friction clays will show only cohesion that part we will start discussing slowly and slowly. So in short what we have done is we have device direct shear testing again to characterize their response and this time what we have done is we have included the state of stress to which they are getting exposed so from this stage if I want to lift it let us say because of flooding I have to lift the embankment so what is going to happen the sigma 1 prime becomes sigma 1 prime sigma 1 prime not in that way let us say sigma a prime clear. So this sigma a prime is going to be from sigma prime to sigma a prime so C phi is getting converted slowly and slowly to maximum C and less phi texture and friction truly speaking for fine-grained materials or coarse-grained materials no you cannot mix it up. So in fine-grained material when we talk about the texture this is the pore structure alright and that is what is going to govern the texture and that is what is going to govern the cohesion so write this question maybe after third lecture we will discuss about this OCNC comparison just write down at the back of your notebook I think I asked somebody else also to write to you or somebody else to write a question so that time we will discuss about the fine-grained texture thing okay. In coarse-grained material we do not define texture as such so texture is a mesonomer for coarse-grained materials coarse-grained materials are basically particle shape size specific gravity and vice-versa gravity so that the particle should not get crushed so if you are dealing with pure quartz you know that is not going to get crushed up to 30 MPM so this graph is going to be linear but suppose if you are working with a soft mineral like sandstone sorry suppose let us say calcium carbonate or calcite it is going to yield very easily so for coarse-grained materials we normally do not use the word texture alright time dependent consolidation of the materials yeah so at a constant stress time dependent deformation of the soil mass so the best possible example is you take a candle put it on a table in a dingy room forget about it and come after 5 years or 10 years what happens the initially the candle would be like this and then constant stress as gravity time dependent deformation that is creep so normally we do not take into account creep effect much in soils unless you go into the theory of rheology. So read the papers by Rakshit Shetty and he has worked in the creep of fine-grained materials so for all your practical purposes the settlements are going to be either immediate settlements or majority of them are going to be consumption settlement provided you are dealing with fine-grained materials correct so you must have realized that we stopped somewhere at 90% in the test and we said that this is going to be maximum time factor for 90% and beyond which we did not ask a question so beyond this consolidation creep takes over and we say that this time tends to infinity in concrete you must have taken a creep coefficient to design your concrete beams and columns is it not so this factor is a function of some multiplier point not something multiplied by delta t now let us switch over from 2d to 3d which is going to be more realistic so let us start this dialogue between the plane strain versus a triaxial state we know the pros and cons of conducting direct shear box test that means the plane strain idealization and we said there that most of the time when I take out a sample from the ground this is going to be a 3-dimensional situation correct so this is more realistic as compared to plane strain however it is very difficult and expensive to create a 3d situation in the laboratory and test the parameters and complicated also but more realistic so suppose if I take an element and if I apply sigma 1 over here and because of sigma 1 application these trains are epsilon 1 sigma 3 epsilon 3 and sigma 2 epsilon 2 so plane strain is the condition where the strains in the perpendicular direction of the system are negligible or 0 or they do not change embankment on which the trains pass by clear so this is the width of the foundation this is the top width this is the length tending to infinity this is the height of the embankment in C323 we analyze this embankment for seepage analysis agreed and the sequence of construction you borrow the soil from somewhere compacted and achieve certain density because all the parameters are going to be dependent upon the density typical plane strain condition normal stress clear confining stress nothing is going to change in the perpendicular direction that means epsilon 2 is going to be 0 for plane strain condition today I mentioned condition all right and if I say that the l is the length b is the width h is the height what is the volume of the system l into b into h you must have done this enough in your 10 plus 2 physics pj and now if I say what is delta v upon v I hope you can compute this so delta l upon n plus delta b upon b plus delta h upon h these are nothing but the strains now this becomes the volumetric strain I will be using it quite a lot fine so this is the volumetric strain which is being experienced by the sample under triaxial condition sigma 1 sigma 2 sigma 3 and depiction of the triaxial condition is for a quick reference what did we do we plotted sigma 1 sigma 3 where is sigma 2 in between and we have ignored it so this is sigma 2 this is the intermediate principle stress sigma 1 is maximum or sorry not maximum major principle stress sigma 3 is minor principle stress and sigma 2 is intermediate principle stress clear so this is the volumetric deformation which I am talking about volumetric deformation happens in 2D case also plane strain case direct shear box what did we do we measure delta v separately and we measure delta h separately agreed what remains constant is area of cross section but in assignment number 2 I have written find out the changes which happen because of the change in the area of cross section of sample anyway so if I assume that the area remains constant over here which is the gross negligence you should normally apply the area correction in triaxial case imagine sigma 1 sigma 2 sigma 3 are acting we have epsilon 1 epsilon 2 epsilon 3 now what is going to happen this will be equal to epsilon 1 plus epsilon 2 plus epsilon 3 what is the relationship between epsilon 2 and epsilon 3 what we are assuming is we are assuming that the sigma 1 is the cause remember clear which is causing the deformations under applications of sigma 2 and sigma 3 otherwise life will become very complicated and what we are trying to study is because of application of sigma 1 and sigma 2 sigma 3 how much epsilon 1 epsilon 2 epsilon 3 get generated in the system that is the typical triaxial condition the simplification of this would be when I put epsilon 2 equal to 0 that means when I say epsilon v triaxial this will be equal to epsilon 1 1 minus 2 times mu epsilon 1 you know is this okay typical 3 dimensional condition what about the epsilon v under plane strain condition clear so when you did a consolidation test and your redometer ring was a steel ring to put the sample there and compress it from the top you assume that epsilon 2 and epsilon 3 are 0 understand this concept clear typical unidimensional loading that is why we call it as 1 dimensional consolidation loading so in a consolidation setup you apply sigma 1 and what you measured is epsilon 1 the steel ring is giving confinement and there are no strains because sample is not free to deform in the epsilon 2 epsilon 3 way alright so this is a typical 1 dimensional loading which we have used under consolidation loading concept alright 2 dimensional is direct shear box 3 dimensional is triaxial test so we are graduating now from 1 dimensional to 2 dimensional to 3 dimensional for the equal volume changes if I say that these 2 are equal ultimately the soil does not know whether you are assuming this as a 2 dimensional system or a 3 dimensional system so what is the relationship you are going to get you are going to get this will be equal to 2 times triaxial what is the meaning of this plane strain always gives you a higher Poisson ratio as compared to the triaxial condition what is going to happen to the friction angle so if I plot let us say nu versus confinement can you help me in plotting this suppose if I say this is one graph and this is another graph which one is going to be plane strain the top one so this is the plane strain and this is the triaxial alright the more and more you confine the sample the deformation the lateral directions are going to be extremely less that is the logic so what ground does what nature does when you take out a sample from let us say a infinite soil mass homogeneous isotropic semi infinite clear so if you take out a sample from here the neighboring soil is confining it okay the moment you have taken out the sample to the laboratory what has happened the effect of confinement is lost so you have to recreate this effect of confinement to get the parameters which are realistic parameters and hence you have to expose the sample after bringing out from the field to the 3rd dimensional loading and you have to go for triaxial it is a typical triaxial condition so normally you know what we do is sigma you are basically talking about epsilon 2 epsilon 3 it is a cylindrical sample which we are taking out so there is a axis symmetric case there is a symmetry about this axis so whether this is sigma 3 and sigma 2 does not matter which one because your epsilon 2 and epsilon 3 for triaxial samples you know we are talking about the triaxial sample are going to be same because this is a cylindrical sample triaxial sample is always a cylindrical sample good and concrete technologies what do they do they do not break cylindrical cubes cylindrical sample sorry they believe in cubes all right because they are more interested only in the ultimate strength and the crushing strength but for us there is lot of story before the ultimate or the crushing state is achieved so our philosophy of designing the systems is different okay now there are few relationships which you can write phi of plane strain minus phi of triaxial the friction angle which you get is approximately 0 to 8 degree and there is another relationship which has been given phi equal to 1.1 minus B upon L multiplied by phi triaxial so this is multiplied by 1 upon 10.