 Next part of this lecture is tensile failure and pull out failure first part is your pull out length if you come back to last class there are two zones one is active zone other is your resistant zone. So, particularly in this case l e i is your acted upon by this resistance zone now this pull out length it is if you look at there is a reinforcement of this this part is acted upon by this soil and sigma v i is your soil over this it is gamma z at the bottom also it is gamma z. So, p r i is equal to two sigma v i l e i tan delta and t i maximum is equal to j gamma z gamma z is your over burden or soil field plus q if is there any searchers into k times s b into s h s b is your spacing in vertical direction s h is your spacing in lateral directions. That means, suppose this is wall if you are placing like this that means spacing in vertical direction s b if this wall is going in a long distance like this. So, spacing in lateral also horizontal direction also s h now in assessing bond performance for the purpose of design shear stresses developed between the soil and the reinforcement are assumed to act uniformly over the embankment length. This is the assumption it will assume to act uniformly over the embankment length in frictional fields the magnitude of this shear stresses is taken to be the product of vertical effective stress vertical effective stress is this particularly the magnitude of shear stresses that means magnitude of this shear stresses is vertical effective stress sigma v i and the tangent of the interface friction angle delta and the tangent of the interface friction angle delta. The angle of bond stress is determined by direct shear test how to find it out this delta that means coefficient of friction between this soil and this material. Now, if there is a shear box test in that shear box test one side you can put it at the bottom soil above this you can put the reinforcing material and from there we can get it the value of delta get the value of delta sigma v into tan delta is your sigma h into l i over the length for grid reinforcement the boundary conditions in the direct shear test may give rise to a measured value of delta greater than phi. Such a value cannot be realized in the field and the maximum value of delta used in design cannot exceed phi look at this the maximum value of delta the condition is the frictional angle between soil and this reinforcing material that means your delta it should not be exceeded to your phi that means inter frictional angle of the soil. Now, pull out length pull out resistance is calculated to be the product of surface area of the reinforcement along the bond length tan delta and the vertical effective stress operating on the bond length the value of tan delta is represented by coefficient mu the value of tan delta you can take it as a coefficient of mu if you look at is it is a product of sigma v i into tan delta l e i is your length and over this surface area it acts for full width of this reinforcement the maximum possible value of vertical effective stress and disregarding any surcharge is taken to be overburden pressure above the reinforcement without any surcharge without any surcharge it comes out to be 0 q is your surcharge. So, this will be a gamma z into s b into s h now if you look at this pictorial view if I take it in a pictorial view this is the spacing if this is the spacing this is the spacing in lateral direction or horizontal spacing once you place one layer once you place one layer of your reinforcement these are all your reinforcements bars these are all reinforcing bars once you place a bar then once you feel it then again once you place another bar this direction is your spacing in vertical this is your spacing in lateral or horizontal direction pull out resistance is calculated to be product of the surface area of this reinforcement along the bond length as I said tan delta and the vertical effective stress operated on the bond length the value of tan delta is represented by coefficient mu now the another term is coming into picture that is your n n means how many number how many numbers in that direction you can write it in terms of n this is your n. Now two panel width if there are two panel if you look at here the panel shape is the panel shape is it is like this and it is like this. So, one will be connected here one will be connected here if it is a two panel width then two into one point five generally three meter of the spacing we can keep it this is all about your pull out length what we have discussed tensile failure and pull out failure or pull out length now come to the next types of reinforced soil walls what are the different types of reinforced soil walls one is your vertical geosynthetic phase that means reinforced wall can be arranged in such a way that it will stand vertically with geosynthetic phase that means this is your geosynthetic phase in vertical direction other is your sloping geosynthetic facing that means you can arrange you can make a ground reinforced at wall. So, that you can make it as a slope with respect to your horizontal you can make it as a slope this is called sloping geosynthetic facing then third one is your sloping when I it are structural facing after in this case what will happen first prepare the reinforced this is your reinforced soil wall sloping soil wall as it is like this then a structural facing along with this after this reinforced soil wall has been prepared then a structural facing you can place it over the side then third one is vertical precast concrete element facing other that means either you can construct it by means of geosynthetic by means of reinforced wall one by one that means one reinforcing material you are taking and hold it then fill the soil then another reinforcing material you are taking hold it so what will happen no structural element is required fourth one is in this case precast concrete element facing you can take it these are all your precast this is precast concrete facing element then in this precast concrete facing element layer by layer you can place your reinforcement here layer by layer with connected to your precast concrete element facing these are all your four types types of reinforcing soil walls also first four types then second one is your sloping soil and sloping soil and vegetation facing what happen for economy point of view this because once you are making a sloping once you are making a sloping face of this reinforcing wall reinforcing wall then these are all exposed to outside these are all exposed to outside to prevent this you can go for you can do it by means of vegetation you can allow the vegetation that means you can allow grass so that it will be protected third one is your by stepping geosynthetic gabion that means you can geosynthetic gabion by means of mesh and wires or geosynthetic wires you can provide the gabion wall by stepping fourth one is vertical cast in place concrete or masonry facing that means you can straight way instead of earlier is that if you look at here vertical precast concrete element facing that means you can take one precast another precast place one over other and connected then go for your reinforced wall construction but in this case you can go for a single vertical cast in place concrete this is your single vertical cast in place concrete with masonry facing these are all your masonry facings then allow this reinforcement to be placed then vertical mbw facing also you can place it you can you can do it also then these are all about basic properties and how this pullout length how is your failure and what are the different types of reinforced earth walls are there now you are going for analysis first analysis is your liquid limit equilibrium method in limit equilibrium analysis in case of limit equilibrium analysis a limit equilibrium analysis consist of a check of overall stability of the structure once you go for limit equilibrium method that means you are checking this overall stability of the structures the types of stability that must be considered are external internal or external internal both the stability you are going to check particularly in case of limit equilibrium method that is your external and internal and either external or internal or external internal mix external stability if I say external stability external stability involves the overall stability of the stabilized soil mass overall stability of the stabilized soil mass considering as a whole taking into consideration as a whole of soil and reinforcing our earth wall as a whole what is this overall stability and is evaluated using slip surfaces outside the stabilized soil mass it has been evaluated by using a slip surface outside the stabilized soil mass in case of internal stability analysis you can evaluate internal stability analysis evaluating potential slip surface within the reinforced soil mass once you are saying that internal that means what happened internally inside your reinforcing materials what type of failures in some cases the critical slip surface is partially outside and partially inside the stabilized soil mass and the combined external and internal stability analysis may be required in some cases what happened the critical slip surface is partially inside the soil mass and outside the stabilized soil mass in that case you will consider both external as well as internal as a combined stability analysis now if you look at this external stability if you look at this external stability because if there is a soil mass in the soil mass it is acted upon by surcharge then you can find it out because of surcharge what is your active earth pressure because of soil what is your earth pressure acting on this because of other load what is your earth pressure acting on it you take into consideration of all forces then find it out what is your resultant of lateral forces this is your resultant of lateral forces then if I am going to consider soil mass if this is the soil and these are all my reinforcing material reinforced material then this entire soil mass and reinforced material it has its own weight it has its own weight that is your own weight w is equal to own weight if I am considering a b d f of this own weight then you can find it out the own weight how much is your own weight how do you find it out by if you know the unit weight or the density of the soil as well as the reinforcing material then you can find it out its own weight then it will you can find it out where is your c g it will act on the c g then based on that what is your reaction force at the bottom you can find it out how far this reaction force is going to act from the centre of the centre of the soil mass and the reinforcing material and what are your lateral forces acted below the reinforcing material if you look at this external stability this in combined I have shown this in combined I have shown if you go to the external stability external failure modes of geosynthetic reinforced soil retaining walls first one is your sliding if you look at your age your sliding that means what will happen it may possible that entire soil mass along with the entire soil mass with your reinforcing material it may slide it may slide suppose it is there the it will slide and it will take a new position from here to here it will slide here second part is your external stability if it is it cannot take the entire load coming to the reinforced earth wall whatever the load coming to it may possible that it may over turn it may over turn at some point so it will over turn at some point this is called over turning third is your load bearing failure that means if this is my reinforcing soil wall reinforcing wall then what will happen it will be it will be placed over the soil mass or the foundation soil or the you can say foundation soil now you can check how much is this load bearing capacity that means what is your bearing capacity whether it is load bearing capacity failure this is also coming into taken into consideration in external stability then deep seated slope failure deep seated slope failure means if there is a possibility that if there are loose field materials are there the failure surface may occur in deep seated means it will cover it will start from this reinforcing mass it will go beyond and it will cross over the foundation soil this is called deep seated failure surface if I summarize external failure modes of the geo synthetic reinforced soil retaining walls first one is your sliding second one is your over turning third one is your load bearing capacity fourth one is your deep seated slope failure bearing and tilt failure if you look at it that means what I said it will it will it will rotate at one point it will rotate if you look at that over turning that means in this case with respect to one side of this it will rotate then if you say that sliding that means if this is the this is the original original shape original mass of the reinforced wall so what happened if this lateral forces are maximum so what happened from this position to this position it will slide so forward sliding this is called forward sliding then third is your slip failure that is failure surface you can take into consideration how this slip failure external stability in overall it is your sliding that means it will slide from its original position to another position over turning if eccentricity is there over turning when it is possible if you go if the resultant force this is my resultant force if it is not acted at the centroid if it is acted at a distance of e this is called eccentricity at a distance e then there is a chance over turning that means eccentricity is there so it will topple or it may over turn at one point then bearing capacity this is your basically foundation failure this is your foundation failure bearing capacity then fourth one is your deep seated stability or rotational stability sometimes we say it will go deep root of the soil mass then next part is your internal stability what are the internal stability if I make it into two parts one is your if you come back to earlier slides where I have shown it active zone and resistant zone if you provide reinforcement there are two zone one is your active zone other is your resistant zone if you take this two into consideration in the internal stability failure now this is your active zone and this is your resistant zone now it from there with this you can find it out how much is your pull out length how much is your pull out length based on your over burden or may be the surcharge so p r i pull out length is your two big why it is two at the top this is sigma v i gamma z at the bottom also sigma v i gamma z and at the surface because two surface one is your top surface other is your bottom surface so two sigma v i tan delta into l c i l e i that is your critical length or you can say that pull out length so from there you can find it out t i maximum from there you can find it out l a now l s you can find it out from here also you can get it if you look at here you can get it l e i l e i from your pull out resistance if you know the pull out resistance p r i then you can find it out l l e i that means for active zone what is your length or pull out length then if you know the maximum pull out resistance t then from there you can find it out l a in this zone l a then l s also you can find it out h minus z if this is the this is the total total is your total height is your say h and this at any distance z it will be h minus z into cot alpha and s v is your vertical spacing spacing s v is your this is your s v this is your s v spacing in vertical direction which is equal to total height h if this is my total height h if this is the total height h then it will be h by n n is equal to number of reinforcement n is equal to number of reinforcement now come back to internal failure modes of geosynthetic reinforced soil retaining walls if you come back to internal failures there are one is your geosynthetic rapture it may possible that this geosynthetic walls if these are my geosynthetic wall that means wall one two three four five six seven eight these are all the reinforcing walls it may possible that over the period of time this geosynthetic style walls may rapture it may rapture so what will happen this is called one of the internal failure then geosynthetic pull out if it is exposed to if it is exposed to this outside then what happened by means of animal or by means of cattle it may possible that it may be pull out number one number two case is that if the pull out resistance will be less than whatever this whatever the lateral resistance then what what may possible that there may be a pull out failure of this geosynthetic reinforcement then connections that means facing element suppose it has not been properly connected if you go back to this connections look at here here particularly here this walls this geosynthetics are reinforced reinforced reinforcing materials it has to be properly connected with your wall it has to be properly connected with your wall here there is a proper connection with your wall if there are not proper connection between this wall and the reinforcing material what will happen it is called connection failure suppose this is your wall this is your wall and you have connected one by one so there suppose in between at this point one say point three there is no connection there is no connection by or may be a faulty the connection is not connection failure is there what will happen over the period of time this wall will come out from the reinforcing mass also this wall will come out from the reinforcing mass so there are three types of failure you can say that internal failure modes one is your geosynthetic rapture that means it over the period of time it may possible that geosynthetic will rapture second is your geosynthetic pull out because one of the geosynthetics may be pull out then third is your connection failure that means facing element if it has not been properly connected it may fail by means of connection failure these are all your two for limit equilibrium analysis if I summarize there are two stability analysis one is your external stability other is your internal stability for this stability analysis what are the recommended factor of safety as given by federal highway administration f h w a what is the recommended value for external stability it has been summarized one is your external other is your internal external stability for sliding for sliding the factor of safety should be greater than one point five or if it is a m s e w wall it is one point five if it is r s s it should be one point three eccentricity at base it should be less than equal to six otherwise there will be a tensile stress below this below this wall so it should be less than equal to that means e eccentricity should be less than equal to b by six bearing capacity the factor of safety should be greater than equal to two point five if it is not greater than that means there is a bearing capacity failure deep secret stability factor safety is greater than equal to one point three compounded stability factor safety should be greater than equal to one point five seismic stability more importantly this we are going to discuss later on seismic stability factor of safety should be greater than equal to 75 percent of static factor of safety that means for seismic stability the seismic factor of safety should be greater than equal to 75 percent of static factor of safety all failure modes then internal stability if you come back to internal stability pull out resistance for pull out resistance the factor of safety should be greater than one point five for all walls internal stability for r s s factor of safety should be greater than one point three allowable tensile strength for steel strip reinforcement there are different types of reinforcement for steel strip reinforcement it should be zero point five five f y for steel grid reinforcement it should be zero point four eight f y for geosynthetic reinforcement t a is design life of this below these are all the recommended values these are all the recommended values of federal highway administration f s w a in united states of america different recommended factor of safety values now we will start this design methods for inextensible reinforcement means it will be there are two types of reinforcement one is your extensible reinforcement other is your inextensible reinforcement in inextensible reinforcement number one is your external stability the current method of limit equilibrium analysis uses a coherent gravity structure approach look at here uses a coherent gravity structure approach to determine external stability of the whole reinforcement similar to the analysis for any conventional or traditional gravity structure that means the current method it says as like conventional or traditional gravity structure it has been assumed for external stability it will be taken as a whole mass whole reinforcement the state of stress for external stability is assumed to be equivalent to a coulomb state of stress with a wall friction angle delta equal to zero with a wall friction angle delta is equal to zero that means it is a smooth wall delta is equal to zero means coefficient of friction between soil and the wall if it is supposed to be zero that means it is called as a smooth wall similarly design methods for inextensible reinforced internal stability first one is your external stability second one is your internal stability for internal stability evaluation it consider a bilinear critical slip surface look at here for internal stability evaluation it consider a bilinear critical slip surface that divides the reinforced mass in active and resistance zone as you have discussed also earlier that divides the reinforced mass in two parts one is your active other is your resistance zone and requires that an equilibrium state be achieved for successful design for internal stability a variable state of stress varying from multiple of k a k a is your active earth pressure to an active earth pressure state k a are used for the design that means for internal stability a variable state of stress varying from a multiple of k a multiple of k a means multiplication of k a k a is your active earth pressure recent research has focused on developing the state of stress for internal stability as a function of k a type of reinforcement used geotextile geogrid metal strip or metal grid and depth from the surface inextensible earlier was earlier what we have discussed that is your inextensible reinforcement external as well as internal stability now second one is your extensible reinforcement external stability for external stability calculation the current method assumes on earth pressure distribution look at here in this case whole entire entire reinforced mass has been consider as a one mass for inextensible reinforcement for extensible reinforcement extensible reinforcement it assumed an earth pressure distribution earth pressure distribution and consistent with the method used for inextensible reinforcement first it has been assumed for earth pressure distribution then once earth pressure distribution has been made then it will follow the similar procedure for external stability in case of inextensible reinforcement similarly internal stability for internal stability computation using this simplified coerent gravity method the internal coefficient of earth pressure is again a function of type of reinforcement the internal stability internal coefficient of earth pressure internal coefficient of earth pressure is a function of type of reinforcement where the minimum coefficient k a is used for wall constructed with continuous sheet of geotextile and geogrid for internal stability a rankind failure surface the difference if you look at here in this case a rankind failure surface is considered because the extensible reinforcement can elongate more than the soil before failure I will stop it here then we will start detail discussion about british standard and other method along with this seismic design also next class thanks a lot