 that is reinforced earth. So, that means here how to design a foundation or in a retaining wall if it is constructed by reinforcement. Now, before that first we if I discuss what is a reinforced earth. Now, as it is similar to we can say that it is a like of a reinforced concrete as we can know that concrete cannot take the tension and reinforced to take the tension we provide the reinforcement. Here the similar way the soil cannot take tension. So, if any tension is developed within the soil that has to be taken by some elements. So, that elements we provide that is as a reinforcement. Now, the question is why the reinforcement is required. Now, if when if a soil is there if I want to construct any foundation on that before that before soil testing will go for whether will go for which type of foundation either will go for the shallow foundation or whether will go for the group foundation. Now, in the shallow foundation we can first try for the isolated footing then combine footing or if it is a raft. Now, if this shallow foundation is not suitable on that particular soil then before we go for the deep foundation or pile foundation then there is option that we can improve that ground and on that improve ground we can construct the foundation. So, now this basically this reinforced concrete is a improve ground improvement technique. So, there are so many others ground improvement techniques are available, but on that I will discuss only the reinforced earth in this section. Now, before I go to the design part now first what is reinforcement? Now, reinforced earth means suppose if we have this existing ground and on that ground this is the foundation. Now, suppose this soil is not suitable to take the load which is coming for this from this superstructure through this foundation. So, here we are providing as a isolated footing always B with is B. Now, when here the one option we can place some reinforcement like this suppose if this is a section. So, we can place the reinforcement below this foundation. So, that can be single layer or that can be montere. So, these are the reinforcements. So, if this is foundation then these are the reinforcement. Now, this reinforcement is this is the section actually this reinforcement are a sheet type of material suppose this is the this is one type of reinforcement this is sheet type of material. So, here we can get this is one reinforcement or the this is we can say the reinforcement. Now, here we are talking about the geosynthetic reinforced earth. Now, what is geosynthetic reinforcement? Now, geosynthetic reinforcement is a basically polymeric material which have some groups one is geotextile, next one is geogrid, third one we can geonet, then geomembrane, then geocomposite. So, these are the different categories. So, this is all are called the together called the geosynthetic. So, these are the different types of the geosynthetic. Geosynthetic means it is a polymeric material which is available in the in the market. So, that means here we get a sheet type of material here which is which is available in a in a roll type. So, here we will get the required geosynthetic according to our basic requirement. Suppose if it is a below the foundation if I place so we will place that is the L and the B if it is a rectangular footing. So, if I take the section this one you will get the this type of so that means inside the soil we place this sheet type of material to increase the bearing capacity of the soil. So, that means first and basically this geosynthetic type of reinforcement as we have to insert it in the soil and it is placed horizontally. So, because it is placed horizontally. So, that means it is basically suitable for filling type of material. Suppose if this in the this area first we will place the reinforcement and if it is existing soil above that we can place some soil or filling soil granular type of soil and then inside this soil first we will place the reinforcement then again we place the granular soil then again we place the another reinforcement then we can place the soil then another reinforcement and then the foundation will be constructed. So, basically the filling type of material is this geosynthetic reinforcement is suitable and again we are talking about the geotextile, geogrid, geonet, geomembrane and geocomposite. So, these are basically used for different purposes. So, that means we are talking about the geosynthetic is suitable for the bearing capacity improvement. So, that is not only purpose of geosynthetic. Geosynthetic it can acts as a separator, it can act as a bearing capacity improvement material, it can act as a drainage purpose it can we can use and we can use it for a barrier purpose. So, suppose the geotextile it is if used if it is bearing capacity mainly we use that is for the geogrid. Now, geomembrane for the barrier purpose, geonet for the drainage purpose and geotextile is for all less all purpose. Now, here geocomposite basically we if we use for multiple purpose suppose we want to use for the bearing as well as for the drainage purpose then we will clap this geogrid and geonet and from a new type of material that is geocomposite. So, basically here we will talk only the bearing capacity improvement part because we are dealing with the foundation. So, only the bearing capacity improvement part basically the geogrid is used and this geotextile is also used. So, this two type of material generally is used for the bearing capacity improvement. So, that thing we will discuss in this class. Now, here we are talking about the. So, when you place the geosynthetic within the soil for the bearing capacity improvement. So, then what are the design factors that is very important. So, first design factors. So, first design factor is the number of reinforcement. So, then the next design factor the where we will place the top reinforcement layer that means this is the u is the where we will place the top reinforcement that is one thing that we have to decide that is u. Then the spacing between two reinforcement layer the spacing is also we have to decide and then what would be the length of the reinforcement. So, this is spacing another one that is the material property of the reinforcement. So, these are the design factor for the reinforcement and obviously as usual for the unreinforced soil the soil properties and the load these are also some design factor. But these are the additional design factors that we have to consider during the design of the reinforced earth. So, now the first we have to decide what is the number of reinforcement that we will provide then the where we will place the first reinforcement layer and why this u is so important. Then the spacing between two reinforcement layer now the length of the reinforcement why the length of the reinforcement is basically very important and the properties of material properties of reinforcement of geosynthetics. Now, first we will discuss that why what are the different types of failure of this reinforced earth. Now, first we will discuss what are the different types of failure of the reinforced earth that means the various. Now, first type of failure is that this is the failure if that reinforcement suppose this is our foundation and this is our existing soil is here and we apply the load on the foundation. So, what will happen that it will perform in this form and then this is the failure surface and this is the failure surface. Now, if that reinforcement is placed below this failure surface then if this is the reinforcement say if reinforcement is placed below this failure surface then if it is then this soil will act as a unreinforced soil. Because most of the failure surface of failure has been occurred before above the reinforced earth soil. So, that means the effect of reinforcement will not come into this foundation. So, that means here the basically this material will be wastage. So, there will be one type of failure. So, that is why placing of reinforcement is very important. Reinforcement is the first layer and it is recommended that, but this U cannot be greater than 30 centimeter. So, that means from the ground surface. So, that means for 30 centimeter depth one reinforcement layer we have to provide to avoid this type of failure. So, that means this is one type of failure where reinforcement is placed far below the foundation and all of failures has been occurred above this reinforcement. So, there is this effect of reinforcement will not act or this will not consider in this design. So, that is one type of failure. Now, the second type of failure that when we are talking about this is say foundation this is the existing ground. Now, if we place this reinforcement very small length if I place the reinforcement is small length. Now, what will happen that for this small length this total system will fail. Now, question is why? Now, if this is the foundation failure surface we should have some sufficient anchor length beyond two side of the failure surface. Now, suppose if I place it here what will happen this reinforcement this failure surface will pass and it will not affect this reinforcement. So, this is basically it will similar like a under reinforced soil. So, we will not get any benefit from the reinforcement. When we place sufficient anchor length beyond this two sides of the reinforcement then this is called say anchor length L e. So, this is the failure surface L e and if this is B. So, that means this sufficient anchor length is required for this reinforced soil beyond this failure surface to get give a proper anchor. Now, the question is why this anchor length is required? Now, that is why the length of reinforcement is also a very important issue when you design the reinforcement. Basically if I place the small width or if I place the reinforcement width or length equal to the width of the foundation then this will not give any effective solution for the foundation. So, we have to provide sufficient anchor length. Now, that is why we will provide this anchor length the question is that this when we are applying this load. So, that means this inside soil that will try to move this side. So, suppose if I this is foundation if I apply the load. So, suppose if there is two zones this is the inside zone and this is the outer zone. So, suppose this inside zone the soil will try to move in downward direction and this outer zone the soil will try to move in this direction. So, this soil is basically moving downwards and this soil this is say zone 2 and this is zone 1. So, in this zone 2 soil is going in pushing this zone 1 soil towards this direction and this zone 1 soil is moving going downward direction. Now, and similarly here also this in the failure zone this soil is moving downward direction the center one and side soil is basically this soil is pushing this soil in this two sides and the center one is moving downward direction as well as the pushing the this soil in the other side. Now, what will happen if we place only the reinforcement into this level. So, suppose if I place only that the into this level or further here only for this side. So, what will happen that this reinforcement will also move along with the soil. So, now we should have a sufficient anchor if I place anchor if I extend this reinforcement in this side. So, this reinforcement will provide an anchor this this reinforcement is insert in the soil within the soil it is inserted within the soil. So, what will happen this soil and this reinforcement internal friction that will provide an anchorage within the soil. So, that means this soil outside this reinforcement will hold this reinforcement in both sides. So, this soil because of this internal friction mechanism this soil will hold this reinforcement in the both side and this soil will move downward direction. Now, what will happen now there will be a this type of deformation pattern because there is sufficient anchorage. So, we will get this side of deformation pattern in the reinforcement. So, as we have to provide such that at the end of this reinforcement there is a very negligible deformation. So, that deformation is very negligible, but there is a sufficient anchorage and most of the deformation is in the centre. So, now this reinforcement will not move along with this soil movement. So, it will hold this soil is holding this reinforcement both side and this soil is moving downward. So, that there will not be any movement of this reinforcement along the soil. So, it will be in this position more or less in the outer side and then it will be deflect in this form. So, now if we provide only this length and here also only this length here also this is the failure surface beyond that if I provide the reinforcement then it will give this anchorage. So, that this reinforcement will not move within the soil and it will not come within this failure zone. So, and if I provide only within the failure zone. So, because of the as there is no outside anchorage is provided within this reinforcement then what will happen this reinforcement will move along the soil. So, it will be it will not give any benefit for the improvement purpose. So, that is another type of failure because this is a wastage of the money and then will not get any benefit. So, this is the second type of failure. Now, the third type of failure which is also very important is the third type of failure that when we apply the load here this is foundation this is existing ground and in the insert this foundation we provide the reinforcement. Suppose, this is the reinforcement fine. So, this one these are the reinforcement. So, when you are applying this load and we are talking about there is a sufficient anchorage within the reinforcement then what will happen that because of this anchorage force anchorage that when there is a tension is developed within the reinforcement because why this tension is developed because we can say that when this there is a sufficient anchorage is there. So, that means this soil is holding this reinforcement and this reinforcement within the centre region is moving downwards. So, if we hold something in both sides suppose we are holding this reinforcement both side and this soil is moving downward direction. So, we will one tension is developed within the reinforcement. So, that means and this there is a internal friction is there within the soil and geosynthetic or reinforcement and because of that and as we are applying as if we are holding this reinforcement both side and in the centre region this because of this soil foundation pressure this reinforcement is moving downward direction and we are holding the reinforcement because of this sufficient anchorage length we are giving. So, we are holding the reinforcement in the both side soil is holding the reinforcement in the both side and the centre one is moving downwards. So, because of that the reinforcement will be subjected a tension and this mechanism is that the internal friction is acting and because also that this friction is mobilized this tension is mobilized. So, that means their tension will develop within the reinforcement. Now, if the geosynthetic is not such steep that that can take that tension. So, what will happen there will be a failure. So, that means geosynthetic should be a steep such that and you have to choose the geosynthetic during the design such that the mobilized tension or induced tension within the geosynthetic that tension this geosynthetic can carry. So, if the strength potential strength of the geosynthetic is less than the mobilized tension or induced tension within the geosynthetic then this geosynthetic will fail. So, will not get any improvement. So, that means this geosynthetic should be sufficiently strong. So, that it can sustain or it can take the tension which is developed within the geosynthetic. So, that is another type of failure that is caused our tension failure. Next one is the creep failure or long term failure. Suppose, if there is a geosynthetic reinforced earth. So, we have this is the geosynthetic that we have placed here. So, after very long term what will happen the creep will occur within the geosynthetic creep means that is the strain against constant stress. So, that means at the when you apply the this tension will develop within the geosynthetic. So, that means if tension is developed within the geosynthetic. So, at very long time this if this geosynthetic is under tension for a long time. So, if it is under tension for a long time. So, that means what will happen there will be a strain within the geosynthetic. So, one is the deformation of the geosynthetic that is the vertical deformation due to the soil movement. Another is because of that when the tension is developed within the geosynthetic. So, geosynthetics are under pressure tension. So, because of this tension there will be a strain within the geosynthetic. So, if this strain within the geosynthetic occurs there is a possibility the strength of the material will reduce. So, if the strain is there material will reduce. So, if the strength of the material is not good enough then you will get a failure there is chance of failure. So, that is a and if the strain of the geosynthetic is very high then then also this total system will fail. So, this type of failure is called for the creep failure and in this creep can occur for the reinforcement as well as for the soil. So, now for this creep failure that means it is this this strain within the material because of this tension and this tension strength if this strain is high then this strength will reduce and this total system will fail. So, these are the four different types of failure for the reinforced earth that in foundation on the reinforced soil. Now, we are talking about that we here we are talking about that this geosynthetics will place because of this improvement of the load carrying capacity of the soil. Now, the question is how this improvement will occur because of this geosynthetics. So, now as we have mentioned there is a four different things that one is number of reinforcement. So, another is u u part we have already explained that we have sufficient u and then then the length of the reinforcement that also we have explained then the material property of the geosynthetic that will also that means the this u length would be sufficient length we have to provide such that there will not be any that means this there this there should be a anchorage of the reinforcement otherwise this reinforcement will move along with the soil and then the material property then we have to choose the use and this such that it can sustain under that induced strength. Another is this in the spacing also if the spacing between two geosynthetics very high suppose this is the spacing between two geosynthetics is very high then what will happen the failure will occur within that in two reinforcement because if the failure spacing is very high then if a very large spacing we provide then what will happen the failure will occur within that two geosynthetics within that soil of between two geosynthetics. So, what will happen we have to proper over the total system will fail. So, we have to provide proper spacing within the reinforcement another is the number of reinforcement that is very important issue that that where that how much improvement we will get if we increase the number of reinforcement is it linear that if I improve if I get 10 percent bearing say 100 percent bearing capacity improvement if I provide one layer if I provide two what will be the amount of the improvement that will be 200 if I provide three layer that will be 300 it is it a linear or what is the relation. So, that means we have to now we have to understand how much reinforcement you have to provide why this is not a linear thing then if it is a linear thing then you can provide infinite number of reinforcement which is actually not a good idea or it is not possible but why. So, that thing we will explain that how we will get the improvement for the soil now this improvement we will get. So, because of the two major action one is your confinement effect another is string effect string effect now what is confinement effect and what is string effect. Now suppose this is the foundation this is the existing ground level and this is the reinforcement we are providing this is before loading. Now when we apply the load in the foundation but this this soil will be also loaded. So, we will get one deformation of the reinforcement so this is before loading sorry after loading. So, now if I take this portion of any portion of the reinforcement suppose we are taking this portion of the reinforcement. So, what will happen so because if there is no deformation of the reinforcement there is no friction will develop. Now once we will get a deformation of the reinforcement what will happen there will be a friction. So, there is a relative movement and there is a movement between the soil and the geosynthetics. So, there is no movement between the soil and geosynthetics is it placed as it is no when it will deform there is a movement between the soil and the geosynthetics. Once this movement will start so that the friction will develop it is similar to the pile. So, if I apply the load on a pile vertical pile so that means this friction will act in the side friction will act in the upward direction the leaf loading is applied in the downward direction. The same thing when you apply the load so this tension will develop as I have mentioned. So, if the tension is developed that is because of this that means if the tension is developed so the who is countable is this tension. So, this tension there is a something that will countable is this tension. So, that means these things this friction is acting within the reinforcement. So, here if I take the other side so there is a tension t if I take a symmetric figure. So, this is the friction so t is tension and this is friction. Now, we can say that when we apply the we are applying the load when there is a deformation of the soil reinforcement then there is a movement of the between soil and reinforcement and then this friction is developed within the soil interface of the soil and the reinforcement. Once this friction is developed in the soil and the reinforcement and as a result in this tension is induced within the reinforcement. So, as we have mentioned that if I anchor this soil within and this anchorage force reinforcement is getting because of this friction between the soil and the reinforcement. So, first clear this part that this reinforcement this anchorage force this reinforcement is getting because of this interface friction. So, because of this interface friction mechanism soil is holding the reinforcement and because of that this tension is developed within the reinforcement. And this will occur if there is a deformation between the soil and the the reinforcement. Once there is no deformation of the reinforcement this phenomena this action will not come into picture. When you apply the load in the reinforcement is deformed then you will get this type of action. So, that means this friction is developed and because of that the tension is induced and mobilized within the reinforcement. Now, once we can say this tension is developed within the reinforcement. So, that means somewhere a compression is also acting. So, that means we can say the tension is developed in the reinforcement. So, that means the some amount of the same amount of the compression is also developed somewhere. So, once as I mentioned the soil cannot take the tension it can take only the compression. So, tension is developed in the reinforcement and compression is developed within the soil. So, as soil compression force is developed within the the soil and then what will happen the soil become dense that means if soil is under compression so its strength or properties that will improve. So, if we apply a compressive force on the soil and then its strength or properties that will improve. So, that is called the confinement effect that means it is the soil is under confined condition. So, that is under compressive force is developed it is the confined compressor condition. So, that is why its properties is also improved and strength of this soil that will also improve. So, that is called confinement effect where because of this action this soil strength is improved. Next one is the string effect that is also very important or membrane effect we can say. So, that means the if so there is a reinforcement pattern. So, here the T is developed here here T is tension is developed and this angle is say theta this angle is also theta. So, that means at the top of the reinforcement this force is acting this is the normal force sigma n top. So, because of this things this shear force that will act here also shear force that will act here also the reaction force here this will act in the bottom direction. So, this is sigma n B. So, these are the two stresses that will exist these are the two vertical stresses. So, this is sigma n T is the top of the reinforcement and sigma n B is the bottom of the reinforcement. So, now if I take the cross component of these two. So, these two forces will be cancel out if it is symmetric. Now, we can say that if I take the sin component the sigma n T plus sorry that is equal to 2 T sin theta plus sigma n B. So, sigma n B is equal to sigma n T minus 2 T sin theta. So, that means we can say that the stress below the reinforcement is less as compared to the top of the top of the reinforcement. So, at this top level and the bottom level if I compare the vertical stress that at the bottom level stress is less as compared to the stress at the top level. So, this is is because of this string action or this membrane action. So, that means here we can see this is sin theta if there is no deformation theta is 0 then then sigma n B is equal to sigma n T, but when there is a sufficient deformation then this stress in the lower region that will reduce. So, once the stress is the soil is reduced then the definitely the load carrying capacity of the soil that is increase that means some stress is taken by this mobilized within this reinforcement. So, that means the stress carrying capacity of the soil that will also increase. So, this is this is the one action that is cost string a string. So, because of this two effects one is string effect one is confinement effect this bearing capacity is improved for the reinforced soil or reinforced foundation. Now a very important thing is that what would be the number of reinforcement what is the improvement pattern if I increase the reinforcement. So, one thing is that if I compare and if I compare this see this expression that if theta is if I increase the theta then what will happen the sin theta value will also increase and as the same time the sigma n B will further decrease. So, if there is a more reduction of sigma n B then stress in below the soil layer. So, that means that will efficiency of the reinforcement that will increase that means the if the. So, if there is a sufficient amount of the deformation within the reinforcement layer then the efficiency of this bearing capacity efficiency of the reinforcement that will increase because the stress below the reinforcement that will decrease further. So, that means there is a one very important conclusion that to get a sufficient amount of effectiveness there should be a sufficient amount of the deformation of the soil. So, that means if the soil is very good condition if the settlement of the soil and reinforced soil itself is very less then providing reinforcement will not give any effect it is not beneficial it is very quite obvious. But if the soil is very poor and there is a sufficient deformation of the soil in under reinforced condition in that case if we provide the reinforcement then the effectiveness of the reinforcement that will increase. For example, if I consider in this way that if the soil is good condition this under reinforced condition the deformation is say 20 millimeter and if I provide the reinforcement will get an deformation say 18 millimeter. So, that is a very small amount of the improvement but for say if it is soil is very poor condition deformation is say 100 millimeter. Now if I provide the reinforcement that deformation may come down to 60 or 70 millimeter. So, that is a huge amount of the although that 60 or 70 is greater than that 18 or 20 but the amount of the improvement or effectiveness of the reinforcement that is very high in case of soil with very poor condition. So, that means we have to provide reinforcement when there is a sufficient amount of the deformation within the soil this is a very important thing. So, another thing is that now so the question is if I so this is one thing that we have sufficient deformation another thing is that so should we have increase the if we increase the number of reinforcement how this improvement pattern will change. So, this is the linear the thing is that if suppose we provide a one layer of reinforcement our settlement will reduce if we provide a say another layer of reinforcement then settlement will reduce further if I provide say another layer of the reinforcement it will reduce further. So, what will happen once we get we are trying to increase the number of layer actually we are reducing the settlement and as I have mentioned that there should be a sufficient amount of the deformation to get the maximum amount of the benefit from the reinforcement. So, that is actually that benefit is reducing because as we are increasing the number of reinforcement the settlement is reducing. So, the effectiveness of the total system is also reducing. For example, if for the single layer of the reinforcement if there is a 30 percent or 40 percent settlement improvement of the soil then if you if I provide another layer. So, that will not be if it is 40 for the single layer for the double layer that will not be the 80. So, that will be less than 80 because the as we increase the because of for the first case also the settlement has further decrease if we use another reinforcement the settlement will further decrease. So, because of that the effectiveness of the reinforcement that will also decrease because as the settlement is reducing. So, again if I provide the third layer. So, there will not be so if it is less than 80 for the second layer then that settlement reduction will further the effectiveness will further decrease. So, this is not a linear case. So, after a certain time we will see that if I increase the number of reinforcement then there will not be any improvement because then soil becomes so steep there will be very very little amount of the deformation and the effective of the reinforcement will be very small. So, there will be not so much of the deformation. So, that means we have to restrict with a certain number. So, because after that if we increase the number that is useless. So, that is another case the next one is the similar this is similar to for the length of the reinforcement also because if I increase the reinforcement length there will be a sufficient anchorage length that will increase. So, that the anchor force will that will increase. So, but after a certain length if I increase the reinforcement further so that anchorage length that is useless. So, that is not giving any improvement in the soil because beyond that point that anchorage length is sufficient. So, after that it is not useful. So, that means here we can say that for this one this number of reinforcement that if I increase the number of reinforcement the improvement pattern is not not linear. So, as we number the increase the number of reinforcement the effectiveness of the total system that will reduce. So, up to after certain value we have to stop and that also depends on the type of loading type of soil that we are using. So, all those things that number you have to decide first. So, then spacing and then the placement of the top reinforcement length of the reinforcement. So, those and properties of the how much T so that the this reinforcement can sustain within the induced tension. So, those things we have to check when you design the reinforced part. So, that means this is very important issue we are talking about this reinforced foundation. So, some foundation on the reinforcement. So, that means we have to consider all these things before we when you design this type of foundation system you have to consider the failure pattern you have to consider the this all the design factors when you design this thing. Now, the next one another important structure that is our reinforced retaining wall now this reinforced retaining wall. So, we know this is our suppose they or cantilever retaining wall. So, this is a soil is filled this side and this is the existing soil or foundation. Now, here the soil is giving lateral pressure on the retaining wall. So, this lateral pressure is taken by this cantilever retaining wall, but here we are providing say steel and if it is a gravity retaining wall then the weight of the retaining wall itself is giving the resistance. But, similarly so therefore, this is cantilever retaining wall. Similarly, this things we can constructed by using the reinforcement. Suppose this is our existing ground then we placed the reinforcement layer here then fold the reinforcement layer and place the soil inside this reinforcement layer. Then we place another reinforcement layer top of this sand layer and fold it and then put the sand layer inside this reinforcement layer. Then you place another reinforcement layer then you provide fold it and put the reinforcement here then you place another reinforcement on this top and again you fold it and fill the sand then you place another reinforcement and then fold it and place this sand. So, this is called reinforced retaining wall. So, this is suppose this is the height of the retaining wall here this will be the height of the retaining wall and now the here then what are the very important design factor when you talking about this retaining wall. One is again the if I go for this design factors or design parameters again first one will be one is your spacing between two reinforcement again spacing is very important factor. Then this length how much length will provide for the design that is. So, how much length will provide that is also very important factor for the design. So, that means, the length of the reinforcement then again this material property because again here also this tension will develop then how the why the tension will develop I will explain then, but for this material properties of the that means, this material property of the reinforcement is also a very important design factor. So, that means, so we are talking about these things for the reinforcement case and again for the other case the height of the retaining wall the soil properties of the filling material as well as the foundation material. Those are also very important design factors, but for the reinforcement purpose this spacing this length and this material properties these are very important factor when you consider this reinforcement. Now, this how this tension is developed within the this geosynthetic reinforced soil that means, the tension is developed suppose if this is the existing soil if I another important thing that this folding length this is also very important. So, when I fold this reinforcement so this length is also very important. So, these are that means, the length of the reinforcement this total length and this L 0 also very important design factor. Now, the how this tension is developed so if I place this one if they place reinforcement here with soil then place another layer then place another layer. So, now if I consider a failure pattern like this so this is 45 degree plus 5 by 2 as we know this 45 degree plus 5 by 2. So, if I consider failure pattern then what is actually happening here so that means, this total system this total soil mass along with this reinforcement is trying to slide along this failure surface. So, that but this reinforcement is basically actually holding this soil mass so it will try to prevent it will try to prevent this slide. Now, how it can be possible now if sufficient anchorage length if we provide sufficient anchorage length of the reinforcement beyond the failure surface then it is possible. So, as if the some something is sliding here that means, this soil mass is sliding from this side and this soil mass along with this geosynthetics holding this sliding mass. So, and this is possible if the geosynthetics sufficient anchorage length is provided beyond this failure surface which is same as the previous case in the foundation in the reinforced soil. There also sufficient anchorage length is required beyond the failure surface. So, that means, we have to provide a sufficient length beyond the two side of the foundation. Here also we have to provide sufficient length beyond this failure age so that anchorage so that this reinforcement that means, this soils both side of the reinforcement is holding this reinforcement like the previous case it is holding the reinforcement and then this soil is try to slide. So, when this soil this is the soil is holding this soil and this reinforcement and this soil is trying to slide so what will happen there will be a tension is developed. So, that means, this tension is developed and this is this tension is developed and this anchorage force or this tension is develop that is T and that means, we have to provide the reinforcement such that it can sustain this tension. So, that means, this reinforcement should be sufficiently strong so that it can take this tension. So, that is also very important that is why material property you have to choose such that it can take the tension which is induced within the geosynthetic and again this tension which is mobilized within the geosynthetic that is developed because of this friction between the soil and the geosynthetic. So, in the next class we will discuss about the various type of reinforcement and their application and also how to design a reinforced retaining wall. Thank you.