 So, many times there are installation of caddeliver sheet piles in different types of soil deposits. Now the most prominent type of a situation is when you have a sheet pile and then this sheet pile is sitting in foundations are in sand and the backfill is also a sandy material, alright. So, this is also sand and this is the foundation layer, this is also sand and somewhere here you have a water table, height of the ball is h, height of the water table is hw, this is d, draw the pressure diagram, the first thing you can do it up to here is p1, now what is going to happen? There is a switch over. So, switch over from p2 to some other value for the sake of convenience I am just using the length of the sheet pile, what is going to happen further from here? So, suppose this is p4 and p3 is some fictitious term coming over here, what we have to do is we have to obtain p1, we have to obtain p2, we have to obtain p4 and the p3 which is fictitious term over here. So, this is a situation when you have sands as the foundation of the sheet pile or the embedment and the sands as a backfill material also. So, you can compute p1, if I give you the values like gamma, gamma prime you know and what else is required? Suppose z1 is known, z2 is known and then I can divide this geometrically in different parts. Let us say it is z5, this is z4 and so on. So, d equal to z4 plus z5. The basic concept here is what is the magnitude of the p3? So, this is the active pressure and this is the passive pressure. So, p4 is equal to pp minus pA at point C, that is the only thing which you have to obtain. So, we can obtain p1 easily, p2 easily. What about the p3? p3 will be a difficulty in obtaining, but suppose if I say that this is equal to the entire thing is in kp condition, passive condition, is it not? So, you have to compute the value of p3, just see how much it would be, find it out. p3 and then obtain the value of p4, you can obtain it easily. So, this is a situation when we are dealing with sands over sands. I can easily convert this into a situation where you are dealing with, let us say I can still maintain the backfill as sands, but the foundation material becomes clays. This is a slightly tricky situation. So, what is going to happen in this situation? The pressure diagram would be, any guesses? Yes, right. There is a water table over here. So, the pressure diagram up to this point is easy to obtain, right. What happens at this point? Now, you have touched the clays. So, what is the pressure at z equal to 0? And this is active situation or passive situation, you have to think of that, alright. So, how the pressure diagram would look like? The pressure diagram would be, there will be a pressure which is constant over here and then there is a switch over. Everything of this sort, this goes and meets the tip over here. So, this is how the pressure diagram looks like. This is the most critical thing. So, this will become 4C, why 4C? This is pp minus pa. So, gamma z plus 2C, alright and minus of this whole thing multiplied by kA minus 2C, alright. So, this will become 4C tau. So, that means, I can obtain this also and what about this? The total depth and then this is going to be a difference between kp minus kA. You will have to practice this. The third situation could be where I can make the whole thing more complicated when you have backfill also as a clay. So, suppose there is a backfill which is of clay material and the foundation is also clear. So, what will be the difference? When you deal with the clays, what about this portion? Exposed to the environment, no external loading. So, this is your 2C component, correct, tension crack and this becomes z naught. So, truly speaking, this portion of the wall does not experience any pressure because of being a clay material. First of all, clay should not be used as a backfill material, but here what we are doing is, it is a natural ground where we have inserted the sheet pile and then we have dredged out the soil mass to attain this much of embedment. It is not the other way. So, the moment you do this, there is a possibility of tension crack developing over here. This much portion of the wall does not contribute or does not experience any pressure from the soil mass and this is going to be very detrimental because the rain water will come and sit over here and that will apply pressure on the top of this and then you are seeing the moments are going to get increased. So, rest of the things will remain same. What we have analyzed in the previous case, only thing is this part has to be taken care of. This is a beautiful example of, you know, how to incorporate the effect of tension crack when the backfill are cohesive. So, with this, I am going to close the discussion on the sheet piles analysis and one more concept which I wanted to highlight is, this is what is known as the effect of arching action. Arching is known as a phenomena which is pressure distribution. So, whatever we have been computing so far by using the Rankine's pressure theory in different cases of the retention of the backfill material and the foundation material, this is all theoretical. Now, if you do the field studies and if you measure the stressors, how do they vary in the backfill or behind the retaining wall, the situation is going to be different. Truly speaking, what is going to happen is, if you have the sheet pile over here, what has been observed is that on the passive side, if the theoretical pressures are like this, this is as per Rankine earth pressure, earth pressure theory, theoretical pressure distribution. Truly speaking, in real life, the distribution of the pressure has been observed to be something like this. So, this is the real pressure experimentally obtained. The difference between the two is because of the arching action, that is the pressure redistribution in the pile mass which is violating the theoretical concept which we have studied so far. Now, similarly on the active side, what is going to happen is, if you plot the theoretical distribution of the pressure, this is how the Rankine earth pressure would be. There is a deviation and what has been observed is, the maximum pressure gets mobilized somewhere in the top surface. It reduces, becomes 0 at the DL level and then again it increases in this fashion. So, this is experimentally obtained pressure distribution. What we need to do is, behind the sheet pile, you have to install pressure gauges at the time of construction. You have different types of pressure gauges which are available. You can do stress monitoring, you can do strain monitoring also alright and how much deflection is being undergone by the system. You can measure by using different types of LVDT's here in the laboratory setups. In the pile you can use the deflectometers or you can use a theodolite to see how much the wall is deflecting. So, this is how the complete instrumentation can be done. So, this pressure redistribution is because of the material properties, mostly this type of redistribution of pressure is higher in case of the pure frictional material. This is their inherent property, not in cohesive slides alright. Now, this concept has been utilized to study what is known as bracing or struts. You know we have discussed about bracing and struts earlier. So, there is another application of the earth pressure theory for designing the braces or the struts to stabilize deep cuts. So, basically what we want to do is, we want to create a deep cut facility in the ground. This is the existing ground surface and you are installing sheet piles and then removing this material. So, bringing it up to the dredge level, required dredge level.