 of counter for retaining wall, counter for retaining wall. I am just drawing a single section of counter for retaining wall. If you look at this, if I am taking making it inclined, this is a cantilever retaining wall. With this cantilever retaining wall for height more than 20 meter to resist against the bending moment, counter force has been provided at regular interval. So, that it will resist at one end, so that there will be less bending particularly in the stem in cantilever retaining wall. So, this whole set is called counter for retaining wall. Now, this if I make it to, this is called your upright slab, upright slab, this is your toe slab, this is your counter for this part is called heel slab. So, as I said complete design consist of three parts, one is your dimension, second part is your stability analysis, third is your structural design. In this case is particularly in structural design, you will have to design for upright slab, heel slab and toe slab as well as the counter force. So, first case one, first one is your upright slab. In this case of upright slab, if I take a section here, if I cut it a section here, here then how it looks, look at the forces here. Now, this part is your upright slab. Now, if I cut a section here at this point, this upright slab is looking like this. And now, what are the supports? The supports are this counter force, this is your counter for one, then counter for two, counter for three and these are earlier earth pressure by soil is retaining up to this height, up to this height soil is retaining. So, it is giving your lateral pressure. So, that means it will be designed as a continuous slab, continuous slab spanning horizontal on counter force and it is subjected to lateral earth pressure. So, let P is equal to horizontal pressure intensity, horizontal pressure intensity, horizontal pressure intensity at bottom of upright slab. That means this P is your horizontal pressure at bottom of your upright slab. This upright slab is going like this, at bottom of the upright slab P is equal to horizontal pressure, L is equal to spacing of this counter force. If I draw one more counter force here, if I draw one more counter force here, now, so this is your, this part is your spacing L, L is equal to spacing of counter force, spacing of counter force. Now, maximum bending movement, now maximum bending movement which is equal to plus minus P L square by 12, because this is a continuous slab with this supports are there. So, it will be P L square by 12 and based on this maximum bending movement as I have discussed once you get maximum bending movement, these has to be equated to Q B D square is equal to maximum bending movements. Q B D square is equal to maximum bending movement, from there you can find it out D means what is the thickness D for this upright slab, then design can be calculated. Now, second part is your base slab, base slab, this is your base slab, part B is your base slab, in this base slab generally we take width is equal to 0.6 H to 0.7 H that means width from here to here this width B has to be taken 0.6 H to 0.7 H, H is H is equal to total height of the base slab means total height of this counter force retaining wall. So, it will be approximated 0.7 H to 0.6 H and toe projection, what is your toe projection? Toe projection is how far the toe has been projected away from the wall, this part is your toe projection. So, toe projection is about one fourth one fourth of total width of base slab, one fourth of total width of base slab, if total width of base slab if I write it B. So, this toe projection is equal to one fourth of B, one fourth of B. Now, this third part which is called heel slab, this counter force retaining wall has been designed as a slab design, first one is your upright slab, second is your base slab, third is your heel slab. Heel slab means this part is your heel slab. So, this heel slab if I make it this heel slab I cut it. So, how it looks? Now I have cut it this complete heel slab taking a section heel slab taking a section at this point. I am cutting this taking a section at this point. So, this part is lying heel slab. Now what are the forces coming to this here? The forces are coming here look at here, if there is a soil mass retain in this part the soil has impart your lateral earth pressure upon your upright slab as well as vertical pressure vertical pressure on this heel slab. So, this is your vertical pressure on this heel slab and these are all my these are all counter fort these are all your counter fort. So, what are the loads suppose to come here? The load will be dead load of the strip dead load of the strip that means this dead load or self weight that means if it is RCC concrete then it is a concrete weight of this. Then next part is your weight of earth pressure weight of earth not earth pressure sorry weight of earth above this strip that means if the soil is retained in this part if soil is retained soil has its own weight soil has its own weight that is your weight of your soil or earth above the strip. Then vertical component vertical component of earth pressure vertical component of earth pressure vertical component of earth pressure means if this is the total earth pressure is acting it has two component vertical as well as horizontal component. So, the vertical component downward it is acted that is your vertical component of your earth pressure. Then any super imposed load any super imposed load then upward soil pressure because once there is a retaining wall for heel slab there is a pressure q maximum and q minimum as we have discussed there will be also upward soil pressure. So, then you consider also upward soil pressure upward soil pressure. So, total net load will be what is your net load it is downward or upward if you look at here dead load of this strip is vertical and second part weight of earth above the strip weight of the soil weight of the soil above the heel slab again it is vertical then is your vertical component of earth pressure again it is vertical only and super imposed load any super imposed load is there again it is vertical only upward soil pressure will be your upward. So, the total force will be it will be total load will be downward. So, in this case maximum bending movement maximum bending movement which is equal to q l square by 12 q is equal to net load per unit area q is equal to net load per unit area net load per unit area. So, there will be a positive and negative positive as well as negative that means sagging and hogging movement will be there. So, hogging movement will be over the support and sagging movement will be section between the counter fort sagging will be like this hogging movement will be over the support this kind of things will come. So, hogging movement will be on the support sagging will be between the supports between this kind of fort it will be sagging movement. So, as I said once you get your maximum bending movement once you get the bending movement then you equate to your q b d square then you can find it out the thickness of your hill slab. Then once you get your thickness then find it out how much is your reinforced steel is required for designing of your hill slab area of steel. Once you get area of steel then you can find it out what is the spacing of the steel reinforcement between each other. Then you can design your structural part of your hill slab as there has been three slabs once again I am repeating there has been three slabs particularly in case of counter fort retaining wall one is your upright slab, second is your base slab, third is your hill slab. So, in case of upright slab if I cut a section here. So, that means the pressure because of your soil retain here lateral earth pressure that means in lateral direction will be acted and this will be counter fort will be act as a support. So, it has to be designed as a continuous slab as a continuous slab. So, maximum bending movement will be your p l square by 12. So, p is equal to your horizontal pressure intensity at the bottom of upright slab l is your spacing between your spacing between your counter forts. So, once you get maximum bending movement from there you will have to find it out your thickness of your upright slab then area of steel then design has to be made similarly for base slab, base slab if you look at this base slab there are two parts one is your toe slab, one is your part of this this part is your base slab or this entire is called base slab. So, in this case toe slab has to be designed based on the what are the load coming as the hill slab. So, base slab has been divided into two parts one is your toe slab other is your hill slab the design of toe slab will be as per the design of counter retaining wall the toe slab will be same. In case of hill slab if I cut a section here near the hill slab what are the load supposed to come one is your dead weight of this strip then second is your weight of earth that means the major part is your weight of soil retaining above the hill slab then third one is your any super imposed load any super imposed load because of your traffic load then vertical component of your earth pressure as I said there are two component horizontal as well as vertical then vertical component of your earth pressure then of course there is a because of soil pressure there will be upward pressure at the base slab. So, net component load will be downward. So, maximum bending moment is equal to your q l square by two l q is equal to net load per unit area. Now, this l is your l is your spacing means distance between this counter fort. So, there will be a this kind of bending moment you will get it sagging you will get between this counter fort hugging you will be get at the point of your support you will get it once you get maximum bending moment if you can equate this maximum bending moment is equal to q v d square from there you can find it out your thickness. So, q is a factor it depends upon your grade of concrete and grade of the steel has to be used for this construction or design. So, based on that you can find it out your thickness once you get the thickness then you can find it out area of steel requirement then what are the reinforcement what diameter you are supposed to provide and what is its proportion means spacing and other reinforcements your reinforcement structural design has to be done. Now, next part is your what is your thickness of base width you find it out the base width, but thickness has not yet decided. So, thickness of base slab. So, this may be it should not be less than the following that means thickness should not be less than the following should not be less than the following if you look at here d is equal to the thickness of base slab 41.7 l root over of h and d is equal to 20 l h. So, d is your thickness of base slab l is your spacing between this counter fort h is equal to overall height of the wall overall height of the wall. So, generally it should not be less whatever d provided it should be more than this calculations. Now spacing of the counter fort spacing of counter fort spacing of counter fort the spacing is one third h two half h it varies from it varies from three meter two three meter two three point five meter, but generally spacing should be provided one third of total height h two half of total height h the generally this is the specification for providing the spacing it generally varies from three meter two three point five meter. Now come back to your come back to your bars reinforcement bars if I draw this reinforcement bars how it looks horizontal ties connecting the main counter fort and upright slab. If you look at this upright slab this is your main counter fort this is your counter fort and this part is your upright slab how it has been particularly in this junction how it has been connected this upright slab has been taken to your back to your hill slab sorry this reinforcement of main counter fort has been taken back to your hill slab and this is your reinforcement bar reinforcement bar particularly upright slab if I say this is my upright slab this is your reinforcement bars main reinforcement bar has been provided. So, at this point between counter fort and upright slab this has been connected these are all these are all yours your reinforcement. So, that it will be connected upright slab as well as your counter fort if I say this is my reinforcement for counter fort for counter fort and this is for your upright slab. So, these are all your shear ties or shear reinforcement. So, that there will be a proper connection between connection between upright slab as well as for counter fort reinforcement for counter fort. Now vertical ties connecting counter fort and hill slab you see why I am discussing this these counter forts these counter forts of reinforcement bars has to be connected with your upright slab as well as your hill slabs it has to be connected. So, that it should not be separated after this design is over. So, now if I take it how it has been connected this is your vertical link vertical link and this is your main reinforcement counter fort reinforcement counter fort reinforcement and this is particularly your this part of your hill slab hill slab if you look at here look at this hill slab. That means look at this hill slab it is going. So, these are the bars of this main reinforcement of your hill slab and if you look at this counter fort walls it is inclined. That means it is passing from here to here I put it counter fort main counter fort reinforcement here to here. So, that there is a link this vertical or shear reinforcement has been connected. So, that it will be in intact without any changing it will be in intact once this design is over once this design is over that means these counter fort retaining wall will be intact with your upright slab and this counter fort counter forts also will be intact with your hill slab in both way that means if you look at this section particularly this junction say number one and this junction say number two. So, this is your number one point this is your number two point. In this case number one point upright slabs this is your upright slabs. So, these are all your main reinforcement and counter fort walls counter fort counter fort is going on. So, this is your horizontal links between upright slabs and counter fort reinforcement now similarly in this case counter fort is passing particularly hill slab it is connected at an inclination and hill slab is going in this directions. So, in this case this counter fort is inclined then this is your hill slab vertical link has been connected between this counter fort as well as the hill slab. Now main main then then come back to your main counter fort counter fort in this counter fort let us say h is equal to height of cantilever above the base height of cantilever above base this small height h is equal to height of cantilever height above the base from here to here the total height h is equal to from here to here, but h small h is equal to here to here this is your height of cantilever above the base. Let us say l is equal to spacing of counter fort alpha is equal to searcher's angle alpha is equal to searcher's angle in this case the horizontal pressure earth pressure p h is equal to k a gamma h square by 2 l cos alpha if you look at this l is equal to spacing l is equal to spacing this is alpha is equal to searcher's angle l cos alpha it is coming. So, maximum bending movement is equal to or bending movement is equal to p h into h by 3 which is equal to k a gamma h q by 6 l cos alpha. Now area of steel area of steel area of steel is equal to m by q d t second half of the length of alpha because area of steel is equal to bending movement l cos alpha it is a reverse one by cos alpha it will be a sake alpha movement by q d t sake alpha is your area of steel requirement. Now curtailment of bars now this curtailment of bars particularly in counter forts area of steel is equal to a s t is directly proportional to if you look at here it will be m by d d is equal to varying m by d which is equal to m by h. So, which is equal to directly proportional to h q by h m e if you look at the m is it is in terms of h q which is equal to h q by h that means it is directly proportional to your h square total height of the h square. That means curtailment of bar at the bottom means at the top there is no means it is required how much bars you are going to curtail that requires your that depends upon your height square. So, based on that curtailment of bar has to be done. So, next class I will solve a complete problem of this counter fort retaining wall including structural design completely. Thanks a lot.