 Last class, we discussed factors for ground settlement. So, in this section, soft soil characteristics one factor, then shape and size and depth, then type and thickness sorry type and stiffness, stiffness of strut, then method of exervation and of course, last part is your time. Now, if you look at this, these are the factors I have discussed in the last class. What are the factors affected in the ground settlement? Because ground settlement is your prerequisite criteria as the existing structures are there. So, it should not happen that because of ground settlement, there will be any settlement in the existing structures. So, it depends upon your soft soil characteristics, but that means as I said earlier, it is either in soft soil or may be a firm soil or hard soil shape, size and depth of your exervation, how, what is your shape, what is the size and how, what is your depth of your exervation, accordingly the ground settlement also increase or decrease and type and stiffness of strut and methods of exervation and time. Now, if you come back to there are certain case studies in the Kolkata soil, if you look at this case studies in the Kolkata soil, this is settlement, settlement delta and this is your spacing and this start with 0, 1, 2, 3, 4, may be 6. If you look at this experimental investigation before starting of Kolkata metro rail, Kolkata metro rail is your best example of underground exervation or breast exervation. In this case this example means there are experimental studies particularly Kolkata metro rail means beyond a spacing, beyond a spacing if you look at here the diagram is slightly wrong. Beyond spacing, spacing greater than 4 meter, if this is my spacing it is in terms of meter and settlement delta in terms of m m beyond spacing 4 meter, the settlement increases rapidly. There is no such criteria means ground settlement there is no such criteria as I said shape, size and depth, type and stiffness of your strut, type and stiffness of your strut. If you look at here the spacing of the strut for Kolkata metro, Kolkata soil if it is increased more than 4 meter, if you look at the initially the settlement range up to 4 meter it will be negligible. It is kind of a negligible beyond 4 meter of your spacing of the strut, the settlement increases very rapidly, very rapidly this is an experimental investigation particularly Kolkata metro rail that means in this case they have considered your spacing up to 4 meter that means they have taken up spacing 3 to 4 meter is recommended, the spacing between 3 to 4 meter has been recommended as an optimum spacing. As I said stiffness of the strut how what is the spacing should be there. So, that what should be your spacing if you look at here these are the struts, these are all your struts it will hold this particularly wall in vertical position that means how rigid the strut it depends upon what is your spacing, what is your spacing between the struts. Now particularly Kolkata metro they found that from experimental investigation if the spacing has been kept between 3 to 4 meter then there is a less chance of lateral movement of your wall. These are all case studies may be it may vary from this is only for Kolkata soil Kolkata metro for Delhi metro this will be a different case study. So, these are all all depends upon your type and stiffness of the strut it indirectly depends upon your how spacing then come back to next parameter last one that is your time. If you look at the time profile for Kolkata metro this is time in days final settlement by initial settlement 30, 60, 90, then 120, 1.2, 1.4 it goes up to say 2.0 if you see look at this time in days particularly settlement it should be the construction should finish within the 30 days of time. This is based on your case study of Kolkata metro if the construction finish within the 30 days of time that means settlement less settlement will be encounter means which settlement I am talking about ground settlement will be encounter everything should finish within the 30 days of time beyond this the settlement will be more. It may possible for Kolkata soil it is 30 days it may possible that for Delhi metro it may be 40, 45 days it is varying from time to time before doing this kind of structures particularly breast excavation. These are the parameter important parameters you have to study first then you are based on this important parameter study then your recommendation will go then your design will follow. Then it may possible that sometimes what happen there are during construction as I am I am going both 2 and 4 means top bottom and back like this time has gone then now method of excavation method of construction during the construction it may possible that there might be weak joints while construction care should be taken this joint should be leak proof the joint should not be like it is it is leaking it should be leak proof. So because of this weak joints what is happen there will be a leakage of water. So by leakage of water once there is a leakage of water will start what will happen the enter part will be it will drag down that means if there is a water flowing in this joint there is a leakage. So that means it apply pressure to this wall once it apply pressure to this wall that means it will moving out moving out away from this your field. So there will be a ground settlement. Now if you look at that at the station if I go once you are starting particularly at the station these are all called these are called joints this is called steel lagging if I take this diaphragm wall what will happen at station particularly when you start at the starting point at the station you need more weight you need more weight at the starting point that means at the station because how the construction work will start you need the more weight. So to prevent that more weight you need to have your joints it should be water proof. So there is a chance there is a chance that at the beginning at the beginning they may be at the station point there will be a leakage it will start once there will be a leakage will start at the station point suppose this is your station point once there is a leakage will start what will happen because of leakage this will try to push this wall away from the field once wall has been pushed away from the field by means of water pressure there will be a ground settlement. Then come to next part this is all about your breast excavation in particularly clay now breast excavation in sand or breast caught one phenomenon is called piping in if you are doing a breast excavation particularly a sandy soil one phenomenon is called piping what do you mean by piping in piping hydraulic gradient critical hydraulic gradient critical hydraulic gradient critical hydraulic gradient under which under which particularly effective stress in sand is equal to zero effective stress in sand is equal to zero that means effective stress is equal to sigma minus u is your pore water pressure sigma is your over bottom or vertical stress. So with this sigma minus u over water pressure effective stress in sand is equal to zero how it comes particularly in case how the piping will occur. So you start doing your flow net from flow net what will happen how the drainage will occur the drainage generally excavation drainage will start from here to here. So if I increase if I increase this particularly drainage path this is your initial excavation of your diaphragm wall with this this is your flow net if I increase the drainage path that means if I increase the drainage path suppose initially the drainage is going flow is going from here to here if I increase the drainage path like this then what will happen the critical hydraulic gradient particularly effective stress will not be zero. So in that case what supposed to be done there will be at the bottom you put some strut so that it will be close form and this will act as a cut of wall that means by increasing this drainage path the hydraulic gradient will decrease critical hydraulic gradient will decrease that means it will be safe what will happen particularly in this there if you look at there are two exceptions I put this wall up to this side. So after suppose this is my requirement of this vertical excavation beyond this vertical excavation you extend this wall up to depth some of the depth. So what will happen instead of instead of the flow instead of the flow is going if you look at here the flow is going like this look at the drainage path look at the drainage path or maybe look at the flow pattern here your flow is moving from here to here it is directly touching your cutting wall cutting wall now what will happen I am increasing the drainage path from here how it is moving it is going around the periphery periphery and at the bottom it takes that means this drainage path once it has been increased immediately your hydraulic gradient will decrease then this will be safe particularly in case of sand. So this is there are two cases particularly in this case there are two cases and for Kolkata soils generally it is given by Terzaghi and others they have given some certain design charts particularly in sand will see case one and case two case one sand of infinite depth what does it mean this sand is infinite depth that means the depth of the sand will be infinite. So there is no finite below this the sand will be there up to infinite say 50 meter 100 meter there is no finite depth finite depth means 5 10 or 20 meter. So in this case suppose this is my h u total height of excavation and this is the depth below your height of excavation below this this is depth. So particularly this case the design chart has been given it can be used directly there are two cases one is your loose sand other is your dense sand. So factor of safety say 1.5 and 2.0 1.5 2.0 dense sand also factor of safety say 1.5 factor of safety is equal to 2.0. So b by h u what is your b b is your width of your excavation h u is your actual depth of excavation if you remember well earlier I have discussed this is my actual depth of excavation beyond this depth of excavation this dry phagum wall has been extended. So that this increase your drainage path that means so this is your b by h u so this is your 0.5 for different b by h u 0.5 1 2 3 and 4 1.0 2.0 3.0 and this is 4.0 and this is 4.0 so this will be coming 1.2 1.75 1.05 1.7 1.1 1.50 0.85 1.3 for 2 0.9 1.20 0.60 0.9 and 0.8 1.05 0.5 0.75 then 4.00 0.75 1.04 0.5 and 0.7 these values these values your d by h u d by h u means this d is unknown this d is unknown beyond this depth of excavation what should the value of d I should go so that the critical hydraulic gradient will be less or minimum so that this in drainage path will be less than 0.5 0.7 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0 0 0.5 so this d has to be calculated based on this experimental investigation laboratory test terzaghi and others they have proposed this is your design charts for loose sand as well as dense sand taking factor of safety 1.5 two 0.0 and 1.5 and two 0.0 so different value of b by h u suppose if I say b by h u equal to 0.5 that means b value of 0.3 h u of 0.51. So, it is ratio of width to depth ratio of width to depth for particular that ratio of width to depth suppose you are taking a factor of safety suppose you are saying that I will provide a factor of safety of 1.5 then what is the value of d by h u 1.2. So, h u you know so d value will be 1.2 times of h u. So, beyond this it has to be extended. So, that it should not piping effect should not occur in this case. Now, case 2 sand of finite depth case 1 is your sand of infinite depth now case 2 will be your sand of finite depth sand of finite depth means after depth d there is a sand layer after depth d there is a sand layer of h 1 very close to your depth of exhibition that is why it is called sand of finite depth that is why it is called sand of finite depth in this case in this case also they have given certain design charts these design charts are based on your experimental investigations by Terzaghi et al or Terzaghi and others authors Peck also there. So, based on that this design charts has been arrived. So, if I take it b by h u suppose say this part I am writing this part I am writing h 1 by h u h 1 by h u is equal to 1 then here h 1 by h u is equal to 2 then in this case also h 1 by h u is equal to 1 then h 1 by h u is equal to 2 now this is for this is for factor of safety say 1.5 factor of safety this is for factor of safety say 2.0 and these values are like 0.7 0.55 let me write all 0.4 0.35 and 0.35 1.1 0.8 0.65 0.45 0.45 0.8 0.75 0.5 0.5 0.5 1.5 1.1 0.65 0.55 0.55 now these are all values to find it out d by h u other cases if sand of infinite depth in that case there are 2 cases consider 1 case is your for loose sand and another is your dense sand, but sand of finite depth we have not consider in terms of loose or dense it has been put it h 1 by h u h 1 below the depth of exhibition this is the depth of exhibition below this extended depth of your wall and below this at what depth this sand is there up to this sand layer is there h 1 by h u h is your your exhibition depth of exhibition it is 1 or 2 1 or 2. So, based on that there are different value of b by h u then you can find it out once you know this this is given value b is given h u is given once you know the b by h u value then one you can decide what value you are suppose to take h 1 by h u is equal to 1 or h 1 by h h u is equal to why there are 2 value has been given based on these the other factor of safety has to be checked as I have discussed with your piping and other whether it is satisfy with the bottom if any any possibility this other factor of safety has to be checked based on this value suppose with this h 1 by h u is equal to 1 and b by h u is equal to 0.5 with this you are getting d with getting this value of d suppose other factor of safety are not satisfied what you are suppose to do either increase this value of d or if you are not increasing you can take h 1 by h u is equal to 2 then check your other factor of safety that means these are the range where this factor of safety other factor of safety has to be satisfied. So, let us see let us see one one typical example before we will go for a complete example how to solve or complete problem of your breast excavation complete design problem now this is the value of given say b is equal to 10 meter h u is equal to 8 meter and d value is not given d either way either you choose d value of arbitrarily arbitrary value of d or check whether this factor of safety is coming within that range or not or you take that factor of safety find it out your value of d. So, in this case d has been chosen arbitrarily and this is your h h 1 this is a finite sand of finite depth. So, let us say assume d is equal to assume d is equal to 4 meter and how this d has been assume this d has been assume taking into consideration of less than half h u if you start assumption of d then you take the value of d which should be less than half of h u less than equal to if it is 8 meter. So, half of h u less than equal to is your 4 meter. So, d has been assume is equal to 4 meter. So, h 1 h 1 also once d has been assume this h 1 is equal to because this total depth is given. So, h 1 also you take it 7.5 meter. So, h 1 by h u which is equal to 7.5 by 8 approximately it is coming 1. So, from table h 1 by h u is equal to 1 h 1 by h u is equal to 1 with your b by h u b by h u is how much it is coming b is equal to 10 by 8 1.2 or you can extra point the value between 1 and 2 this value extra point and find it out what is the value of factor of safety. So, h 1 by h u is equal to 1 and factor of safety I am taking is equal to 1.5 it is generally normally we take factor of safety of 1.5 then b by h u is equal to 1.25 then from there once it is 1.25 you find it out value of 1 what is the value of 1 what is the value of 2 how much it is increase then for 0.25 how much it is increase then you add it with your 1 1.25 how this this is the way you have to extrapolate this value from this table. So, once you get this so 1.25 factor of safety is equal to 1.5 then d by h u is equal to d by h u which is equal to 0.5 that means d is equal to 4 meter. Now in this case what will happen if you look at here in this case what is there I put arbitrarily value of d is equal to 4 meter means d value should you choose it there is a thumb rule less than equal to half of h u I can take 3 meter I can take 2 meter with the assumed value of d you proceed the calculation and take your factor of safety value of 1.5 with this value of factor of safety 1.5 find the value of d if d is not coming with this value whatever the value d is coming next iteration suppose here I am taking suppose here I am taking the value of d is equal to let us say 2 meter. Now here d value is coming so 2.5 meter that means these 2 are not matching then next iteration d you take 2.5 meter calculate like this you go both the d will be approximately it should be matching whatever assume whatever calculated then this is your value of d once you get the d and draw then afterwards you draw the flow net and check your other factor of safety how it is coming whether it is satisfy or not will solve a complete problem in the next class 2 problems next or next to next class 1 is for cohesive soil other is for sand thanks a lot.