 last class, so we have finished this basic about your reinforced earth wall and stresses in the soil mass. Now, continuing with this Mohr's circle of stresses, we have discussed this what is the pole with respect to pole, we can find it out the failure envelope and this sigma and tau at failure. Now, if you look at this Mohr's circle and the failure envelope, if this is the failure surface, this is the failure surface and soil element at different location. One can say that soil element inside this failure envelope or soil element outside this failure envelope, so for failure inside this failure envelope tau f is equal to c prime plus sigma prime done phi. Now, let us take a soil element y, let us take a soil element y outside this failure surface. Now, if I draw the Mohr's circle, now it is not touching this failure envelope, that means this soil element is stubble, that means soil element taken at position y it is stubble. If I take a soil element along the failure surface and draw the Mohr's circle, soil element along the failure surface let us say x and draw the Mohr's circle, that means it will touch this failure envelope, that means soil element along the failure surface it is called it is in failure. Now, initially suppose this is a ground surface ground level, this is your ground level, initially take a soil element at position of y at position at point y. So, in this case what happened sigma c is your confining pressure, sigma c is your confining pressure. So, initially Mohr's circle is a point Mohr's circle is a point. Now, you add additional surcharge let us say now with additional surcharge of delta sigma with adding additional surcharge of delta sigma, now this Mohr's circle has been built of sigma c plus delta sigma this will be your sigma 1, this is your sigma 1 and this is your you can say that sigma 3. Now, again increase this that means what will happen the soil element does not fail if the Mohr's circle is contained within this envelope, that means if the Mohr's circle is below this envelope soil element is not going to fail. Now, add additional surcharge so as loading progress Mohr's circle become larger initially it is a point initially it is a point adding surcharge. Now, this is Mohr's circle become larger and larger finally failure occurs finally failure occurs when this Mohr's circle touches this envelope that means when this Mohr's circle touches this envelope failure envelope. So, finally that means failure occurs so this is the about stress strain and the Mohr's circle and how this failure envelope this is basically this explains how this failure occurs. Now, if you take this failure envelope failure envelope and if you take this sigma 3 and sigma 1 identify this pole with respect to plane and draw the failure envelope with respect to pole at angle theta it is anticlockwise then draw with an angle anticlockwise theta draw the failure plane where it touches where it touches your mo failure envelope that that gives your sigma and tau at failure plane. So, now this angle is 90 degree so obviously this angle will be 90 degree minus theta now if I draw it total angle if I make it into total 90 minus theta 90 minus theta plus 5 prime is equal to your theta simple geometry from there you can get it theta is equal to 45 degree plus 5 by 2. Now, next step is your effect of reinforcement on a soil element there are two figures one is your unreinforced other is your reinforced figure shows a simple dry sand confined by an external applied load applied confining stress say sigma 3 applied confining stress say sigma 3 and loaded by a confining stress compressive stress sigma 1 and loaded by a compressive stress sigma 1 where sigma 1 let us say sigma 1 is greater than sigma 3 under this loading regime and unreinforced sample will suffer on axial compression let us say axial compression of delta v and lateral expansion what will happen if this is the soil element if this is the soil element sigma 3 is your confining or compressive stress and sigma 1 is your vertical compressive stress if sigma 1 is greater than sigma 3 what will happen this will try to compress. So, this amount of vertical compression is delta v and lateral expansion it will compress at the same time it will expand in lateral direction. So, lateral expansion will be delta h by 2 this lateral expansion will be associated with the development of lateral tensile strain within the soil mass once this lateral expansion will occur. So, this will be associated with the development of lateral tensile strain within the soil mass if several horizontal layers of reinforcement are inserted into the soil like figure b reinforced one like several horizontal layers that means layer 1 layer 2 layer 3 reinforcement are inserted into the soil the same external load applied whatever the unreinforced case external loads sigma 1 is there if the same for reinforced condition has been applied then the resulting deformation are resulting deformation are delta v r delta v r and delta h r in lateral it is your delta h r. So, delta v r is less than delta v if you compare with this this delta v r is less than delta v and half delta h r half delta h r half delta h r is less than delta h by 2. That means expansion in vertical expansion in lateral in case of reinforced case it will be less as compared to in case of unreinforced case. This reduction in magnitude of deformation is a direct result of an additional confining stress delta sigma 3 generated by an internal interaction between the soil and the reinforcement. This will be this reduction will be because of this because of this interaction between the soil and the reinforcing element. This reduction if you look at this vertical deformation is your delta v and with this reinforcement it is your delta v r and it is less than your delta v this reduction because of your interaction between soil and reinforcement. When an axial load is applied to the reinforced soil this generate an axial compressive strain and resulting lateral strain. When an axial load is applied to the reinforced soil axial load is applied to the reinforced soil this generate axial compressive strain and resulting a lateral strain and resulting a lateral strain. If the reinforcement has an axial tensile stiffness greater than that of soil that means if the reinforcement these are the reinforcement. If the reinforcement has an axial tensile stiffness axial tensile stiffness is greater than your lateral greater than that of your soil then the lateral movement of soil will only occur. If the soil can move relative to the reinforcement provided the surface of the reinforcement is sufficiently rough and movement of the soil and relative to the reinforcement will generate shear stresses at the soil reinforcement interface. These shear stresses induced tensile load in the reinforcement which are redistributed back into the soil in the form of an internal confining stress delta sigma 3 internal confining stress delta sigma 3 which is additive to any external applied confining stress of sigma 3. The net external effect of this internal interaction is a reduction of both axial and lateral deformation compared to unreinforced soil. Because of interaction between the soil and the reinforcing material the net result will be it is a reduction of your both axial and lateral deformation as compared to your unreinforced soil. Similarly in the above illustration both reinforced and unreinforced samples are subjected to the same magnitude of external applied load and the addition of reinforcement decreases deformation compared to your unreinforced case. As I said compared to your unreinforced and this reinforced soil as a less deformation the addition of reinforcement will also improve your soil strength it will also improve your soil strength that means it will improve your bearing capacity. If the unreinforced soil is confined by a constant stress sigma 3 and the magnitude of sigma 1 is progressively increased then the soil will be subjected to a progressively increasing shear stress of sigma 1 minus sigma 3 by 2. General shear failure of unreinforced soil ensure as this applied shear stresses approaches this shear strength of the soil. Now for unreinforced soil this is my failure envelope now the moment you increase increasing that means if you look at this increasing with your sigma 1 this failure stresses this move circle will increase it will touch your failure envelope this is your failure stress sigma 1 plus delta sigma 1. Now effect of next part is your effect of reinforcement on a soil element when the soil is reinforced that means a larger value of sigma 1 is needed to cause failure that means once the soil is reinforced whatever the earlier part of your sigma 1 that means you need to have larger value of sigma 1 for this failure that means you need to have delta sigma 1 will be more. This is because increment of sigma 1 induce increments of delta sigma 3 which lead to relatively small increment in applied shear stress that means sigma 1 plus delta sigma 1 minus sigma 3 plus delta sigma 3 by 2 a practical limit is imposed on the strength of the reinforced soil either by tensile rupture rupture of the reinforcement or a bond failure caused by slippage at the soil reinforcement interface. Now look at this reinforced soil so this is your sigma 3 shear stresses for unreinforced soil and shear stresses for reinforced soil. If I go initially it is a point as I explain for a unreinforced soil both this confining pressure are same sigma 1 and sigma 3 now it is increasing as I apply the confining pressure that mean increasing sorry as I am apply this surcharge that means it will increase your sigma 1. So if you look at this this more circle shear stresses at the reinforced the more circle at the which touches this failure envelope is a larger as compared to your unreinforced soil that means increase you will be that means you need to have more delta sigma 1 to get the failure. So what does it mean the more circle is larger that means figure shows a steep slope in dry cohesion loss soil with a face inclined at an angle beta s to the horizontal where beta s is if I provide a reinforcement that means a steep slope will generate because it require larger load to get the failure. So beta if I if I make it at an angle of beta s it is greater than that internal angle of shearing resistance that is your 5 without the benefit of soil reinforcement the slope would collapse that means without this without the soil reinforcement if I do not provide the soil reinforcement it is not it is not possible to provide the provide a steep slope that means slope slope may collapse. So however if I incorporate or you can incorporate a suitable soil reinforcement soil may be rendered to stable same soil if it is not stable if you provided it is possible to have a steep slope investigation of the basic reinforcing mechanism reveal that the soil in the slope comprises two distinct zones soil in the slope comprises two distinct zone now there are it is shown in figure. So without reinforcement without reinforcement the active zone is unstable and tend to move upward and downward with respect to resistance zone there are two zones one is your active zone other is your resistant zone. If you look at this figure that means there are two distinct zone one is your active zone other is your resistant zone without providing this this active zone is not stable if the soil reinforcement is installed across the active and resistant zone it can serve to stable the active zone. If you are going to provide a soil reinforcement both active as well as in resistant zone then it is going to make stable the active zone a single layer of reinforcement in the figure in the figure with a length of l a j that means embedded in the active zone and length l e j embedded in resistant zone a practical reinforcement layer layout would continue in multiple layer this is just a for example it is showing only one layer if you go to practical case it is a multiple layers multiple layers of reinforcement. However single layer is shown in figure for illustration the precise reinforcing mechanism will be affected by the properties of the reinforcement definitely this reinforcing mechanism will affect your reinforcing reinforcing properties of this reinforcing material flexible reinforcements provides stability to a reinforced mass of soil by transferring transferring destabilizing forces from the active zone that means destabilizing forces from the active zone to the resistant zone to the resistant zone where they are safely observed in this process purely axial tensile loads are observed or dissipated by flexible reinforcement axial or tensile load whatever the axial load or tensile load coming to the soil it will be dissipated by flexible reinforcement provided a reinforcement develop an adequate bond how it will dissipate provided the reinforcement will provide an adequate bond between the soil as well as the reinforcement. These tensile strength are transferred from the soil to the reinforcement through the mechanism of soil reinforcement bond means whatever this particularly if you see this lateral or vertical stress transfer to the reinforcement between soil to reinforcement and this mechanism is called soil reinforcement bond that means there should be a sufficient bond between your soil as well as reinforcement. The tensile strength developed in the reinforcement in the active zone give rise to a corresponding tensile force in the reinforcement in the active zone if the total length of the reinforcement is limited to say say I am not going to provide in resistant zone. So, suppose say total length of the reinforcement is limited to only l a j then the transfer of load from the soil to reinforcement in the active zone would not prevent collapse of the active zone. If I say this is my active zone if I provide only reinforcement only if this is the active zone if I provide only reinforcement up to the active zone then it is not going to prevent collapse of the soil in the active zone to achieve this the reinforcement. So, to make sure that to block this failure the reinforcement has been extended beyond your active zone that is called resistant zone provided the reinforcement has sufficient tensile strength it should have a also condition the reinforcement should have a sufficient tensile load. So, that it will be observed from the active zone it will be shaded these into the soil in the resistant zone that means if a if it has a sufficient tensile strength what happen whatever lateral or vertical stress coming to this from soil to reinforcement the reinforcement in the active zone it will transfer it will transfer this tensile this tensile strength beyond your active zone that is called resistant zone as in the active zone load is transferred from reinforcement to the soil by mechanism of as I said by mechanism of soil reinforcement bond this is called soil reinforcement bond bond between soil and reinforcement this is called soil reinforcement bond the tensile load in the reinforcement over the length L E j is not constant if you look at here tensile load in the reinforcement over the length L E j is not constant, but decreases towards the free end of the length L E j that means it decreases towards the free end length of L E j remote from the slope face remote from the slope face as the load is shaded into the soil as the free end of the reinforcement in the resistant zone the tensile load in the reinforcement is zero at the free end of the reinforcement in the resistant zone the tensile load in the reinforcement is zero the tensile load in the reinforcement it will be zero here at the free end flexible reinforcement is incorporated in the field during the construction what happened during the construction how the slope has been prepared you have to construct the slope during the construction the flexible reinforcement has been provided like this will see consequently the layers of reinforcement are horizontal generally the layers of reinforcement are horizontal flexible reinforcement is also inserted into cut section during construction in the form of soil nail in the form of soil nail at an inclination close to the horizontal sometimes what happened flexible reinforcement also you can provide along the slope in the form of soil nails if I at an incline if I provide a soil nail inside the slope that also possible either you provided during construction horizontal or may be some construction is over then you can provide soil nails in the form of incline that also possible this inclination is convenient since it coincides with the general inclination of the tensile strain developed in the soil in the active zone now let us see this construction of your reinforced walls now if I go there how it has been constructed if you look at here it has been constructed over side by side because this is a cross sectional view it will go along the length wise then how it has been fixed it has been taken top and fix it in between two walls these are all kind of a per meter length then you can make it along the width direction how it has been fixed if you look at here it has been fixed at the intersections one wall one with each other so how it has been arranged if I look it this is my wall other wall has to put it that means what happened this wall has something like tinted or outside say there is some group other wall has also same group so this is a ball and socket joint it will fix inside so that it will be placed in the vertical position now look at this once the wall has been there then you can place your soil layer by layer now this is the things which we have discussed this reinforcement once you place a layer of soil once you place a layer of soil along with this layer of soil you can provide a reinforcement layer this is your reinforcement layer in the form of mesh or grid then this reinforcement has been properly tied and fixed in the soil mass you see earlier what is your reinforcement in the case of mesh these are all single reinforcement single reinforcement in terms of plates small thin plates it has been placed with this spacing it has been placed in the layer of soil layer over this then once this reinforcement has been placed above this reinforcement you place again you start construction of another layer of soil mass I am talking about how the construction has been done another layer of soil mass you can place it over the once the reinforcement has been placed then you can do the roller compact it by means of by rolling it then that layer is over then again you place another layer of reinforcement then fill a soil then compact it so this construction will be layer by layer that means it is consisting of a soil layer compacted over this reinforcement then soil layer compacted then over this reinforcement next part is your reinforcement bond or pull out length what is the pull out length within the reinforcement mass differentiation is made between that part of the length of the reinforcement which falls in the active zone and remaining length which falls in the resistance zone if you look at here if this is my slope if there is a reinforcement bar is there that means this active zone generally you provide for stability so that the slope can be made so that it will be more stable and there is a differentiate you can differentiation made it into two parts length in the active zone length in the resistant zone the length of the reinforcement in both active and resistant zones and its bond characteristics govern the loads that can be carried this length this particular length will be decided based on the whatever the load it particularly that layer if I am taking let us say there are three layers of reinforcement layer one layer two layer three so this reinforcement of l a j means length along the active zone length along the resistance zone it will be decided based on this whatever the load carried by how much load because between this to these these are filled by this is filled by the soil so this will be decided the load coming on to this reinforcement the length of the reinforcement falling in the resistance zone is the bond length generally the length of the reinforcement falling in the resistance zone is the bond length or the embedded length or the embedded length particularly here if I can say this is bond length or embedded or embedded length which influence transmission of forces from active zone to resistance zone that means if there is there are there is excess force in the active zone it will transmit this force from active zone to resistance zone and this length is called bond length or embedded length in case of flexible reinforcement where the force in the reinforcement is axial tension the bond length should be sufficient to prevent reinforcement being pulled out of your resistance zone that means why this resistance zone if you look at here if there is a soil along with this if this is a wall along with this wall this reinforcement has been connected what will happen there should be a sufficient length beyond your active zone why once this wall is pulling away from this field this will this will try to pull also your reinforcement that means there should be a sufficient length beyond your active zone so that there is a bond between your resistance zone and soil so that it can resist this pull out it can resist this pull out force of your entire reinforcement that is the basic reason if the bond resistance of a reinforcement is greater than its tensile strength if the bond resistance of a reinforcement look at here if the bond resistance of the reinforcement is greater than tensile strength of the reinforcement then the ultimate limit state is controlled by tensile rapture of the reinforcement this is called tensile failure or overstressing failure conversely if the tensile load in the reinforcement is greater than the bond resistance the ultimate limit state will be controlled by bond failure if the tensile there are two things one is your bond resistance of the reinforcement is greater than your tensile strength of the reinforcement that means whatever the bond resistance coming whatever the bond resistance there in the reinforcement if it is greater than your tensile strength then you can say that it will be tensile failure that means ultimate limit state is controlled by tensile rapture if bond resistance is greater than tensile if tensile resistance is greater than your bond then the ultimate limit of state will be controlled by bond failure means whichever the minimum that will be controlled means ultimate limit will be controlled so it will be limited there in first case it will be ultimate limit state is controlled by the tensile rapture second case it will be controlled by your bond failure this is called as a pull out failure if your ultimate limit state will be controlled by bond failure then this is called pull out failure i can stop it here then next we can go for next class tensile failure and pull out failure detail derivations