 In this course, this is application of soil mechanics. This is basically all applications of basic soil mechanics and in this course, the books are particularly followed. One is foundation design and analysis by your bowels, then mechanics of soils by then soil engineering by Ringler, principles of foundation engineering by B. M. Das. So, in an way these are the books particularly followed in this course and this books has been referred particularly this course. Let us start with this piles, seed piles, cantilever seed piles. If I draw a cantilever seed pile, now where it has been used this cantilever seed pile, if this question is where it has been used, then you can say particularly in offshore structures when this seep is coming and burthing cantilever seed pile has to be connected by this. So, once if this is my water table somewhere else is water table here or this side or this side may be soil, here it is soil, if this is the water table. So, what will happen once this seep is coming, seep has to stop somewhere else and burthing and people should come out and this is your ground surface, this is your completely ground means this is your ground surface. So, people has to come out, this is one case means particularly this cantilever seed piles has been used in case of offshore structures as well as particularly onshore structures means ports and harbours this cantilever seed piles has been used. Now sometimes either you can provide this is your seed pile, this is your cantilever seed pile, why it is called cantilever, this entire load has been taken by this cantilever action of this seed pile and it has been embedded inside this ground surface of this soil below this. So, what will happen it will take this entire load coming here will be taken by this cantilever seed pile by means of cantilever action, by means of cantilever action that is why it is called cantilever seed piles and once again it has been used particularly port and harbours offshore and as well as onshore structures it has been used. So, this cantilever seed pile may be it you can say that anchored or without anchored if I sometimes what happen if the bending moment is much high. So, what will happen to resist this bending moment or resist the moment at top of the cantilever seed pile to stop the failure sometimes anchor has been provided. So, there are different modes of failure depending upon that how the cantilever seed pile is there one is rigid other is your flexible. So, depending upon that means in this case what happen this anchor has been provided to your cantilever. So, this is called anchored seed piles anchored seed pile if anchored has not been provided it is simply called cantilever seed piles cantilever seed piles. So, these are particularly this seed piles and others these are particularly to retain to retain the soil mass one end and other end is that it has been used for particularly port and harbours. If I go this two parts one is your rigid walls and another is your flexible walls retaining of the soil retaining of the soil I can say that retaining structures. So, that means in this retaining structures what will what will happen at one part of this one part of this wall this soil has to be retained soil has to be retained. So, that is why it is called retaining structures. So, these retaining structures are called sometimes rigid retaining wall or rigid wall or flexible wall rigid wall or flexible wall. So, rigid walls are called retaining walls because this is a massive and it will fail by means of rigid it is rigid it is very high other one is called flexible this flexible is nothing, but is your seed piles and it will take load by means of cantilever action. If it takes by means of cantilever action you can say that cantilever seed pile if will resist the load by means of anchor you can say that cantilever anchored seed pile. So, depending upon that the classification will be there. So, retaining structure I can made it into two parts one is your rigid other is your flexible. So, flexible next class I will show you what are the things and rigid what are the things. So, basically two parts retaining of the structures means it will retain the soil mass at one end it will retain the soil mass at one end it will not allow the soil mass should be get disturbed what may be soil mass should be eroded particularly it will retain one one side. So, if it is purely rigid the structure then it is called rigid retaining wall or may be retaining wall if it is flexible in nature. So, it is called seed pile or anchor seed pile depending upon that functions how it works. Now in this case before I go in detail what are the different analysis and others and classification. So, let us start with this basic physics means basic mechanics of this cantilever seed piles cantilever seed piles what we want to find it out what are the parameters from this cantilever seed pile once I am saying that what are the actually parameters required to be determined what are the parameters required to be determined. So, parameter one is your depth of driving or penetration then second is your size or cross section and cross section of seed pile then in this case size and cross section of seed pile what you are supposed to find it out you are supposed to find it out stress maximum bending movement and by maximum bending movement because of your lateral load then third is your if you provide some anchor may be anchor capacity anchor if necessary. If you look at this cantilever seed pile then why first part is where this seed pile has been used as I said earlier it has been used particularly for harvors dock and harvors. So, where the ship will come and rest and people can come out. So, one end what will happen one end ship will be tied if ship is berthing here this will be tied here. So, that people can come out outside. So, this is this is the case this is the purpose where it has been used this is the purpose first one second part is if it has been used then what are the different parameters we are supposed to find it out the different parameters is that depth of driving or penetration means below this below this surface I could I will not say this is exactly ground surface because this water table here we ground surface somewhere else else the definition is that this is your degrade line dredge line that will tell later. So, what is that depth how much depth it should be penetrated below this level below this level. So, that whatever the entire load is coming at the top it will be taken by below this level. So, it will be stable. So, this is first and foremost criteria means parameter to be determined then size and cross section why we need size and cross section because depending upon the size and cross section what is the stress induced on this wall how much stress induced and what is the maximum bending movement because depending upon the bending movement you can find it out how it will how it will bending how how the movement will come whether it is within this permissible limit or not with respect to your lateral load then this size and cross section depending upon that you will have to find it out this to stress and maximum bending movement then other one is your anchor if you provide anchor if suppose this bending movement is very high or means very high value of movement you are getting. So, it will fail by means of bending then what happen you will have to as I said you will have to provide anchor if you want to provide the anchor then what should be its capacity at what depth you are going to provide suppose I provide the anchor here now what is its capacity anchor capacity then up to what depth means up to what length this anchor should be provided. So, that it can take your bending movement it can take your bending movement. So, these are the parameters we are going to determine from this cantilever sheet pile walls then let us start before going to the classification let me start with a brief of cantilever sheet pile walls then we will go to the in details backward about this classifications now if you come back to this there are two soils either it may be purely granular that means cohesion less soil or may be cohesive or c phi soils for granular soils what are the assumptions because this has to be theoretically analyzed theoretically you have to analyze means analyze then find it out what is its capacity so that it can take this amount of load. So, with that suppose if I know theoretically if I know suppose this is my height h depth of the penetration if I know the soil property of the phi I can find it out the capacity based on that based on that I can say that what is its maximum lateral capacity what is its maximum lateral capacity this sheet pile can take. So, that whatever the seep and others they are building how much the capacity will they have that can be said ok this sheet pile wall can take maximum of two term one term three term five term per meter length. So, depending upon that other parameter has to be also determined or may be fixed. So, assumption is earth pressure horizontally and angle of friction angle of friction this is angle of friction between the wall angle of friction between the wall and the soil this is called delta. So, delta is zero delta is zero what does it mean first assumption is earth pressure acts horizontally that means it is not a curved earth pressure it is not a curved earth pressure this is a simple earth pressure act horizontally and second part is your delta is supposed to be zero first one is simple assumption delta is zero that means friction between wall and soil should not be there that means this wall should be assumption is a smooth wall it is a smooth wall then assumption second assumption sheet pile within the soil is considered to be in elastic that means it is a rigid body then third assumption is if it is a rigid if it is a rigid then for particularly this is for these are the assumption has been taken for particularly granular soils that means granular soil means it is cohesion less soil. So, there is a rotation rotation called pivot rotation called pivot point o pivot point o that means it is assumed once there is a this load is there there this is rigid. So, what will happen it is not flexible this is a rigid wall. So, it will rotate somewhere else the wall will rotate somewhere else some point. So, this is called o or this o point is called a pivot point where the wall rotate this is called pivot point. So, it is located x 0 unit of length below the ground surface that means this is at a distance of x 0 below the ground surface look at the assumption 3 assumption 2 and assumption 3 that means sheet pile within the soil mass if you look at the soil is here the sheet pile within the soil mass that means below the soil mass it is in elastic that means no elastic deflection no elastic deflection. So, no elastic deflection means it is a rigid body it is a rigid body rigid body. So, the moment assumption 2 followed sheet pile wall for particularly granular soil within the soil mass it is rigid body the moment we follow what will happen what will happen second part will come that if it is a rigid. So, it will rotate somewhere else. So, the moment you say that it is rigid the sheet pile is within the soil mass particularly granular soil is a rigid body that means there will not be any deflection there will not be any deflection it means it means there is a rotation this means this wall will rotate some point some point that is called point o and this point is called pivot point and it is located at a distance x 0 below this where the soil starts it is located. So, these 2 assumptions are main assumptions then 4th one is also that is also important for stability for stability analysis for stability equation of static equilibrium is to be applied what does it mean equation of static equilibrium that means summation of forces in horizontal direction summation of forces in vertical direction and summation of movement at point o is equal to 0 summation of forces in horizontal direction summation of forces in vertical direction summation of movement at point O at the pivot point for stability that means the equation of static equilibrium has to be satisfied that means static equilibrium equation has to be satisfied for stability so these are the main four assumptions for particularly granular soil or cohesion less soil has been used first one is your earth pressure act horizontally it is horizontal means it is not curved one earth pressure is simple horizontal it is not curved one then the friction angle between the wall and the soil this is called delta is equal to zero that means the wall is a smooth one wall is a smooth one this is your second assumption third assumption is your seat pile within the soil that means seat pile below the soil mass assume to be a rigid body for particularly cohesion less soil once it is a rigid body that means it will not deflect it will not deflect that means what will happen it will rotate at a point O below this soil below this soil this point of rotation point O is called pivot point this is called pivot point then once there is a rotation there is a pivot point then this distance of this pivot point should be at a distance x zero below the soil below the soil not below the ground below the soil if I say this is my ground surface because once there is a seep is there it has to be bird so this is the ground surface they are going out this may be full of water this may be full of water no actually where the soil soil mass starts or the foundation soil starts below this up to the pivot point it x zero or any distance any distance that has been said x zero then fourth one is your for stability analysis fourth one is your for stability analysis factor of set p means sorry forces in horizontal direction forces in vertical direction and movement about point O should be zero this is called stability analysis that means static equilibrium has to be satisfied for stability analysis static equilibrium has to be applied and it has to be satisfied that means any in balance force has to be balanced and put it to zero and you can get it so these are all four assumptions now let us understand the mechanics of this cantilever retaining wall sorry cantilever sheet pile inside the granular soil or cohesion less soil this case one say a inside the cohesion less soil so what will happen as per the assumption b or second assumption it is a rigid body because of rigid body it will rotate some point point O and this point O will be located at a distance below this soil this is your soil mass at a distance say x zero so if this is my point of rotation point of rotation or O pivot point O so what will happen it will rotate that means what exactly happen look at this what exactly happen now if I say this is x zero and say this is called p one and this is called p two so this is say point d and this is a point h now what you understand how the mechanics how you are going to find it out you can look at this this is a wall suppose this is a wall this wall has a rotation point point O and below this this is a soil will happen you know earlier what is active state what is passive state it is basic soil mechanics active state and passive state because this is an application of soil mechanics so active state is if there is a wall if this is a wall for retaining of soil if this side is soil if the wall is moving away from the soil the wall is moving away from the soil mass moving away from the soil mass the pressure generated by soil to the wall is in active state or active earth pressure similarly in case of passive state if this is the wall and if it is the soil mass if this wall if this wall is here what happen moving away from the soil mass if this wall is moving toward the soil mass that means it is moving toward the soil mass so what will happen the pressure generated by soil is nothing but is your passive state or passive earth pressure passive earth pressure this is these are the two basic things we are going to apply this is your soil mechanics for active state and passive state if you look at here that means top of top part of this take this there are two part because there is a point of rotation part one and below the point of rotation this is a part two so part one this part is moving away this is your soil this part is moving away that means this is your active state from o to this because this is moving away at the other end at the other end it is moving towards this side of the field it is moving away this side of this it is moving towards that means this will be in passive state now if you come back to here below the below the point of rotation this part is this part is moving away from the soil mass because it is from here it is going like this moving away means this is an active state and from here to here this part is moving towards the soil mass so that means this is in passive state so if you look at this basic physics behind it the top part of active state and passive state is in reverse order of the bottom part of the bottom part so what will happen we will see how this mechanics how it has been derived we will see it