 So, let us talk about some other pressure distributions on the braze sheet pile wall are given by different researchers. So, the first one is you know sands and we have already discussed about one of the pressure diagrams which was given by Tazagi and Peck and this is for dense sands for loose sands the pressure diagram looks like this, this is 0.2 H, 0.8 H and this axis remains same as 0.8 K into gamma H, this is for loose sands Tazagi and Peck. There is another pressure diagram which has been proposed by Sheboterov, these are all empirical pressure diagrams 0.1 H, 0.2 H, 0.7 H and this is 0.8 K into gamma H. The name of the person who assessed this pressure is Sheboterov, this is for sands and for clays. So, this one is the dense sands for clays, the pressure diagram is 0.3 H, 0.55 H and 0.15 H and this is gamma H minus 4 C, this is again given by Tazagi and Peck. However, the pressure distribution given by Sheboterov for clays 0.6 H, this is 0.4 H, so this is the pressure diagram 0.3 times gamma H, 0.2 times gamma H, this is for temporary support stiff clays and for permanent support in medium clays these values are 0.75 H, 0.25 H, this is 0.375 H into gamma and the whole thing is 0.5 H into gamma. So, these are the pressure diagrams which have been proposed by different researchers who have worked in this topic. So, hope you can analyze these problems quite easily. The deep cuts which require support are supported by sheet piles and further by installing braces and struts and then you are supposed to find out the cross section of these braces and struts for that the force is required. So, the moment you know the force, you know the stresses, you can select the right cross section of the element. The pressure diagrams are assumed which are known or assumed. So, per impulse on these structures go for the equivalent beam method and analyze them. So, with this I will finish my discussion on the application of shear strain theory, another application of shear strain theory yes which is the analysis of retaining structures. And the last subtopic which I would like to discuss would be the slurry trenches, how slurries are used to stabilize the cuts or the trenches which are made particularly in offshore regions particularly wherever you have the soft trace alright or for geo-environmental applications where you are having the storage of let us say different type of chemicals or different types of industrial sludges, biosolids and so on. I would like to show you a video on how the slurry trenches are being executed in the real life. These are also known as soil bentonite walls and here you can see a cut is being created or a trench is being created by excavation and the point is how I am going to stabilize this trench. So, in the background you can see the trench which has been created and this is a thick slurry which could be of bentonite. You remember we have talked about bentonite slurry being used for the stabilization of the cuts. These are mostly used for geo-environmental applications. So, look at this trench has been created and then if you want to stabilize this trench you have to fill this trench with the slurry of the bentonite. So, a fluid which is denser than the soil. Applications of this type of development would be that it is a landfill. If I want to isolate them from the geo-environment so that the leeches do not come into the nearby area, you create trenches and then fill them up with slurries of bentonite because of you are interested and watch few more videos which are available on the YouTube. So, depending upon the situation, there is another good video of a slurry wall. Create a trench by cleaning it. This is the excavation going on. Sometimes we also call them as the cutoff walls. I can fill this trench with cement slurry also if I want to create a system which is highly impervious or a bentonite slurry can also do. So, bentonite slurry just for stabilization purpose and if you want to create a completely impervious wall which is embedded inside the ground then in that case a cement slurry, lean concrete can be or a fly ash mixed with the soil like soil creed can be you know pumped in. And what we will like to do is we like to analyze these type of situations that up to what type of height of the cut the bentonite can be used for stabilizing the cut. This is for pumping the slurry. This is the slurry. All right. So, there are several videos of this sort which you can have a look at and let us come back to the analysis part. So, suppose we are creating trenches soils and we want to stabilize them the way it was shown in the video. So, there are two categories of the problems. One is in trenches in clays and the second one is trenches in. So, the statement of the problem is like this. This is a trench which I have created in a clay soil of height h up to what height I should be filling the slurry unit weight of s is the unit weight of the slurry. This becomes h1. For the maximum possible protection what we can do is h1 can be equal to h also depends upon how much the factor of safety you require against the failure. And this situation I will like to analyze. So, you can use again the concept of the salvage. The weight is known. The normal stress can be obtained and this is the shear stress pure cohesive material. All right. So, what is the angle? This will be 45 degree. Now you can resolve the forces and you can obtain the factor of safety. So, tau is basically T u, unrained cohesion of the soil mass. What is the force coming? As far as stabilization is concerned the force is coming in the form of because this is slurry. So, I can assume that this is the pressure which is which is exerted by the slurry or pure. So, this is the force diagram. Now, can you show that the factor of safety for this type of a system will be equal to or would be a function of T u gamma of the soil and gamma s of the slurry and what else h height of the trench and h1. So, these are the parameters which can be utilized for designing the whole thing. So, for the sake of simplicity we are doing h1 equal to h and can you just apply your common sense to find out what will be the factor of safety for this type of a system upon gamma s minus gamma into h. How will you obtain this? Just equilibrate the forces and take their components. So, you have the p slurry t component n is not required n can be eliminated and then other equation comes in the form of w and tau. So, this is the factor of safety of the system when you are going for a slurry trench. I have done a mistake here. This should be gamma minus gamma s because gamma is the unit weight of the soil and gamma s is a slurry. So, gamma s cannot be more than the unit weight of the soil you are right. Thank you. Now, C u undrained can be obtained. I know the value of the unit weight of the slurry. The gamma is known. So, this is the factor of safety against the failure. So, how will you read this? The more the cohesion factor of safety is more, more the height of the cut or height of the trench factor of safety is going to be less. So, truly speaking for the critical situation or the limiting situation this value is equal to 1. What we are getting is 4 times C u equal to gamma minus gamma s into h. This 4 times C u is an offshoot of 2 c. What is 2 c? The earth pressure which is coming in cohesion case, all right. K a gamma h minus 2 c root K a. So, root K a equal to 1. So, this becomes minus 2 c that term is coming over here. Now, this becomes the limiting condition which you will obtain by analyzing the free body diagram of this system. Let us try this. This concept can also be extended to the sands, all right. How will you do that? In case of sands, I will assume that this angle is theta rest of the things are same and this is going to be equal to 45 plus alpha by 2 let us say because phi is not known or phi is known both. So, phi is known. So, we will assume this as phi. Now, what I want to do? I want to again compute the factor of safety for a situation when I am retaining the sands. So, if you use the same concept in the free body diagram what I should be getting as factor of safety 2 times gamma into root of this upon gamma minus gamma s into what term? This is something interesting to remember. Say tan phi, what is the significance of this? Factor of safety is equal to 1. That is what is being obtained by this term the deviation of the flurry from the soil mass and then friction angle is the friction angle of the material. So, this becomes a sort of a penalty term on the friction angle of the soil mass. Try to work it out. These are interesting problems. We know the W. We know the pressure which is coming from the flurry, ok. So, W upon P f is a sort of a tan of 45 plus alpha by 2 term and tan of alpha and tan phi by tan alpha itself is a factor of safety term. So, these are the good examples of how the simple concepts can be applied to obtain the solution to the most critical but practical problems which we are facing. Good. So, we have discussed lot of things, particularly related to the application of shear strength theory in the form of earth pressures. These are all applications of the earth pressures which are acting on this one. And earth pressure itself is an application of shear strength parameter. So, interestingly what we have done in this course so far is spent enough time in understanding how to obtain the shear strength parameter or the characteristics of the soil mass. We have defined the state of stress in the soil. Using that concept and the shear strength parameters, we have obtained the earth pressure which are acting on the system and then we discussed about so many applications. So, we have studied the rigid earth retaining structures, flexible retaining structures like sheet pile walls and then within the sheet pile walls we have talked about the cantilever sheet piles, we have talked about the bulkheads, we have talked about the you know trenches, bracing, struts and then at the end how to use flurry to stabilize the trenches. So, with this I am going to close the discussion on earth pressure theory.