 We discussed about this design of this federal highway as given by federal highway administration FHWA or enforced earth wall. We discussed also this these are all review one or two slides external seismic stability. This external seismic stability has been considered taking into consider as a monolithic block of this material. Then this approach bearing capacity calculation assume that the base of the reinforced zone act as an eccentrically loaded footing with an equivalent footing width of by taking this measure of approach. Then by considering this measure of approach we can go for this first we will find it out the pressure distribution diagram one first one is your surcharge then is your because of earth pressure then because of your seismic load all three will be combined and we will find it out resultant earth pressure at the resultant pressure at the base and how far this resultant pressure from this centre of gravity or CG of this entire soil mass as well as your reinforced earth walls. Then based on that this stability analysis has been checked earth pressure as I we have these things we have discussed so k active earth pressure it is your tan square 45 degree minus 5 by 2 with a vertical wall with a surcharge slope this kind of slope earth pressure we can get it from this equations this also I have discussed. Then for external stability analysis you can find it out sliding factor of safety against sliding it should be horizontal resisting forces by horizontal driving forces that means PR by PD it should be greater than 1.5. So horizontal resisting forces and horizontal driving forces if you come back here this is your horizontal driving forces a resisting forces and there is a driving forces because of your earth pressures lateral earth pressure then external seismic stability we have discussed also this peak horizontal acceleration coefficient we can find it out then additional dynamic earth pressure can be calculated additional dynamic earth pressure because of your this. So it is a 0.5 gamma h square k a e minus k a then based on that we can find it out k a e which is your k a e is the seismic active earth pressure coefficient it is the seismic active earth pressure coefficient. Then after finding out seismic active earth pressure coefficient the effective inertia force PIR can be found out by k h w a g i e then once you get this we can find it out the pressure distribution because of your this is your pressure distribution because of your seismic force and the resultant will act means the resultant will act at a distance 0.6 h from the base of the wall. So by we can find it out by doing this we can find it out also factor of safety against sliding failure and we can check it taking into consideration of earthquake forces we can find it out factor of safety against sliding similarly we can find it out factor of safety against overturning as well as eccentricity failures then we can find it out in terms of this overturning and eccentricity failure in terms of e by h is your eccentricity h is your total height in terms of active earth pressure k a n k e a e then next is your bearing capacity failure this also we have discussed bearing factor of safety against bearing capacity is your ultimate bearing capacity this you can get it we can get it by mayor of distribution c n c 0.5 gamma b l minus 2 e into n gamma and sigma b we can find it out total vertical forces divided by l minus 2 e then next part is your of your internal stability that is your earth pressure this we are going to start earlier this up to this we have finished your external stability as well as some part of your internal stability that is your extensible reinforcement now we will start this internal stability that means of earth pressure if you look at this internal stability of earth pressure it doesn't include polymers deep reinforcement it doesn't include this polymers deep reinforcement now if you look at this figure this is the total height and at a this height of the wall and depth below the top of wall j depth below the top of the wall j that is your geo synthetic that means it is your metal if you look at k is coming about to be 1.7 it is varying at a distance of 6 meter to 0 to 6 meter it is going up to horizontal of 1.7 then metal bar metals and welded wear grids it is coming up to 2.5 that means we can find it out k is equal to k 0 1 minus z by z 0 then from there plus k a z by z 0 for z is less than equal to z 0 that means z 0 is considered to be 6 meter and k is equal to k a that means if there is a wall height suppose say up to 6 meter of wall height we can find it out earth pressure k 0 into 1 minus z by z 0 plus k a z by z 0 for a wall height of 6 meter this variation we can find it out from this equations and beyond this 6 meter k is equal to k k a it should be k is equal to k a for z greater than z 0 that means z z this is your distance z is greater than z 0 z 0 is your 6 meter is greater than z 0 is your 6 meter it greater than this it is is your k is equal to k a z is the depth measured from the upper level of the mechanical height h internal stability next part is your pullout length so pullout length we can find it out from your at a distance z at a distance suppose this is your distance z at a distance z these are the reinforcing bar 1 2 3 4 5 up to j j number of bars so for these pullout length we can find it out by taking into consideration of pressures of the soil that is your sigma vi at the top that is your gamma z sigma vi at the bottom gamma z to p r i is equal to 2 sigma vi l e i tan delta t i max is equal to gamma z plus q k into s b into s h s b and s h is your spacing in vertical direction s is your spacing v for in vertical direction s is your spacing h for is your in horizontal direction spacing in vertical direction if this is the wall height this is your spacing in vertical directions then if I move towards in plain strain or the length wise then this spacing will be in horizontal direction internal stability that means tension failure or rapture failure or overstressing failure safety margin against tension failure of reinforcement as per f h w a guidelines specify that the available tension that means tensile resistance provided by the reinforcement layers must exceed the look at here this available tension must exceed or equal to the design tension to guard against the rapture failure of the reinforcement layers for stability against tensile failure the reinforcement layer under consideration the design tensile strength of the reinforcement layer under consideration t d should be more than the maximum load in the soil reinforcement under consideration that means t d should be more than t i maximum the factor of safety against tension failure is given by factor of safety f s is your factor of safety t for tension failure which is equal to t d by t i maximum t i maximum based on vertical spacing if you look at here t i maximum is your based on vertical spacing s b and horizontal spacing h h s h can be written as t i maximum q plus gamma z q is your surcharge gamma z is your gamma z is your weight of the soil above this gamma z into k r k r is your reinforcement force coefficient k r is your reinforcement force coefficient into s v into s h s v is your spacing in vertical direction spacing in horizontal directions so f h f h w a guidelines also specify that the reinforcement pull out failure analysis has to be performed to verify that the length of the reinforcement is sufficient to carry the design loads that means length of the reinforcement should sufficient to carry the design loads when the length of the reinforcement within the resisting zone is unable to mobilize sufficient here resistance the reinforcing elements tend to pull out produce gross distortion in the structure or even triggering a collapse that means length of the reinforcement should be sufficient if it is not sufficient it will produce a gross distortion in the structure and even triggering a collapse the available design pull out resistance of individual reinforcing elements must be equal to or exceed the design tension in the reinforcement to guard against a failure the available design pull out resistance of individual reinforcing element must be equal to or exceed the design tension in the reinforcement to guard against the failure due to pull out of reinforcements that means available design pull out resistance of individual reinforcing element it should be equal or greater than the design tension in the reinforcement pull out resistance of reinforcing element is computed using the overburden pressure as I said using the overburden pressure that means your gamma h and surcharge load that is your q surcharge load q acting on the length of the reinforcement emitted in the resisting zone for stability against pull out failure of reinforcement the available resisting force PRI on the embedded reinforcing reinforcement length of layer under consideration should be more than the maximum load in the soil reinforcement under consideration that means TI maximum PRI should be more than TI maximum TI maximum the factor of safety against pull out failure that is your PRI by TI maximum the available resisting force PRI on the embedded reinforcement length of each layer LEI beyond the failure surface is given by the following equation this is your PRI you can find it out this is your two times sigma VI because if this is the reinforcing element so this is your one side this is your other side that means this is your two sigma VI LEI tan delta so sigma VI is your as I said this is your surcharge plus overburden gamma z we can see and LEI is your length effective length tan delta is frictional force along one surface between the wall and the soil two is your both the sides it will occur so the factor safety against pull out failure if I write it in terms of PRI and TI maximum it should be two sigma VI LEI tan delta I gamma z plus q k s b into one why it is one this is generally if I take this is the retaining wall if this is the retaining wall and this is your spacing in vertical direction also you have this spacing also in length direction also in length directions you have this spacing also spacing like this you have your spacing that is your s h generally in design we are taking into consideration of per meter length that means one meter one meter length in this length direction we are taking into consideration that is why this s h becomes to be one then internal seismic stability this seismic load produces an inertial force P1 acting horizontally in addition to existing static forces as we have also earlier discussed this seismic load produces inertial force P1 acting horizontally in addition to the existing static forces these force will lead to incremental dynamic increases in the maximum tensile forces in the reinforcement it is assumed that the location and slope of the maximum tensile force line does not change during the seismic load this is the drawback or you can say that this is the assumptions that means the location and slope of maximum tensile force line does not change during the seismic loading that means it will same as during the static loading conditions calculation steps for internal stability analysis with respect to seismic loading these are like this so P i is your internal inertial force duty weight of your back field within the active zone this is your P i or P1 if you look at here this is your P i because of seismic loading inertial force then l e i is your length of reinforcement in the resistant zone length of reinforcement in the resistance zone l e i then t maximum is your load per unit load per unit wall width applied to each reinforcement due to static forces load per unit wall width applied to each reinforcement due to static forces and t m d is your load per unit wall width this is your load per unit wall width applied to each reinforcement, this is your load for unit wall width applied to each reinforcement due to dynamic forces, one is your due to static forces, other is your due to dynamic forces that means, T maximum and T M D, now the total load for unit wall width applied to each layer that means, T total at each layer T total is your T maximum this is because of your static, T M D this is because of your dynamic forces, this is your because of static, this is because of your dynamic forces. So, maximum acceleration in the wall and force P 1 per unit width acting above the base that means, P i is your A m into W a, A m is equal to 1.45 minus A into A, where W a is the weight of active zone, shaded area in this figure weight of the active zone, shaded area in this figure this is the weight of the active zone these are the shaded area. Now, dynamic increment we can will have to calculate T M D, T M D directly induced by the inertia force P i in the reinforcement by distributing P 1 P i in the different reinforcement proportionally to their resistance area L e on the on a load per unit wall width basis. So, T M D can be calculated P i into L e i by i is equal to 1 to n that means, number of layers into L e i. Suppose, this is your T M D so P i is your inertia force. So, this is your L e i then this is your number of layer this is 1. So, you have to 1 2 3 4 5 6 7 like this n number of layer. So, total T total you can find it out T i maximum into T M D this is because of your static as I said this is because of your dynamic load this is because of your dynamic load. So, factor of safety internal seismic stability factor of safety T D by i maximum T i maximum plus T M D. So, factor of safety in terms of T factor of safety in terms of P. So, P r i by T i maximum plus T M D. So, this is all about this seismic design or reinforced reinforced earth wall design. Reinforced earth wall design if I summarize if I summarize looking at one figure let me take out this one figure. If this is the case if this is the case forget about this there are two parts one is your static part other is your dynamic part. If there is a static part if there is a only static design has to be checked this is because of your inertia force because of your dynamic loading this thing has to be neglected entire soil plus reinforced earth wall to be considered as a one unit that means it has to be constructed monolithically. Then this weight of this earth wall it will act at the C g then you will have to find it out this earth pressure earth pressure because of your surcharge q this is because earth pressure because of the surcharge and its resultant forces acted and earth pressure because of your soil and its resultant forces and total will add it and this total will give your lateral resistance forces and with this with this w will have to find it out what is the resultant forces acting at the base and how far it is how far it is from the centroid based on that will have to find it out the eccentricity is equal to eccentricity eccentricity and based on this eccentricity once you get it you can calculate the factor of safety different factor of safety one is your factor of safety against sliding whether this will slide or not this would be greater than equal to 1.5 other is your because of your overturning whether this will overturn at the toe and bearing capacity that means whether this soil below this means above the soil above the ground where this reinforced earth wall is there below the reinforced earth wall the soil is whether this bearing capacity is bearing capacity is within this permissible limit or not you have to check it then once it has been checked then you will go for then you will go for internal stability internal stability that means for internal stability you have to consider for a rapture stability against rapture and stability against pull out and stability against excessive deformations. So pull out length there are two parts one is your active zone other is your resistance zone. So this resistance zone l e should be sufficient so that it should taken it should take care of your additional tension force tensile force because of your reinforcing reinforcing wall reinforced earth wall then if you are going to do it both static and dynamic load conditions both starting and dynamic load condition in that case dynamic load conditions the inertia force because of your dynamic load has to be consider the assumption is that this inertia force because of a dynamic load it will act at the c g of this reinforcing earth mass and this pressure distribution because of your inertia earth force p r i it should be find it out and this pressure distribution diagram is given and with this pressure distribution diagram you will have to find it out the resultant and are the resultant will act at 0.6 s from this base of the ground and are this three pressure distribution diagram pressure distribution diagram because of your searcher pressure distribution diagram because of your soil pressure distribution diagram because of your inertia forces are all of these three and find it out this total pressure distribution diagram then you calculate then after taking into consideration then check this stability considering overturning sliding as well as as well as this overturning sliding then bearing capacity then as well as also internal stability that means pull out resistance you have to check it the for pull out resistance we have considered we have considered pull out resistance there are two parts we have considered as I said total total t total is your t i maximum and t m d t i maximum is your because of static t m d because of your dynamic load then find it out is then check whether this should be this factor safety is satisfied or not then this completes your complete design methodology or procedure for your reinforced earth materials or reinforced earth structures or reinforcing materials or reinforced earth structures then one part is still remaining I will go for this this is about your reinforced earth design so one part is left that basic earth pressure to start with this something some some part of this retaining structures introduction to retaining structures and what are the earth pressures comes into picture that means earth pressure and retaining wall design if you consider that is your this is in addition to this because you should first know what are the different earth pressure selected and how the retaining wall has been designed then once you know it then for reinforced earth wall you can go for both static as well as dynamic loading just geotechnical application k0 that means what is k0 means earth pressure at rest then active and passive states rankine earth pressure then coulomb's earth pressure theory these are this is just a brief review of this retaining wall earth pressure theories in geotechnical practice how this lateral support occur particularly cantilever retaining wall if you look at here this cantilever retaining wall this cantilever retaining wall that means it will retain the soil mass because of your cantilever action and breast excavation generally this excavation has been done below the ground surface to support to support this vertical cut then anchored sheet pile also this I have discussed also anchored sheet piles this anchored sheet piles has been provided to anchor a sheet or flexible flexible piles now lateral support this retaining wall if you look at there is a gravity wall soil nailing wall and reinforced earth wall so this reinforced earth wall we are discussing this reinforced earth wall already we have finished so this is your reinforced earth wall soil nailing wall and gravity wall so you should know little bit about your retaining wall now gravity wall gravity wall if you look at it will enter load will be taken by means of gravity actions gravity actions and some photograph I have shown this gravity wall one of the gravity wall some photographs has been shown good drainage it allow gravity wall it is a good drainage allow plant to grow then soil nailing wall if you look at the soil nailing wall these are all reinforced wall you can say if you look at the soil nailing wall this is your slope along the slope the soil nail has been provided if you see this is your soil nail walls if you see one second soil nail wall soil nail wall this nails how this nails has been provided here this nail here one nail here one nail along the length of the wall so this is again a reinforced earth wall you can say that by means of soil nailing then second is your third is your reinforced earth wall so layer of reinforcing material layer of reinforcing material has been provided in the reinforced earth wall so mechanical stabilized reinforced earth wall it is called MSE mechanical stable mechanical stabilized earth wall that means mechanical it has been stabilized so this is reinforced earth walls then sheet pile walls how it looks earlier in the beginning we have finished the sheet pile walls in this applications of soil mechanics how this sheet pile walls has been built up one by one have been constructed constructed during the installation and sheet pile wall how it looks one side how it looks then look at this earth pressure at rest if there is a ground level if you take a soil mass so there are you can say that sigma b and sigma h so so the ratio of sigma h prime by sigma b prime is k that is called coefficient of earth pressure at rest that is your k0 to arrive k0 state there are no lateral strain during the loading that means in earth pressure at rest condition there are no lateral strain during the loading that means 1d consolidation only in vertical direction there is no lateral strain so you can find it out k0 k0 is equal to 1 minus sin pi for normally consolidated soil for over consolidated soil k0 is equal to 1 minus sin pi into OCR sin pi for elastic analysis k0 for elastic analysis k0 is equal to mu by 1 minus mu this is your poisons ratio mu by 1 minus mu this is your poisons ratio then we will discuss little bit about active pressure earth pressure and passive earth pressure if you look at active and passive earth pressure by animation I will show you once again active and passive earth pressure this is a soil mass there is a retaining wall this is your retaining wall and this is a smooth retaining wall and now because of your earth pressure it rotates it rotates or may be translate it can be go by means of translation that means the soil will act pressure on the wall that means with if this is the wall wall will move away wall will move away from this from the soil in that case it is called active state look at this this is your active state in this condition wall is moving away from the soil that means it will act as a active state in this case wall is wall is moving towards the field wall is moving towards the field that means it is in the passive state if you look at this active state active earth pressure if this is the sigma b prime initially at rest and sigma h prime initially there is no lateral movement initials there is no lateral movement initially there is no lateral movement and sigma h prime is equal to k 0 sigma v prime that is your k 0 gamma z as the wall moves away from the soil if this is my wall it moves away from the soil what will happen sigma v prime remains same sigma v prime remains same sigma h decreases till failure occurs this is called active state for normally consolidated soil that means at k 0 conditions if you see this is at this stage then walls moves away from the soil walls moves away from the soil now for failure envelope develop that means decreasing value of initially from if this is the origin this to this will your sigma h prime so sigma v is not changing so sigma h is decreasing decreasing decreasing so it is coming the failure envelope means if this more circle touches your failure envelope that is called active state so this is all preliminary or may be review of this active state and passive state in diagrammatically or in ppt form I will discuss tomorrow for passive state also some of the review of the slides I will stop it now