 So, in the previous lecture I have discussed in details about the sheet pile walls particularly the anchored heads. I have also discussed about the analysis of anchored bulk heads by using different methods. The first one which we discussed was the simplified method and the second one was the pre-urse support method and the fixed earth support method and the statement of the problem is for a given height of the bulk head or the retaining wall or the sheet pile wall you are supposed to find out the depth of embedment. And at the same time I also introduced this concept of how anchoring is done by using tie rods or the cables attached to the anchorage systems to enhance the stability of the sheet pile walls or the anchored bulk heads. I will go a bit more into the details of the analysis of anchored bulk heads because these systems are becoming very contemporary in today's infrastructure development and I wish that all of you should become an expert in this subject for analyzing these anchored bulk heads. So by definition an anchored bulk head is you have a retaining wall say this is the sheet pile and this is the dredge level we call it as BL, this is the ground surface and this is the backfill. So the whole idea was to attain much higher heights of H all right above the dredge level so that I can make a higher wall and which can retain lot of soil mass. So what we did is we introduced a tie rod or anchorage so this is a tie rod at the depth of say about A from the top of the bulk head. Now without having an anchor this tie rod or the bar is not going to be affected so what is done is this tie rod is connected to an anchor so this becomes an anchor. Now these anchors could be the independent units you know this could be an anchor a block and this block will be connected to the tie rod like this let us say. This could also be a beam of length L so this could be a continuous beam of length L also. So otherwise the spacing between the two blocks all right so if I consider another block over here the spacing could be S so S is the spacing between the anchors in case you are having a continuous beam then the length of the beam is L. Now one of the most critical question here is what should be the length of the tie rod in other words where this block should be located within the back bell why it is so. As far as analysis is concerned what we have done is we have obtained the d value the depth of embedment by using different methods we can obtain T also we can optimize A also depending upon the parameters which are known and unknown. Now the question is where should be the anchor placed in the back bell why this question is being asked suppose if this anchor is very close to the tie rod in such a way that this sits in the active wedge all right. So suppose if this is the failure slip surface all right and this becomes the active wedge so if this is the active wedge do you think that this anchor is going to be active or going to be useful no why at the time of failure this entire rigid body is going to fail by deflecting the wall so what you have to do is you have to make sure that this anchor is sitting in the passive block not in the active block all right that means what I have to do is graphically I should find out what is the zone of active pressure and what is the zone of passive pressure and then locate the anchor in the passive pressure zone fine big question is what is this point through with the slip surface is passive so this point normally defined as X could be at the tip of the wall we can obtain from D or this could be 75% of the D value which is obtained by fixed earth metal so there are two ways of obtaining the value of X or the point of point X so the location of X is either this is D which you get from pre earth support method this could be 0.75 times D when we are using a fixed earth support method now once the point X is fixed what I can do I can draw the location of the active earth pressure zone this would be 45 plus 5 by 2 so say this is the active earth pressure zone so A B X is the active earth pressure zone what will be this an angle this angle will be 45 plus 5 by 2 okay remember the Mohr circle if I want to find out the conjugate plane on which the passive earth pressure conditions are acting what I should be doing from this line if I draw a perpendicular so this angle is 90 degree what will be the inclination of this line this will be 45 minus 5 by 2 so this block B no let us see not be there B and B onwards let us say so this goes up to BC so this zone is going to be the passive earth pressure zone so this is 45 minus 5 by 2 so what we have done is by using the simple concept of analysis of the sheet pile walls anchored bulkhead we have obtained the value of D I can take either D as the location of X that could become the pile tip or 0.75 D the location of X start from here horizontal line 45 plus 5 by 2 this becomes the active earth pressure zone and having obtained this perpendicular to this plane would be the flip surface for passive earth pressure zone okay what about the zone in between X B and C so all this zone which you are seeing over here this is this is KA condition this is KP condition so what about the in between zone this becomes K naught alright nice so this is how we analyze the anchorage and position of the tie bar with the anchors there is one more thing suppose if I consider that B is the height of the block and depth of embedment is let us say normally we define this as the DA the free body diagram is like this now suppose if I magnify the pressure which are acting on the anchors I hope you will realize that this is how I can draw the anchor this is the ground surface anchor is being pulled up towards the left hand side with respect to horizontal what would be this surface this zone active zone correct so this is equal to 45 plus 5 by 2 and what about the passive zone when you are pulling the anchor on the left hand side this soil mass is trying to resist the movement of the anchor block so this is going to be 45 minus 5 by 2 this is okay the height of the anchorage is B which should be not less than DA by 2 where DA is this whole thing this is the first condition that means there should be enough overburden on the anchor so that active and passive earth pressure mobilize the more and more passive earth pressure gets mobilized the anchor is going to be more effective I think now you can realize the tension in the anchorage comes because of two things one is because of the deflection of the sheet pile which is not acceptable clear so how is going to come it is going to come because of the passive resistance which is being mobilized by the soil mass so that means the net pressure which is acting on the bar would be T multiplied by S, S is the spacing between the two anchor blocks and T is normally in kilo Newtons per meter tension per unit length of the wire and that length defines you know how much these blocks are going to be spaced with each other so this is T and this is T I hope you can realize we can go for the equivalent forces which are going to act on the anchor so I can take at S by 2 and S by 2 1T so T into S is the total force in the tie bar and this will be equal to what is the net pressure half kp-ka unit weight of the soil into da square depth of embedment multiplied by L now one thing is missing over here we are not very sure about how much the passive earth pressure is getting mobilized in fact we are not sure about how much kp get mobilized so put a penalty function or put a factor of safety on this so far what we did we applied only factor of safety uncertainty in terms to kp only now the net kp-ka we are applying a factor of safety of F and hence we are equilibrating the forces which are going to come in the tie rod and the force which is getting exerted on to the anchorage system so I hope you can realize if it is a continuous beam what is going to happen S will be equal to L so this normally gets cancelled out and we are left with total tension equal to this now I can convert it into a design problem for a given tension which I am expecting for a anchored bulkhead to mobilize would depend upon the kp-ka that means in other terms phi value the unit weight which can be obtained by compacting the soil mass or by changing the water table correct so there could be a situation where you have a water table over here only thing is going to change is that your gamma term is going to change and depth of embedment or burial so this is the depth of burial is this fine we have discussed lot of concepts over here regarding the anchored bulkheads now few more concepts before I switch over to another topic you must have realized that installation of this anchor tie bar is not so easy is this correct what we have to do is we have to keep on filling the soil if you are doing stage wise construction this is not possible you are doing dredging let us say you brought the soil mass by cutting from this level to this level it is extremely difficult to put an anchor bar over here or an anchorage system over here okay so this type of systems can be done only when you are back filling something stage wise layer and then you can lay the system over here and again bury it and then compact it hope you are realizing so a better way would be what any idea next time when you pass by a highway or in the hilly terrain or maybe sometimes the systems where you are seeing a retention of the soil mass nowadays what is being practiced is people are inserting nails now this is what is known as nailing the purpose is same to stabilize the retaining wall so these red systems what I have shown are the soil nails and what you must have realized is intentionally I have been lowering down or decreasing the length of the soil nails why look at the zone of influence of active pressure these nails are going to be effective once they are extending beyond the active pressure zone so as if you are stitching this block ABX with the parent body is stitching you know if you remove this what is going to happen this block has a tendency to get detached from the system so soil nailing is quite prevalent in today's infrastructure development projects what is normally done is you define the angle of inclination with respect to horizontal and the length of the anchor or the soil nails so length of nails and their inclination is normally fixed I wish to show you some of the videos in this case so in the simple form this is how a soil nail wall looks like there is an existing road and you wanted to widen it so you have cut down the hill this portion has been cut and then there is a face here and then the entire slope has been nailed followed by grouts in most of the airport projects tunneling projects retaining wall projects highway projects these type of structures are being designed this is a typical anchor you know they are after creating a cavity you put the steel bar grout it use a nut and bolt and fix it at the base of the base here this is how the installation is done this is how the finished product looks like so sometimes there is a wire mesh which is placed you know somewhere here not for the vertical section but for the inclined section so sometimes you know a heavy duty steel mesh is also provided which gives more strength to the retention several projects are being executed by using these concepts I would also like to show you a video on a typical sheet file failure which causes excessive loss of up to the time money and populace could be fatal even systematically if I explain there is a deep excavation very close to multi-storey buildings alright suppose you are constructing a swimming pool quite deep or maybe some carpark area alright in the basement so you can see the coming in has already started the soil mass is almost on the verge of failure such type of failures are quite challenging to control and they could be disastrous few years back there was a major failure which was in the national network very close to IIT Bombay alright during the rains I am sure you must have come across that one has to be very very careful while designing such systems which is the entire infrastructure road parking lot or the facility which has been created has already collapsed and fortunately these buildings are not sitting on this pad you know or the foundation was not provided within this pad otherwise this would have been really fatal you can type on net and see several failures which have occurred in the recent past