All right Well, we'll maybe we'll talk after class that you have to speed a little bit But for your information, too, I'm taking this class and dynamics So if you don't want to be caught on camera, don't come up here They for this homework set I put up Spolt chat both editions of the book both the seven Sammy eight edition book I just put them up there That's some of you mixed and matched some of you. I don't know what you did so You can now check your problem see if you did okay on right any questions Where are we still let's see We're still a bit away from the first exam, so we're okay And you click everybody's TJ Right. That's where you go by TJ. Yeah, that's that's You're out you officially appeared so is that your full official name? We'll find out what it that's DJ. He's your little brother I don't know. What's what's de-steem TJ doesn't stand for anything I That's always amazing when people Name a kid something and then immediately go to some nickname of that. Why didn't you just name them then the first place? My brother is not Daniel. He's Dan because that's what my folks wanted at all So are you the junior? Yeah, so are you DJ? Yes Okay Well, people will be able to track you All right, if you remember we were working on on Tuesday on Strings we come up with one and Like the stresses there's more than just one but all we had on Tuesday We come up with on Tuesday was what we call The normal string. Oh by the way all the Videos I think are up to date on itunes you You miss something But you guys want to don't miss a what you can't you can catch up the entire semester Only take about eight hours to download But how long they took me to upload? I need to download Press them and upload and all that took about four hours a class hour The thing I had two days to do nothing All right, we had the normal strain remember what that was what was our symbol for normal strain Excellent actually I believe a lower case epsilon to find as This is this is what we're finally doing here is actually looking at how these materials these engineering materials Deformed so we're looking at deformation of these materials For the most part in engineering sense what we're looking at is elastic deformation It's okay with it's it's not that it's okay that these things to form is that it's unavoidable When things are under some kind of load There's going to be some kind of deformation in these realistic materials in these real life materials that we're finally looking at What what is the the design concern is that we Understand these deformations allow for them and then expect them to disappear when the load disappears Just like when we unload a spring we expect it to go back to its rest length. That's kind of the thing We're expecting here that these materials Will respond to this load respond predictably to this load And then respond to Predictably to the removal of that load. So this was our first real look at a material in deformation under load Remember how it was defined from Tuesday? Not new notes What did you do on Tuesday? Dell Over L Dell being the amount of the deformation in our simplest picture We imagine some piece under some simple axioload whether it's Tensile load like I drew there or a compressive load. It doesn't really matter what happens is in tension we expect a an elongation of The material and that will make them the strain positive L being The original length so it's the change in length over the original length often Often put as it as a percentage if you look through some of the problems yet in this or You remember the load that we did on Tuesday These are very small numbers on the order of 10 to the minus 6 So very very small numbers as we're finding out as we go through this stuff We really got to keep an eye on The units anyway, so let's warm up problem So here's a here's some kind of axial some kind of some kind of member Under some axial strain and We're going to look at two of the possible deformative responses of this One let's imagine Well, we don't imagine it does that it elongates by some measure But since the volume is constant Not only does it elongate But it's going to narrow down a little bit It is a very same thing when you when you stretch a rubber band or something if you look at it closely If you stretch it enough you'll see that not only does it get longer, but it also gets narrower So we're going to look at this response. Of course exaggerated in this picture Start with an original length of 500 millimeters We have an elongation here of 300 micrometers an original diameter of 16 millimeters and A change in diameter We may all call that Dell sub D for the change in diameter minus 2.4 Micrometers so in this case we have actually two strains we need to look at we need to look at the strain in the Length direction the axial direction, but we also need to look at the strain Across the diameter So just as a warm-up sort of get used to the numbers again that we're working with here That's your warm-up problem in here yet. I put the Solutions from both addition sets up there Remember, I don't grade these so much for specific Content you can check the results itself as much for for Your ability to lay out a problem of solution Itself that we may have a focus a little bit better. That seems you can see some of the numbers now. So First couple days are a little sketchy All right easy numbers to work with You need to keep track of the the magnitude of these things but also and I kind of took care of it for you anyway take care of the Plus in the minus signs because we do have strain possible directions. We got to know which of this class is on the scene I don't remember that first day Never in the same sense for it Degree you were what? Yeah, I didn't get to do that physics one this year because I preempted That with an email to everybody's was it jettison couple From a distance, which is you know, it's kind of like firing somebody fire somebody without an election will come in The eyes a lot easier Remember that if you ever become a manager somewhere hello Brandon We got everybody here today Cancel class and celebration All right, what do we got should all agree certainly we can divide two numbers by two numbers DJ GDX has this calculator here today, so There's no trouble then Do you agree? Everybody agree? You don't know That we got a little Terrorist cell over here and a little terrorist cell over here and the gulf between New is Micro tends to be about the the magnitude of these these type of numbers in the strain Calculation so everybody agreed that this little this little conclave Here and over here this group's not talking to each other. You'll sit together, but you're going to communicate with each other Jake's Desperately trying to cross the goal and trying to try to reach out of hand That's had nothing to do with it What do we have on this one remember there are thousand different ways to present it your choice So Pat, what'd you do? 60% 60% if it was that long it's now this long 300 micro meters. Yeah, watch this stuff This is this stuff is very very sensitive to them the magnitude on these numbers That's the thing you have Whole bunch of different ways to present back one of I guess the accepted way is just to say 600 Micros, but I think that agreed with what everybody said the six times 10 to the month fourth It's it's a it's a bit of a It's a well, it's a bit of a hangover a hold over Whoops a bit of a hold over from the old days that generally try to keep the The powers on the 10 to multiples of three That's where the best known Science si prefixes are it's a bit of a whole over from the years the days when we used to use slide rules to calculate this stuff So rather than a six take six times ten minus four six hundred times ten to the minus six Or six hundred micros is generally a little bit more acceptable though. Your number wasn't all just to make communication with the Old white man you're going to be working with when you actually get to an engineering firm because that's what the vast overwhelming of Presenting them are you'll be able to communicate with them? How about the strain in the diameter? diametral direction Jake No, I just want the answer. That's what you got all the answer boom The new guy making friends fast By when you have DJ is negative remember we need to know what direction this goes in One way to pretend Micro all right, so good start on This simple Division of one number by another It's been back to the days teaching math one away We're gonna do that stuff with them. All right That's just a review or reminder for us now. We'll look at the other type of strain that we look at in this class Again like this one Very very much depends upon your ability just to see the geometry in the in the problem So we'll start with a look at a simple Element of some type whether this is actually a piece of the material or represents the physical Description of a small square on a material which is one way that these type of strains are are determined for the purpose of illustration will imagine that one side is Secure to some immovable object of some kind and that there's some shearing force Across the top we'll give it a side a height of L there The width is not a concern to us in this At least in the geometry shown, but the height of it is the response of this then is For this element to deform in That way due to this shear stress, so this is called shear strain What we're concerned with here is the response in an angular way, so We'll again call that Dell Book this orientation we tend to call that Dell x so the shear strain then is Defined as that's a lowercase gamut This will be the average shear strain defined as that deformation Over the original like essentially what that is then is The is the tangent of that angle that's formed For very very small angles, and you can check this on your calculator if your calculator set to radians for very very small Angles the tangent and the angle are the same You set your calculator radians put in a very very very small angle Take the tangent of that you'll get essentially the very same number back except for several Several decimal places down the road So it's an angular deformation as you might expect from the response in the material to shear Deformation if we if we look at the limit as L approaches zero of this average shear then we get the the Precise shear at that angle that can be more of a concern if we have a material That responds in a slightly different way than the implied shear It could depend upon the material it might even depend upon how the material is fastened down where it might deform something like that where then we do have a Different angle of the shear down here, then we would have got We would have gotten if we take in the average We're not going to concern ourselves too much with that kind of precise detail Since this is an introductory class into this so there's there's I guess the notion sort of of a instantaneous shear just like we had when we develop the Calculus of limits in the first place All right some of the some of the greater details of this if you remember also on Tuesday we set up a look at the Shear across an entire element Determine that there could be shear stresses like that Under that kind of load the material will Deform again in a highly exaggerated sketch Would deform something like that Remember we're talking about very very small Deformations or couldn't possibly sketch those bless you so we're very much concerned with With the full picture here So this is a a deferment a change in a 90-degree angle in response to these Shear stresses so it's the 90-degree angle then minus Minus the shear that we're seeing back here So if you think about the geometry a little bit If we brought this down so that these bottom two surfaces are the same we Pretty much have this same drawing here So it's just a in essence a slightly different way then to to look at the two different problems another possibility is That the shear stresses are in the other direction then the response of the material is Hard to draw yeah, I might do something like that under shear stresses in the other direction this will give us a positive shear stress response this we consider a Negative shear spot the shear stress response But either way they're they're calculated in the same way.  Oh, and are you in that? You're doing better More and more cognizant of what you're putting down a little bit Okay, all right, so that's that's the setup for it for for these problems again, it's a lot of the problem is just a Geometry problem So we'll look at a couple simple setup simple possibilities of What we can do with these all right, so imagine we have a thin plate of some some rectangular size 720 by 480 millimeters in original unstressed Dimension and then due to some applied load we get a response again, of course Exaggerated something like see that All right, so I'm still happy. I don't want Oh There's a All right, so that's a little better. There's there's the exaggerated response of this to some shear stress You can see we have two Places where we have the shear strain So we need to look at the response here. We'll call that 0.5 Millimeters and the one down here 0.25 millimeters. You can figure out the Shear strain from that Again, just a geometry problem One of the things we're looking for is the total Shear strain here where that gamma is two shear strains put together think about the geometry to change remember in that Original 90-degree angle always in this class and your others be very careful with your units We're talking about angular changes here Expression is it radians? Usual Love the idea of buying a fourth grade or a hundred dollar calculator I have to keep my editorial comments and my death threats really only two choices to make We tend to turn those two choices once right one's wrong. So let's see what we figure out which is which How you got that Left yourself bad notes. Do you ever look at your notes again? Oh But if you ever go to publish them for journals, you got that here to very strict DJ agree with anybody or still feeling kind of socially isolated Oh Do you agree this is my favorite group Never had force dudes on average Did you agree? Did you guys sort it out somehow? Yeah Well for you, and you're still not talking to TJ All right, let's see general definition whatever deformation we have here along the Topics that happens to be in the x direction Generally, it's on here. It's not too Terrifically important here 25 millimeters over there, and then the discussion the back here was which goes under it Would you finally decide what goes under that point five seven zero? 720 But where were the units? I'll just keep the units the same between the two And you'll be okay, and I'll just cancel and you left over whatever number you're left over What we get for that one is positive in this case? Yeah, six ninety-four of my brothers micrometers per meter or What are one of the other 25 different ways to look at it? Sigma two or a gamma two This year straight in the other direction. I guess that would be fine LX like that Hey, you know what to put for that. You guys agree on that one, too. Finally, who was right? It was wrong What he was right and wrong? Is this a positive or negative? This one's also positive by convention and so the strain in that direction then was 521 micros and then the total strain Was the sum of those two? Which is what 12? 15 an angular deformation your question was Units radians it if you put in degrees which you could I guess no reason not to but That's There's no reason to Since this is sufficient for or what's understood for the strength the sheer strength All right already tired two solid days and clearing my driveway since nobody came down for extra credit to help We a mile away like you don't it's in the sheriff file I think the sheriff knows exactly which one of you knows where I live and which one doesn't All right What in the tape back? What I know exactly what you said No on that one we did have that that If we wanted that angle, yeah It's it's a I know I find this a little bit confusing I don't know I don't this is not my my engineering background in this field, so I Find it a little bit confusing that all the different ways they report some of this stuff So I don't know sometimes it just seems like the game. All right, so it's Friday So let's do a Get out of class question. There's the original shape. It's a square Ten inches on the side. It's original unstressed for when stressed the response is In the y direction the response is something like this You can you can do an entirely different problem if you'd like from the response, of course exaggerated is something like that 0.2 inches That's 0.3. So I want you to find those Strains call this and down here also find Significantly that's a gamma key Along along one of the edges First person to get that it's million bucks Anybody gets a quarter in class gets to leave her been shown time and time again with the proper motivation People will rise to the channel Jury how many millions can you have It's pointless after you offer double figures for a number of millions not sure it's strain. This is remember. This is the normal strain Along one edge problem. What are you doing? Let's say you're not quite right. Good idea. I Would check it. It's not really good, but you got the right idea. Just check your numbers almost if you're having on it is with Not the upper number more. Let's see in the x-direction. It's Well, it's a decrease so it's a minus zero point three inches Okay, if you guys catch the minus But then remember you divide it by the original length the original length of that piece that now decreased by point three Is that piece there? That's the piece that that's the direction that decreased by The point three inches Doesn't matter you get the same thing That length across there is 207 then the same type thing in the y-direction only it's a positive increase Get these minus sign when Appropriate swear that's gonna be on my gravestone and finally missed a minus sign That makes sense now you see that and for the one on the edge It's the same type of thing the original length of an edge is 10 inches The new length of an edge is Whatever this full diagonal length is So you have to do a little category and they're I mean Come up with that Normal stresses. What was that? What's the new length of the edge? Are you doubled it? Yeah, you don't want to double that one It made sense to double the other ones if you wanted to but this one ten inches isn't actually double It's a single single length So yeah, take this decrease length over that increase length Yeah Yeah, but remember you don't want the original or you don't want the new length here you want to change Yeah Yeah, that's why I get point 066 Thank you All right, that's that's just stuff to work out right at the end now so Let's at least lay out how you're gonna find the shear strain remember this here's called theta p That's pi over two minus the shear strain. We're looking for So this is pi over to the original 90-degree angle minus Whatever that angle isn't you can figure that out from the geometry you're given So that that number there then is you take it back in the class on Monday. Oh No, we're looking more like micro rags. Well, hang on. Let me see. No, well, we're that's still pretty darn big by a factor of Something


I've been I mean I've been trying to figure that out ever since I came out of the game. You know I just watched the tape felt like felt like I couldn't get him to swing a miss I had zero swing misses so that that's kind of the biggest red flag a lot of close pitches that were taken really good at bats by them and you know when I did throw it over the middle they hit it really hard so it's obviously a recipe for a disastrous ending but I don't know I've never quite had it in quite like that before so just trying to digest it now a little bit how tough is that to take especially considering the state of the team right now it's tough it's the worst feeling in the world you know you let you let your team down and you know we really wanted to win tonight obviously been grinding here as a unit so it hurts a lot but you know that's the nature of the game you sign up for it so try to put it behind behind me and behind us and keep going forward. Take the next one from Marley Rivera. Hi Adam you're someone who is always very accountable how difficult is to be in the clubhouse today knowing how important this game was for your team. It's it's it's always tough when you're the you feel like you're the reason why I lost the game so you know it's always tough I mean I've been in a situation a few times with the teammates so you know it's nothing new know how to handle it but at the same time I mean you know obviously I want to do better and feel like I should always do a lot better than that so it's just it's just a tough feeling but like I said you try to take the emotion out of it because it's over now I can't change it now. Are you someone that can turn that page very quickly? I've gotten better at it over my career but my personality is to hold these things with me a little while I mean say the truth so but again like I really try to do a good job of stripping away the external noise and the emotion behind it and get after it tomorrow and try to be confident and you know get on a roll here. Thank you very much. Thanks. Next one to Kristi Eckert. Hi Adam you said that when you don't get the swings and misses like that that's a red flag for you what is it a red flag that it indicates to you what does that indicate that's coming? It's just bizarre I mean my myself and Greeny didn't get any swing and misses that whole inning that you know we're both well above average swing and miss pitchers so kind of rely a lot on that I'm not pitching a contact out there I'm trying to strike eyes out so not getting swinging misses it's an indication that either my stuff wasn't wasn't good my location wasn't good or that they had something on me you know they had a great approach or knew what was coming or any of that but I don't have any of those answers right now all I know is that I didn't get it done and I got to go back and look and look inside myself figure out figure out what to do next.


Let us start our today's lecture for this NPTEL video course on Geotechnical Earthquake Engineering. So, for this video course, currently we are going through module number 9, which is seismic analysis and design of various geotechnical structures. Within this module 9, a quick recap what we have learnt in our previous lecture. In the previous lecture, we discussed about seismic design of waterfront retaining wall or sea wall. So, what we have learnt that generally this kind of waterfront structures or waterfront retaining wall, which are provided to protect the shore and the properties from the sea. Those are nothing but generally massive structure to defend a shoreline against wave attack and design primarily to resist wave action along the high value of coastal property like we have in Mumbai also in Merindrive. We have also seen that what are the available literature on the individual work on the area of earthquake engineering for retaining wall design and on the tsunami and hydrodynamics effect on these waterfront retaining structures by these researchers. But none of them had considered the combined effect of this earthquake and tsunami together because citing that both are extreme events. It is highly not so possible that both the events are occurring together. However, in the very recent 2011 March Tohoku earthquake in Japan, entire world had experienced that from the experience of Japanese in Tohoku region that along with tsunami even the post earthquake or aftershocks of considerable magnitude can come which need to be considered. So, that is why it is very important to study the combined effect of this earthquake along with the effect of tsunami on this waterfront structures or retaining walls. So, for this sea walls design what are the basic two things needs to be considered as I have already mentioned this is the PHD thesis work of my second PHD student Dr. Sayyad Muhammad Ahmad who completed his PHD in 2009 at IIT Bombay and currently he is a lecturer at University of Manchester in UK. He studied for his PHD program under my supervision at IIT Bombay that the for design of waterfront retaining wall or sea wall basically two important aspects or two important cases will arise. One case is when tsunami is attacking the wall and another case is when tsunami is receding away from the wall or going back to the sea. So, within both of the cases the major two aspects are one is sliding mode of failure and another is overturning mode of failure both in this case as well as in this case. The first case can be referred to as passive state of earth pressure whereas the second state can be considered as active state of earth pressure based on the movement of the wall towards the backfill soil or towards the shore. So, as we can see here when a wall is standing like this and suppose this side we have wave that is water side and this side we have shore or the ground side with backfill soil. So, when the tsunami wave is hitting this wall wall tends to move towards this soil. So, it is a passive state of earth pressure that is tsunami attacking the wall and after it over tops the wall after sometime through weep hole etcetera the water goes back to the sea. So, the tsunami always recedes back and goes back after sometime to the sea that time it drags the wall towards the sea side that is it moves away from the backfill soil which is nothing but active state of earth pressure. So, both these state of earth pressures are considered along with the tsunami wave pressure and earthquake forces acting on the wall. Then we had seen this basic diagram how the model has established by Dr. Ahmad. So, this can be found out in the detail in journal Chaudhary and Ahmad 2007 in journal Applied Ocean Research published by Elsevier this is the volume number and page number. This case is for the passive case using pseudo static approach of earthquake loading. So, this is the direction of wall movement which is nothing but the passive state. This side is the shoreline or ground surface with backfill soil at a certain height there is a water table whereas, this side is upstream side where there is water. So, this is the height above the steel water level which is nothing but the height of the tsunami. This is tsunami wave pressure then this is hydrostatic water pressure these are the inertia forces acting on the wall and this is weight of the wall along with this is the passive earth pressure acting from the soil side. So, considering the equation of hydrostatic pressure or pressure force given by Westergaard this equation p hydrodynamic and the tsunami wave pressure force the equation as proposed by Crater and considering the variable other parameters like average unit weight in the downstream the passive earth pressure on this side has been estimated using this equation and also from the downstream side the static pressure and from the upstream side the hydrostatic pressure are obtained using this relationship. Then we had seen that for the passive state these are the results which shows the factor of safety against sliding mode of movement with respect to various seismic horizontal acceleration coefficients k h value and for various height of tsunami height of the water compared to the static height of the water in steel water level. So, when it is 0 then that means there is no tsunami but when the tsunami starts coming there can be variable height. So, based on that we found that factor of safety against sliding for this water front retaining wall or sea wall is significantly decreasing as the seismicity is increasing like with increase in k h as well as as the tsunami wave height is increasing. So, the combined effect can easily be obtained from this proposed design chart by us suppose at k h value of 0.2 g there is a height of the tsunami wave height say 1.125 then we have to go to this line at this point this will give us the factor of safety of the wall against sliding for a chosen other input value as shown over here. So, if it is not satisfying the stability criteria of 1.15 minimum factor of safety against sliding under earthquake condition then we have to redesign this wall section to withstand both seismic acceleration as well as the tsunami wave height at a particular region. And this equation gives us the closed form solution factor of safety against sliding using which one can easily design the cross section of a retaining wall to withstand certain value of seismicity coefficient as well as the tsunami wave height. Similarly, for factor of safety against overturning mode of failure also the closed form solution is given over here and the variation of that factor of safety with increase in k h and with increase in tsunami wave height is shown over here. Another case that is design solution for the active state of earth pressure that is when tsunami wave is going back to the sea using the pseudo static approach for earthquake loading it has been proposed the solution or design solutions are proposed by Choudhury and Ahmed in 2007 this journal paper Choudhury Ahmed 2007 in the journal ocean engineering published by Elsevier this is the volume number and page number you can see the factor of safety against sliding mode of failure when we are considering this mode that is when tsunami wave is going back to the sea that is receding back in that case for each of this mode of failure that is sliding and overturning we have two different conditions what are those two different conditions as we have discussed in our previous lecture it is based on the permeability of the backfill soil and also how the drainage through the wall using weep hole etcetera or filter design etcetera has been provided. So, based on that one condition can be free water movement that is when the permeability of the backfill material is good as well as there is a free drainage provided in the wall section. So, that no water stands in the backfill soil when tsunami is going back to the sea, but there is a possibility or a case when the permeability of the soil is not very high also the design of filter drains and weep holes are not properly designed in that case it should be considered as restrained water case in the backfill. So, considering these two criteria as I have said factor of safety against sliding small r denotes restrained water condition and small f denotes free water movement condition. So, under both these conditions we can have the closed from solution of factor of safety against sliding similarly for factor of safety against overturning restrained water case as well as free water case are proposed by us using by giving this equations. And the results shows typically over here like factor of safety against sliding with respect to k h value as we can see k h value increases factor of safety drastically decreases for this chosen input value and the variation with respect to the restrained water or free water case also can be seen over here. So, in this case as we know tsunami wave height does not matter because tsunami is receding back or going back to the sea. Similarly, factor of safety against overturning also dependent on the values of k h k v and other input parameters like restrained water height condition and free water height condition. Then we had discussed in our previous lecture also about this active state of earth pressure for water front retaining wall using pseudo dynamic approach of earthquake loading. So, for pseudo dynamic force this is the direction of wall movement because it is the active state tsunami is going back to the sea. The details are available in this journal paper Choudhury and Ahmed 2008 published in the journal of waterway port coastal and ocean engineering of ASCE USA. This is the volume number and page numbers and the results of factor of safety against sliding and overturning with respect to k h values are shown over here and compare this present study results with the available results in the literature as proposed by Ebeling and Morrison in 1992 which is used by US Army Corps of Engineers for design of sea wall or water front retaining wall. And you can see the present study gives the critical solution compared to the pseudo static result because pseudo dynamic results considered the dynamic effects of this earthquake forces and tsunami forces effectively compared to pseudo static result. Next we had also discussed the seismic design of reinforced soil wall in our previous lecture. We also mentioned as given by Tatsuyoka in 2010 that during and after 1994 Kobe earthquake in Japan it was found that geosynthetic reinforced soil wall they survived that big damaging earthquake of 1994 Kobe whereas the conventional structures or conventional buildings and walls they could not sustain that or could not survive that huge magnitude of earthquake of 1995 Kobe. It automatically shows the application of geosynthetic reinforced soil wall which can withstand more earthquake loading compared to conventional retaining wall without reinforcement. Then we talked about the analysis for reinforced soil wall to make it earthquake resistant design considering the internal stability criteria because there are two stability criteria for reinforced soil wall one is internal stability another is external stability as we have discussed in previous lecture. Internal stability looks into the aspect of failure of this reinforcement within the soil in terms of pullout in terms of strength of the material. So this is the reinforced soil zone in which each layer through each layer there is a infinitesimal small element was considered and the forces acting on that element is shown over here through the analysis using pseudo dynamic approach for by considering the seismic horizontal and vertical accelerations as given by these equations. Finally the strength of the reinforcement required to withstand a particular magnitude of earthquake is proposed by this non-dimensional parameter K and T j is the strength of that reinforcement in j th layer and the length of that layer to be provided for thus pullout resistance stability is expressed by this expression. This analysis is available in the journal paper of my first Ph.D. student Nimbalkar et al 2006 Nimbalkar Choudhury and Mandel 2006 published in the journal Geosynthetics International published by in institute of civil engineers London UK. This is the volume number and page number. We have seen the results that finally the design charts were proposed like how much reinforcement force is required for different values of k h and k v. So using this design chart one can easily estimate the amount of reinforcement strength required as well as how much is the length of that reinforcement is required to be provided against pullout failure of this reinforcement for a particular value of k h and k v through this proposed design charts. Then we had compared our results the pseudo dynamic results of this geosynthetic reinforcement strength as well as the length required with respect to the previous researches result who use the pseudo static approach like Ling and Lechensky's results and Ling et al 1997 results and Shagoli et al 2001 results for various values of seismic acceleration coefficient. We can find here that the present study of using pseudo dynamic approach always gives a critical design which automatically shows that importance of using the pseudo dynamic approach compared to conventional pseudo static approach. Then we had also discussed in our previous lecture about the external stability criteria of this reinforced soil wall where the reinforced soil zone has been subdivided into two portions. One is wedge A two zones wedge A triangular wedge and wedge B is rectangular wedge both sliding as well as overturning stability in terms of this external stability criteria was considered and the entire analysis can be obtained in the journal paper Choudhury et al 2007 Choudhury Nimbalkar and Mandel 2007 which is published in geosynthetics international journal published by institute of civil engineers London. This is the volume number and page number and finally, the results are shown in terms of required length of reinforcement for direct sliding stability as well as overturning stability for a particular value of k h and k v. So, when somebody is designing this reinforced soil wall they need to provide the reinforcement strength as per the internal stability criteria as we have discussed and the length to be provided in terms of either external stability both sliding and overturning and considering internal stability of pull out criteria among these three whichever gives maximum length that needs to be provided for this earthquake resistant design of reinforced soil wall. Then we had compared our results of pseudo dynamic approach with respect to Ling and Lachansky's 1998 results in terms of non-dimensional length to be provided to withstand the direct sliding for different seismic acceleration as you propose by using pseudo static approach and one can find out that pseudo dynamic approach gives the most critical results. So, with that we had completed our previous lecture. So, in today's lecture we will start with the seismic design of waterfront reinforced soil wall. In waterfront reinforced soil wall also the similar method has been adopted using pseudo dynamic approach. This is the waterfront reinforced soil zone, this is the upstream side and in this case both linear as well as poly linear failures were considered for the analysis by Dr. Sayyad Ahmed under my supervision at IIT Bombay for his PhD thesis. So, this details are available in the journal paper Ahmed and Choudhury 2008 in Geotextile and Geomembrans Elsevier publication this is the volume number and page number. This linear failure surface is just for the sake of academic interest, but as we know from the experience that mostly at side the poly linear failure surface like this will get formed. So, we have provided the results and compared the results for both the cases considering also the hydrodynamic pressure as it is acting for the case of waterfront retaining structures using this reinforced soil wall concept. So, this is the final design chart here again the how much reinforcement strength is necessary to withstand the hydrodynamic force and also this earthquake force of k h and k v different magnitude. One can use this design chart to get this non dimensional parameter of reinforcement strength which is necessary to be provided for stability. Also the external stability criteria for reinforced soil wall used as waterfront retaining structure was considered using two wage mechanism wage A and wage B considering both direct sliding mode of failure as well as the overturning mode of failure and the details of this external stability analysis are available in the journal paper by Choudhury and Ahmed 2009 in published in the journal Geosynthetics International Institute of Civil Engineers London UK this is the volume number and page number. And the results here again the design charts have been proposed to calculate how much reinforcement length is required in the non dimensional form the design charts are provided. So, that designers or practitioners can use it very effectively and easily for different values of input seismic acceleration how much value needs to be provided for overturning mode of failure similarly for sliding mode also the values have been provided. Then this table shows the comparison of pseudo static approach results as given by Ahmed and Choudhury in 2012 compared to pseudo dynamic results of Ahmed and Choudhury 2008 which we have mentioned just now. You can see over here that the value of this k that is the reinforcement strength which is required as far as pseudo dynamic approach and pseudo static method is concerned you can see pseudo static method in this case is giving higher value. So, it is not always necessary that pseudo dynamic will give the lowest possible value it can depend on the various input parameters etcetera. So, for the water front retaining wall reinforced soil case we found that pseudo static results are giving the optimum value or the design value or critical value of results. So, these details are available in the journal paper Ahmed and Choudhury 2012 published in journal ocean engineering published by Elsevier this is the volume number and page number. Now, let us come to next subtopic that is seismic design of shallow footings. Now, shallow footings or shallow foundations we use extensively for several structures like small buildings like one story or two story building at various places. So, how to make these foundations earthquake resistant or how to design this foundation to withstand certain magnitude of earthquake. So, that there is no damage this topic will mention as how to design those shallow footings or shallow foundations which can withstand certain magnitude of earthquake depending on the soil conditions. So, this is the analysis you can see over here this is the line diagram of a cross section of shallow isolated strip footing this is the width of the footing B this is the depth of embedment of the shallow footing D f and as per Terzaghi's definition if it is shallow footing then this ratio of D f by B should be less than or equals to 1 and this is the length of the footing this length has been considered much larger than this width of the footing. So, that we consider as a strip footing for the analysis as Terzaghi did for the static case of bearing capacity factor determination this dotted line shows the typical failure surface as per Terzaghi's failure mechanism is concerned. Now, this dotted line is actually symmetric under the static condition. So, whatever we see on this side the similar thing we can find on the other side under the static loading condition. However, it is not the case in case of the seismic loading why because at seismic loading when we are considering the pseudo static approach for the seismic loading suppose k h is the horizontal seismic acceleration and k v is the vertical seismic acceleration the net effective load in the vertical direction will be 1 plus minus k v q u d is nothing but ultimate bearing capacity of the soil times this B width of the footing. Now, this q u d we need to estimate as far as Terzaghi's method in static case is considered we need to find out in dynamic case for the proposed solution as we are detailing over here and k v is vertical seismic acceleration it can act in both upward as well as downward and we need to consider the critical direction which gives the minimum value of this bearing capacity under dynamic condition and at one instant this k h value can act in this direction. So, that it gives us one sided failure mechanism because if it acts in this direction obviously the other side the full passive earth pressure is not going to get developed because of that it will not develop a failure surface in the other direction, but it will develop failure surface only in this direction. So, it will be one sided failure mechanism like this and these are the three typical zones under the seismic condition the details of this can be obtained in the journal paper published by Chaudhary and Subbarao this is the part of my ph d thesis work under the supervision of professor K S Subbarao at I S C Bangalore this paper Chaudhary Subbarao 2005 is available in journal paper geotechnical and geological engineering published by Springer this is the volume number and page number. So, the forces acting on this three different zones. So, this is the failure mechanism this is zone one zone two and three is nothing, but we can imagine this d e as a imaginary retaining wall as was considered by Terzaghi for static case also, but in this case it will be all the dynamic forces and this exit angle will no longer be a static angle, but the dynamics exit angle and this what are the important changes with respect to static and static these two angles are equal as we know for Terzaghi's analysis with rough footing this is phi value where as in this case these are non equal alpha one and alpha two alpha one will be more than phi and alpha two should be less than phi. So, we have to find out what should be the value of these two angles corresponding to this will be full phi that is one sided failure mechanism. So, this angle of internal friction between this zone and this zone which is nothing, but phi soil friction angle, but in this side where the full passive pressure is not getting developed this m factor is a factor which is less than one it will be equal to one under the static case when both the sides are getting formed with the same failure mechanism. So, this phi two value that is the mobilized interface soil friction angle will be lesser than this value of phi. So, we have to do a iteration of these all parameters involved in the analysis and finally, we got the design charts which are proposed in terms of the bearing capacity factors under dynamic condition and this is the proposed equation which can be used to calculate the dynamic bearing capacity q u d equals to c n c d plus q n q d plus half gamma b n gamma d this is the extension of terzaghi's theory from static case, but d indicates the dynamic cases. So, n c d is the dynamic bearing capacity factor in terms of cohesion n q d is dynamic bearing capacity factor in terms of surcharge and n gamma d is dynamic bearing capacity factor in terms of unit weight. We can see that as k h value and k b value increases for different values of soil friction angle phi there is a significant decrease of this bearing capacity factor. So, at k h equals to 0 and k v 0 these values are nothing but the static bearing capacity factors which are equal to the terzaghi's bearing capacity factor as we had extended terzaghi's method, but under dynamic condition our present study shows the critical decrease of this bearing capacity factor which need to be considered at a particular site knowing what is the value of input value of k h and for particular value of phi then for a chosen k v value for design we can get what is the n c d value. Similarly, for n q d and n gamma d also this design factors can be obtained and finally, the design of this shallow isolated footing can be done using this proposed design charts. The comparison of results shows that present study gives a critical value of this design factor bearing capacity factors compared to previous one researchers who did the similar analysis like Budhu and Alkarni 1993 published in the journal Geotechnic, but our values are critical because we considered one sided failure mechanism. Also the partial mobilization of passive earth pressure on the other side as there is no failure surface is getting developed at one instant of direction of acceleration of seismic horizontal acceleration. Then we extended our study for the shallow strip footing embedded in the sloping ground. These are very useful in the hilly terrain like in hilly region like in Himalayan region there are several houses which are constructed in the hilly terrain or hilly region which are of sloping ground like this. So, how to make those foundations seismically stable or earthquake resistant the design methodology has been proposed in this journal paper Choudhury and Subbarao 2006 which is published in international journal of geomechanics published by ASCE USA this is the volume number and page number actually this journal paper of ASCE won the best paper award from ISC MAG in 2008 So, this paper considered again one sided failure mechanism and what will be further difference than the horizontal ground surface that here may not be the full failure surface getting formed that is all the zone 1, 2 and 3 are getting found because of limitation of this portion of the zone which is available on the sloping ground. Based on that the equations are developed using limit equilibrium approach considering both horizontal equilibrium and vertical equilibrium of all the forces involved to find out the bearing capacity factors Ncd, Nqd and N gamma d considering horizontal as well as vertical equilibrium. Then what need to be done in the analysis this parameters m and alpha 2 needs to be varied and based on those input parameters the iteration techniques need to be adopted far till this values of Ncd computed by both the equations matches exactly same. Similarly, for other bearing capacity factors and finally, the design charts for this Ncd, Nqd and N gamma d are obtained and as you can see compared to other researchers results as shown over here the present study gives the minimum value of this Ncd that automatically shows that our present study gives the critical design value needs to be used at practice for design of this shallow strip footing. Similarly, for Nqd and N gamma d also this charge shows that this equation can be adopted for the shallow strip footing in sloping ground condition also. Now, this chart typically shows the effect of ground slope and embedment which is necessary suppose this is the ground slope of beta in increase of this ground slope we can see the seismic bearing capacity factor N gamma d decreases significantly and so for the other bearing capacity factors also for this chosen input parameters and different values of Kv. What does it mean as we know as the sloping ground inclination increases obviously the structure will be more vulnerable for instability that is why N gamma d is decreasing significantly this condition needs to be considered. Suppose at a place at a hilly terrain we have a sloping ground of 20 degree then we should use the N gamma d value of this not the N gamma d value of this which is for beta equals to 0 degree at horizontal ground. Similarly, the effect of the embedment depth df is shown over here between df by b ratio from 0.5 to 1 because it is a shallow footing within that range as it is expected embedment depth increases means the N gamma d value or the bearing capacity value increases because more embedment is more stability. So, that is why you can see over here how much improvement of this bearing capacity can be obtained from this results that is as we increase the embedment depth of this shallow footing we will get to use the higher value of seismic bearing capacity factor. Now, let us look at the seismic bearing capacity of shallow strip footing using pseudo dynamic approach like so far we have discussed about the determination of seismic bearing capacity factors using pseudo static approach. Now, we are proceeding to pseudo dynamic approach this model and the forces considered for determination of the seismic bearing capacity factors for a shallow strip footing in a cohesion less soil was proposed by Ghosh and Chaudhary. This is a professor Priyanka Ghosh from IIT Kanpur who worked along with me we are the collaborators and our work has been published in this journal you can get details here P Ghosh and D Chaudhary 2011 in the journal Disaster Advances this is the volume number and page number. So, what we have done this is a shallow strip footing the base of the footing is shown over here the failure surface is assumed as a two zone failure surface and again one sided failure mechanism in the same way what we have considered in the pseudo static case, but instead of considering a curved failure surface here we have taken the two zone like active and passive this is basically was the extension of the pseudo static bearing capacity factor determination by Richards et al in 1993. There paper we have extended for further analyzing it through the use of this new pseudo dynamic approach. So, within this two zones these are the forces acting here again within this active zone we have considered this infinitesimal small horizontal slice and finally integrating over the entire depth of this active zone we got this seismic inertia forces considering the soil amplification also in this zone as well as in the seismic passive zone or this region we obtained the corresponding inertia forces in this zone considering the infinitesimal small horizontal slice and then integrating over the entire depth of this passive zone. Then passive pressure has been estimated which has been transferred to this place over here. So, considering this and now active zone this has to balance each other so that is the condition right at the interface the values should match right and then you will get what is the total capacity in terms of that Q U D what we have mentioned in the pseudo static case also. So, finally what we have recommended you can see over here now like seismic bearing capacity factor and the comparison with other researchers result those actually who have used pseudo static approach because before this paper nobody has used pseudo dynamic approach for determination of seismic bearing capacity factor. So, this is the result you can see this farm line is showing the present study result that is the results of Ghosh and Choudhury 2011 using pseudo dynamic approach for the bearing capacity factor N gamma D as it varies with respect to K H values whereas other different points which are showing over here all other researchers who have done the work that is determined this N gamma D factor using pseudo static approach. So, it is not necessarily that pseudo dynamic will give us always the lower minimum it depends on the combination as I said earlier. So, we can see here pretty well that even compared to the Richards et al 1993 which method I have mentioned that we have extended from pseudo static to pseudo dynamic. So, this open circles this points open circle this gives little lower values compared to our pseudo dynamic results. However, in pseudo dynamic as we have mentioned we can consider various dynamic related properties like soil amplification share wave primary wave velocity then duration of earthquake motion frequency of earthquake motion and so on whereas the validation was at K H equals to 0 and K V equals to 0 that is at static case it value must match with that of Richards et al 1993 that is a validation. So, that has been matched over here, but remember this present study gives us the result for amplification factor of 1. So, when there is no soil amplification. So, in pseudo static method we do not have the chance to incorporate that amplification factor, but we can take that aspect in the pseudo dynamic approach. So, if you see the results of N gamma D bearing capacity factor how it varies with respect to the variation of K H values for different values of amplification factor starting from 1 to 2. You can see this uppermost value or uppermost curve is for no amplification when there is no amplification that is amplification factor equals to 1 and the lower most curve is showing the value of N gamma D when there is an amplification of 2. What does it mean? Your design value of this bearing capacity factor is drastically reducing or significantly reducing when there is an increase in the amplification factor in the soil. So, this aspect we cannot address or we cannot incorporate in our pseudo static analysis. So, suppose at a region if from the Eurocode suppose we are using the known value of the amplification factor based on the site condition say it is 1.4 and K H value say it is given as 0.2 or you have determined it from your seismic hazard analysis etcetera. Then you need to go to this curve where it is a this cross sign that denotes to F A value equals to 1.4 you can see over here. So, this will be the value of your N gamma D not this value. So, there is a huge change between these two values you can see over here. So, that means the design will be more critical in terms of when we are considering the soil amplification which needs to be incorporated and that can be incorporated only by using this pseudo dynamic approach. Now, let us move to our another subtopic that is seismic stability of finite soil slopes like we will be talking about the stability aspects of soil slopes. Let us see the classical theories in seismic slope stability analysis. There are several slope stability theories as we all know, but we will only consider those which deals with the seismic theory that is the extension of the static slope stability analysis to the seismic level all are by considering of course, pseudo static approach or quasi static approach. The first one is given by Terzaghi in 1950. Then immediate next one which is still widely used around the world is Newmark's sliding block analysis which was proposed in 1965. I will go through this method very thoroughly because this is one of the basic research on this seismic slope stability problem and that is why even today also because of its simplicity and the possibility of determination of displacement as well this method is widely used around the world. Then seeds improved procedure for pseudo static analysis then modified Swedish circle method and modified Taylor's method. There are several other methods after that which have been developed I will try to discuss most of the recent approaches for this seismic slope stability analysis. According to the Terzaghi's concept of pseudo static method which I have already discussed in our present module in one of the previous lecture as we all know pseudo static method of seismic analysis is derived something like that. This is the way we calculate the horizontal inertia force seismic inertia force F h is nothing but mass times seismic acceleration in the horizontal direction which you can express as w times a by g w is the weight of the failure zone on which it is acting the seismic acceleration is acting. So, a generally we take the maximum acceleration a max by g. So, this a max by g ratio is called k h that we have already seen this is called coefficient of seismic horizontal acceleration. Now, how to select this k h value already I have discussed this though but here some other points and recommendations as given by various researchers. Let us look at here various guidelines for the selection of this k h value for any pseudo static analysis like it is will be based on peak ground acceleration some people say the higher the value of the p g a that is a max the higher will be the value of k h and that should be used in the pseudo static analysis. But remember using the exact value of a max as k h will be a gross approximation or it is it will give you an uneconomic design because that is a too higher value which is not sustaining for a longer duration. So, we need to evolve certain criteria based on which we can select this k h value. As I have already mentioned the Eurocode criteria how to estimate this k h value based on different factors etcetera. There are other codes also worldwide which suggest how to find out this k h value. Now, based on the earthquake magnitude the higher the magnitude of the earthquake the longer the ground will shake and consequently the higher the value of k h that should be used in the pseudo static analysis. Now, maximum value of k h when item number this 1 and 2 as outlined above are considered and kept in mind that the value of k h should never be greater than this m x by g that is quite obvious because this is the absolute maximum value possible for k h to have. Now, minimum value of k h what should be the minimum or threshold value? It need to be checked if there are any agency rules that requires a specific seismic coefficient like as we have mentioned there can be some guideline for threshold value of acceleration that will be your minimum value. Like local agencies of California uses the minimum seismic coefficient k h of 0.15 for the division of mines and geology as per as 1997 recommendations are concerned. Size of the sliding mass. Now, use a lower seismic coefficient as the size of the slope failure mass increases. That means, if you consider the extension of failure zone for a larger area you can go for a lower seismic coefficient. The larger the slope failure mass the less likely that during the earthquake the entire slope mass will be subjected to that destabilizing seismic force in the out of slope direction. So, what are the other suggestions like when it is a small slide mass then recommendation is use k h equals to m x by g. But when it is intermediate sliding mass use the value of k h as 0.65 times m x by g that means 65 percent of this maximum value. And remember this factor of 0.65 is also used in our liquefaction analysis which we have discussed earlier in one of our module.  And seed in 1979 recommended that k h value should be 0.1 for the sites where near falls capable of generating magnitude of 6.5 earthquake is possible. And in that case he recommended that the acceptable pseudo static factor of safety should be 1.15 or greater that means minimum value of factor of safety should be 1.15 for that slope that is for design of large embankment or dam or landslide problems. Whereas k h value needs to be used as 0.15 for the sites near falls capable of generating magnitude of 8.5 earthquake. So, for 8.5 earthquake k h value of 0.15 for 6.5 earthquake k h value of 0.1 remember these are recommendations for only large slide mass where large mass is involved. So, this is on the lower side of the ranges of k h which can be used for design. So, these are the recommendations which people can use for practical design purpose unless they have a strict or very clear guideline about the selection of the k h value from the site response and from the local earthquake data. Now, other recommendations like Terzaghi 1950 suggested that the k h value should be considered as 0.1 for severe earthquake, k h value should be considered as 0.2 for violent and destructive earthquake. Whereas k h value should be used 0.5 for catastrophic earthquake. So, those are Terzaghi's recommendation, but remember these recommendations of pseudo static values are way back in 1950. So, in today's design method if somebody are using these values remember it will be primitive in nature. So, you can use it as a first step of your design, but you have to rely on the local seismic motion, local seismic hazard analysis, local site response analysis and all these studies so that you get a proper input value of your k h for design for this pseudo static design. Other researchers like you can see over here Seed and Martin in 1966, then Dakolas and Gazetas in 1986 they use the shear beam model and showed that the value of k h for earth dams depend on the size of the failure mass and in particular the value of this k h for a deep failure surface is substantially less than the value of k h for a failure surface that does not extend far below the dam crest. That means for shallow failure you use a higher values of k h for deep failure you use a lower value of k h that is what it means and Markusson in 1981 suggested that for dams you use the k h value of between 0.33 times of that a max by g to 0.5 times of a max by g. Remember these are the values corresponding to with some factors as proposed in the present day Euro code. Can you see these values this coefficient 33 percent and 50 percent of that maximum value with some influence factor etcetera which we have discussed earlier. Now other researchers they mentioned that based on their recorded 350 accelerogram data in 1984 this Heiners Griffin and Franklin in 1984 proposed that k h value should be used as 0.5 times of a max by g for design of this earth dams. But by using this seismic coefficient and having a pseudo static factor of safety greater than 1 it was concluded that earth dams will not be subjected to dangerously large earthquake deformation based on their analysis based on only this 350 limited accelerogram data remember that. Whereas Kramer in 1996 states that the study on the earth dam by these researchers would be appropriate for most of the slopes because slope stability problem is also applied for earth dam also for the stability of the earth dam slope. So, also Kramer indicates that there are no hard and first rules for the selection of this pseudo static coefficient for slope design. But that it should be based on the actual anticipated level of acceleration in the failure mass including any amplification or deamplification effect. So, remember this guideline or suggestion as given in Kramer 1996 that when you have some actual anticipated level based on your local site response analysis and seismic hazard study you should use that where you can include this amplification and deamplification effect also. Now let us go through Terzaghi's wage method for the slope stability problem which was proposed in way back 1950. This is the basic slope you can see over here this is the slope soil slope and this is the failure plane assume failure plane by Terzaghi was considered as a triangular wage. So, this is the failure mass of the wage weight of this failure zone is W and the pseudo static seismic inertia forces in horizontal direction is F H and in vertical direction is F V and remember it needs to be considered in both the direction like this way as well as this way and F V also need to be considered this upward as well as downward. And for a particular combination of this directions of this F H and F V you will get the critical value of factor of safety or lowest value of the factor of safety for your design. So, what are the other forces over here this n is nothing but the normal force which is acting on this planar failure surface and t is the shearing force acting at this portion.  And for effective stress analysis the values will change to c dash l and n tan phi dash. Now, what is the definition of factor of safety as we all know the definition of factor of safety is nothing but ratio of resisting force to driving force. Now, what is resisting force over here and what is what are the driving forces let us go back this seismic force when it is acting in this direction it is trying to displace the slope it is trying to fail the slope. So, this is the driving force clear whereas, this shear strength that is the property of the soil which it is coming or which it is providing the support that gives the resisting force. So, the from the resisting force criteria using total stress analysis it will be c l plus n tan phi and what are the driving force it will be in that direction it will be f h cosine of alpha plus w sin alpha look at here this component of w and f h component in this direction that will try to fail it in this direction. So, if we simplify this further what will be the value of n n is nothing but the normal force how you will get normal force will be this w is acting cosine component of that and this f v has to be deducted if this is the critical direction.  Now, if you have f v in driving force also you will get another component of f v in resisting force also you will get another component of f v this is without considering the vertical one. And with consideration of the vertical one you can see the factor of safety is given over here the resisting force by driving force c times l length of that a b failure zone plus w minus f v times cosine of beta minus f h sin beta of tan phi because this is nothing but your n clear look at this is a simple mechanics you can see resolve the forces over here and you can get what is the value of n n is nothing but equals to this w cosine alpha and in this case if you denote this angle as beta then w cosine of beta minus of f v cosine of beta because f v can be plus and minus you have to consider the critical value for which you are getting the minimum factor of safety clear. And f h sin beta that is also in the other direction it is giving a component of n right. And what are the driving forces driving forces from f v as I said there will be a component w minus f v sin beta will be one component and f h of cos beta will be another component clear. So, using this formula one can easily calculate the factor of safety and what is the recommendation as we have seen for safety it has to be 1.15 right more than that is safe factor of safety again pseudo static seismic analysis. Now, let us come back to another methodology which was proposed by Newmark. So, this Newmark's sliding block method is one of the pioneering work in the area of this slope stability analysis for soil how it was developed let us see it was developed based on the concept of friction block that is a block which tends to move over a sloping ground like this what are the forces acting on it based on that mechanics Newmark had developed this problem. So, what was considered this mass is the failure mass or failing mass which is failing with respect to a stable zone of soil. That means if you consider this portion is a stable zone this mass is failing with respect to this plane clear. Now, what is Newmark's sliding block method why the name sliding block as the name suggest this is a block soil block that is the failure mass which is sliding or moving over this stable block fine. So, it was developed in the year 1965 in the journal paper appeared in the journal Geotechnic published by IC London. This is a classical work as I already mentioned you can see the weight of the failure mass is w. So, if you resolve it into two directional components n that is your normal forces nothing but w times cosine of i i is this inclination and this forces w times sin i this w sin i is trying the block to slide down and what resist it. So, that is the driving force and what resist it that is the shear strength property what is the shear strength property what is the frictional property there is nothing but this normal force times tan of phi tan of phi because it is the same soil soil over soil otherwise it would have been delta if suppose there are two materials like we solved in our basic engineering mechanics problem friction problem that a block is sliding over another material there will be interface friction between the two materials. So, in case of our soil it is n tan phi that is the stabilizing force. So, the factor of safety is expressed as stabilizing force by driving force. So, stabilizing force in this case is n times tan phi and n is w of cosine of i divided by driving forces w sin i. So, if you simplify it the factor of safety is simply just tan phi by tan i remember this is for the static case. So, initially Newmark has shown this figure to make everybody understand that this is a simple extension of this static problem of friction sliding block method to the seismic analysis for the soil slope. Now, additional factor what are coming into picture this w times alpha c r what is that this is nothing but inertia force seismic inertia force in the horizontal direction. Newmark has considered only the horizontal seismic inertia force he did not consider the vertical one, but later on people had modified this Newmark sliding block method considering vertical force also that you people also can do because it is nothing but a simple mechanics problem. So, when this seismic horizontal inertia forces added what are the changes occurring now you have additional component of this w times alpha c r which is the inertia force along this driving direction and you have another component of this in the vertical direction which is reducing your normal force of this n. So, both way it is damaging the stability can you see that because this is adding to this denominator on this driving force this tau dash and it is reducing the stabilizing force in terms of this n dash is it fine clear. So, using this factor of safety can be calculated. Now, Newmark has gone further beyond what Terzaghi has recommended Terzaghi stopped here that is he mentioned determine the factor of safety and check the factor of safety if it is more than 1.15 then it is a stable slope, but if it is not stable then how much is the displacement up to how much we can consider that it is allowed to fail that is the amount of displacement cannot be considered in Terzaghi's method, but Newmark sliding block method the beauty is it is a displacement based approach also including the force based concept. Newmark proposed that equate this expression of this factor of safety equals to 1 and when you are equating with respect to 1 whatever value of this alpha c r that is this acceleration coefficient seismic acceleration coefficient we are getting for a value of factor of safety equals to 1 that is called critical acceleration or yield acceleration for that yield acceleration beyond that acceleration if actual acceleration is beyond that value then the slide factor of safety will be of course less than 1 that means it is no longer a stable slope it will start sliding down then how much is that sliding how much is the displacement that can be computed based on the difference of the acceleration between this critical value and the actual value of acceleration now integrating that acceleration twice you will get the displacement. So, what I am telling this is the expression of factor of safety as per Newmark's method Newmark introduce this coefficient k y which is called yield acceleration coefficient this yield acceleration coefficient is nothing but that seismic acceleration coefficient for which factor of safety equals to 1 and when your actual acceleration is say capital A acting on the slope you have to find out what is the difference between this a minus a y a y is nothing but k y times g. So, this is your relative acceleration which is making the slope to slide down or to fail. So, that relative acceleration which varies between the time scale of t naught to t naught plus delta t you can integrate it between that time scale to get the relative velocity further you can integrate that velocity between that time scale to get the relative displacement. So, this value of relative displacement will give you the movement of the failed slope which is having factor of safety less than 1. So, this is also very important nowadays as far as performance based design or the displacement based approach of design is concerned clear. So, with this we have come to the end of today's lecture we will continue further in our next lecture.


What is going on guys, today I am back with another Destiny 2 video now people, Destiny 2 is so so close it's unreal, my buddy is ready, how about you? I've never been so excited for a game in my life, I honestly don't think I have. Okay so today I am back at you with another video, this one going by the title you guys will be like, well we know how to get the cold heart, you get it for pre-ordering the game. Well that's true, but there are also other requirements for you to get this thing and I will explain them in this video. But before we go any further guys, I am giving away a Rockstar Destiny 2 in-game exclusive gear code to win one, simply drop a like on the video and leave a comment down below. Okay so the cold heart exotic trace rifle, the only one of its kind in the game, confirmed by bungee. This is something you can only acquire through pre-ordering Destiny 2, so if you pre-order the game you get a code obviously which you write into your console's redeem code page. But what happens next? Do you just simply lug in and find this exotic within your inventory? Will it be waiting for you within your vault? Will it be waiting for you at the postmaster? The answer is no it won't, there are actually further requirements for you to obtain this trace even after entering your pre-order redemption code for this thing. So what do you have to do? Well first things first, you have to complete the entire story campaign, so yes you have to complete all 17 missions in the game and guys it doesn't end there. You then have to be a level 20, now if you ain't a level 20 after completing the campaign and to be honest I doubt you would be as that would be way too easy but you never know. But if you ain't a level 20 after completing the campaign you will then have to go and grind that level by either doing strikes, public events and so forth. Theoretically anything that gives you XP, so eating a lot of Pop-Tarts helps too. So once you acquire that level 20 and have completed the story you simply go to the gunsmith at the farm and you should have this thing waiting for you. Now this information actually comes from the back of the redemption code leaflet for the exotic coldheart trace seen on screen now. Also guys it is important to mention if you didn't pre-order the game you can still obtain this exotic. Problem is you will have to wait until the 5th of December before it comes available for you in-game to earn. So yes there's more to the story of obtaining the coldheart exotic trace and on that note guys I am out. I actually have a spare code for the coldheart on Xbox One if anybody watching this video hasn't pre-ordered the game and needs one. For sure just hit me up on Twitter at DPJSC08 linked within the video description. But guys on that note I am out. Thanks for stopping by I do appreciate that epic support. If you are new around here and enjoy daily Destiny 2 videos be sure to subscribe. Hitting that bell button next to that subscribe button will send you notifications of when I do upload. But again thanks for stopping by and hopefully I will see you on that next one. Always in the wrong where we stand.


Little Boy takes photo of mom, she's lying face down on the floor. Corrigan was trying her best to pay attention. Her son was in desperate need of her attention so she willed herself to keep playing with the Lego pieces. Her son was ecstatic whenever she played with him. As much as she tried, she felt the weight of her eyelids and the shallowness of her breath. She was trying to hang on. Just for a while longer, she thought. Her son's voice began to grow distant as her vision went black and she hit the floor. Laura Corrigan lived in Durham, England as a single mother. She threw herself at her work so she could provide for her family. She might not have been a CrossFit enthusiast but she stayed pretty active in her daily life. At least she thought so. But recently she had always felt tired. She dismissed it as just her letting work get to her. Her friends didn't think so, they were worried about her, and they were right. Corrigan thought she knew the trick for her fatigue, she had a selection of vitamins and over-the-counter meds in the hopes they would work. Vitamin E, vitamin C, vitamin B, zinc, even iron, but they did little to help. After her health didn't improve after weeks, her friends made her see a doctor. The doctor did little to help and sent her on her way with a sick note so she could rest. But Corrigan's illness wouldn't be cured so easily. While Corrigan drove on the road, she remembered her previous night. Her sons were exhausting her energy as usual. Her youngest son was only a baby and would cry all night. He didn't mean to pull her hair or kick her, he was still a baby. But these actions still woke her up. His crying was enough to give her a headache. Then something gave Corrigan a chill that crept up her spine. Corrigan's condition was worsening, she was so pale and had never had any energy anymore. She stopped eating as she just didn't have the appetite for it anymore. Her friends were more worried than ever and they decided it was time she had a second visit to the doctor. They couldn't understand that Corrigan, a strong woman, had beaten the flu weeks ago but was still declining in health. Everyone was fearing about what was happening to her. The doctor took Corrigan much more seriously the second time after seeing her condition. He ran tests to see what the cause of her illness could be. But every single test came back with nothing. According to them, she was perfectly healthy, which obviously wasn't the case. The doctor resorted to an elimination approach. She was put on all the antibiotics the doctor could think of. He hoped to learn more from her reaction to all of the courses she was on. But in the end quite the opposite happened. Corrigan wasn't feeling any better, in fact, she was only feeling worse. Her body started aching and she could barely stay awake these days. Her mental health was the next thing in danger as everything else deteriorated. Everyone close to Corrigan was so worried. Maybe there wasn't an illness and it was just in her head. Corrigan knew this wasn't the case. Something inside her body wasn't right. Even her friends knew her and knew something was severely wrong. Corrigan knew her doctor couldn't do anything more to help her. Instead, she decided to seek answers online. She went on online chats with experts and even tried herbal remedies. Nothing was helping. As Corrigan looked to anybody for answers, no one could tell her what she needed to hear. She felt so alone.   She had to wait a few weeks for the results of her tests to come back. All the while she was still in pain. The phone rang and the doctor asked her to come in and talk to him. She preferred to speak in person anyway. But after leaving the doctor's office she felt a knot in her stomach that made it difficult to breathe. Corrigan felt a huge wave of fatigue hit her.  She found that the images that flashed through her mind helped. She was thinking about what they'd get up to when she got home from work. This distraction was enough to keep her working and made her feel almost all right. But this didn't last long. Back in the car once more, Corrigan was looking forward to being at home. She missed her boys and needed their lightheartedness to erase this weird day she's been having. She arrived at a crossroads and made the turn towards home. She was halfway there when it happened again. The intense wave of tiredness. Except this time, she felt dizzy. Then something else happened and she lunged for the breaks. She managed to pull her car over safely and gave into the pain. Everything hurt. She gave herself a few more moments. Waiting for it to pass. When it finally did, she started towards home once more. Arriving home, she welcomed her boys into her arms with a big smile and hug. She asked if they were hungry and made dinner. But there was only one thing on her mind. She needed to think and she didn't want to panic the boys so she decided to go for a family coastal walk. This was one of her favorite things to do. Being with her boys and by the sea, the worries about her health faded and she began to think more calmly. She was going to spend the rest of the evening with her little men and look for advice tomorrow. Little did she know, it wasn't going to go as planned. Refreshed and revitalized, Corrigan and her boys arrived back home. Finally, some time to relax, she thought. But as soon as she sat down on the sofa, the boys got out the Lego set.  Sighing lovingly, she got down on her knees and began to play. Then everything changed. As she was playing her eyelids grew heavy, her breath shallow, she couldn't hold on. Exhausted, Corrigan finally passed out, a sleep mid Lego battle. Her son took a picture of her and she then posted it on Instagram. But why was she so tired? There was a reason behind all of this. Heart pounding, she decided to reveal the tragic reason as to why she was so tired. She sat behind a desk and started typing. After becoming sick and tired of her mystery symptoms, Corrigan sought medical advice from a new doctor. Soon after, she was diagnosed with bowel cancer. This was notably rare for someone in their mid-30s but doctors were still hopeful for a future. It was pretty hard to process, she wrote on her blog, Cancer, Milk and Rainbows. All I wanted to know was if I was going to die or not and that, they couldn't really answer. She created a blog and overcame the fear of sharing her own personal story online. Corrigan explains how social media was a great form of therapeutic release and support for her. It has helped me, both writing thoughts and feelings down and connecting with others, she explained. But Corrigan had her own idea of help in mind. As well as being a member of multiple different societies, Corrigan gave back to her cancer community by raising money for bowel cancer UK. As a keen kayaker and wild swimmer, she completed a one-mile swim despite being seriously ill at the time. She was never happier than when she was near the ocean and surrounded by nature. It wasn't long until Corrigan was going for chemotherapy on a daily basis. And it was around the time that she began to notice the effect her illness was having on her children. She had to stop breastfeeding her youngest son, Finn. Feeling emotional, she sought solace from her blog writing. This has been the hardest part of my journey so far, certainly harder than hearing the diagnosis. He, on the other hand, after just two weeks, is coping amazingly well, she revealed. But, Corrigan was a self-confessed fighter. She took every day as it came and took every new challenge in her stride. To try to make sense of what was happening and to document her battle, she turned more and more to her writing. I write when I can and have connected with other people a lot that way, as well as in Facebook support groups. Almost one year on from her original diagnosis, Corrigan continues to fight her illness.


Now if you've made it this far, congratulations. I told you in the beginning this first stuff is absolutely If I say boring I think many people are gonna be angry at me because certainly they you know Some of it is interesting, but you've got a way through these things and you've got a wonder to yourself Where is all this going? Does it is going to mean something? This is abstract algebra So when do I get to groups? But this is all the foundation that we are building. I mean this is one way to study abstract algebra You just build this foundation until you get to groups rings fields all of these things or you can just jump in there And then you have to attach all these things Onto it so that you can understand it properly. So in this series We're just building it from the ground up, which means in the beginning. It's awkward You don't know how to do it. You don't know why you're learning these things is this these You know definitions and abstract things that you've got to get together What I do want to say is congratulations You've made it here because we're gonna actually get to one of the more interesting things although it is still part of the building blocks and This thing that we are going to get to is called Operations and I don't just say operations. That means surgery and surgery is what I do for a living It means operations are actually actually quite interesting and you actually know operations before The addition of two numbers the multiplication of two numbers. Those are operations and operations are Nothing other than this product set onto itself. So if I have a set S and I take its product set with s with itself what I'm doing is I'm mapping s into s So, you know, give me one element of s I do some operation with another element of s what I'm ended up with is another element that is just inside of s I mean if you looked at the set of If you look at the set of real numbers and I told you well, let the operation be addition and I'm going to say well 2 plus 3 and that equals 5 Well 2 is an element of R if the real number was my s here 3 is an element of that I do this operation to them and I get 5 and 5 is also an element there So we say that these operations are or these sets are closed under a certain operation So remember that term you're going to come across it many times it is closed under the operation under the operation That means that if I do that operation on a set that I get to another element that's also inside of that set That's also inside of that set. So I'm just mapping a set to itself Product set see how we build all of those things up. They mean something to us now It means we have a better understanding perhaps of what is going on of what is going on here now the specific operations that we are really going to deal with More proper term for that is going to be a binary operation a binary operation Okay, binary in as much as we're going to take this operator on two elements So what we are going to then have basically is this Mapping of two of of a pair of those elements So I could have said that this mapping here under addition is going to give me this operation Two plus three and that is going to map to another element in that set, which is five now you'll come across This idea that we move away from plus and multiplication and we built this generic operation And we have signs for that either it's a little circle or it's a square block You'll see many of these stars sometimes It just means that this is a binary operation on that set so that we can get away from we are we that arithmetic and Everything that you learned before functions. Remember, let me talk about that. I mean we had a function f of x equals three x Other words y equals three of x all I'm doing is I'm building these Product sets I'm building these product sets because you give me One and three and I say well that maps to three So this is an r. This is an r. This is an r But I want to move away from this being a function I want to move to something more generic which is a mapping because that allows us to map all sorts of brilliant things. I mean Mapping of divide is divisible by For instance or just arbitrary mappings between between elements of a set That's just so much richer than just sticking to functions But you were told what functions are you work with functions But just see that as part of something a much bigger and a much more exciting world So let's just look at a few operations. So one that I've listed here is The Addition let's take let's take the even natural numbers under addition even Natural numbers I'm just going to write that they are closed Closed under addition Why is I can take any two elements In that set so two plus four that's going to give me six and six is also in that set If I look at the odd Natural numbers under addition that is sitting not closed under addition one plus three gives me four one Isn't that set three isn't that set but four definitely is not is definitely not in that set Let's have a look at a set a and my set a is just going to be the set zero one two three and four And I say is that set closed under addition Think about it. It is not closed under addition because I can say Two plus three equals five and that is not an element of a Is it closed under multiplication? No, it's not closed under multiplication because two times three Equals six and that is definitely not an element of a So you see where these binary operations where these binary operations are going I think in the next example, I'm going to show you quite an abstract Set and the operations on that set and you'll get an even deeper understanding of this very intuitive Way of looking at it. So operations First bit of excitement as far as I'm concerned in abstract algebra


Right, so regarding the lucid dreaming app that I've created. It's called how to lucid you can find it on the iPhone app store There's been a few comments and feedback about this app already. So I want to just address some of these Firstly, thank you very much for all your positive comments and reviews I've not actually had hardly any negative comments at all about this app The only thing that people are sort of criticizing about it is what I'm going to talk about now So the app has the reality check reminder function. That is the main point of the app now I have neglected to I've made a bit of a mistake So I've made the the reality checks pop up sort of every hour every two hours three hours or randomly The problem with randomly and indeed with the like hourly ones is that there's no setting to turn it off when you go to sleep So as a few people have been saying they've been using it in the daytime But then as you go to sleep, it's still been going off and it's been interrupting their sleep and waking them up and annoying them in some Way, so there's a few a few things I want to say about that firstly. Yes, that is an honest mistake I should have included like a sleep time or a way you can turn the reality checks off Firstly, you could either turn the notifications off when you go to bed every time Okay, or you could set your foot if you have an iPhone obviously you do have an iPhone if you've got the app You could set your do not disturb mode and set the hours from from say 10 at night until 6 in the morning So that nothing will disturb you will notify you during those hours That's what I do and that's the reason I didn't notice the problem myself is because that setting stops it notifying you when you're asleep The other thing you could do which I also recommend doing anyway is to put your phone on to silent mode Face down every time you go to sleep. In fact, I don't even suggest sleeping with your phone near you I would suggest leaving your phone in either another room or way across the room where you can't reach it face down Because your phone is one of the biggest interruptors of your sleep And it's not very good to have it so close to you all the time But that being said I will try and include an update for the app which addresses that problem with it You know fixes the problem of it notifications happening during the night And things like that. There is also an issue with the scrolling So if you've entered a long dream journal entry like some of you have you'll notice that when you then go back to review It you can't easily scroll down unless you press the edit button in which case you then can scroll down So these problems are being addressed. I'm going to be working on them for a new update I don't know when the update will be coming out I've got a few things to figure out before then but ultimately You know the bigger picture of this is I think it's been a fairly big success so far anyway Let me know if I'm wrong like I'd love you to leave a comment letting me know what you think about it and Like has it actually helped you to the reality check reminders work in that way Do you use it as your dream journal? Or is it just like another thing that you've downloaded that you think is kind of cool But it's missing something and if it is missing something, please let me know what that is Because I obviously really want to make it better. I want to improve it. It's my first ever app that I've made So there's obviously gonna be a few problems with it a few bugs things to iron out But I think ultimately it's been okay. I mean I certainly use it myself. I use it for reality check reminders and things like that The other thing I would say is that yeah, there are lots of links in the app Lots of sort of tutorials as well big blocks of text which explain various techniques. Is there anything missing from that? I tried to be as comprehensive as I could like it's got the main techniques and methods It's got a summary of like binaural beats and you know how to do various Things how to sleep better how to meditate. I think it's got things like that It's also got FAQs and acronyms And there are also links to useful things that you might want to get or you know try like binaural beats or supplements or My lucid dreaming bootcamp if you want to like a step-by-step guide to lucid dreaming These things I've mentioned them all before they should be in the description of most of my videos But I felt like you know, it'll be useful to have them all in one place in the app as well Is there anything that you think is missing from that, you know, whether it's a tutorial or a section? Bear in mind the app supposed to be really simple. It's not supposed to be really complicated Because that's what my website is for you know, if you want more detail, you should always read the website Which you can read on your phone anyway But the app is really supposed to be like a lightweight sort of thing That's just going to remind you to do reality checks help you write your dreams down So yeah, is it missing something do you think or is it okay so far and we just need to iron out those bugs? Let me know The other thing I would say is that people have been saying people have been saying it would be good if there was a night mode Like a way you could turn it so that the brightness goes down and it's dark with white text instead of light with dark text That is something that I will consider adding but only if you guys would actually use it because for the most part You when would you use the app when you're sleeping or you know when it's dark? You shouldn't be using it anyway The only time that will be useful is if you were using it as a dream journal in the early hours of the morning before the sun has risen In which case it would be dark and you don't want to have the bright light wake you up too much So I do understand the need for it Personally, I usually wake up when the sun rises. I don't go I don't often wake up in the middle of the night Unless it's a really intense dream But obviously some some people do and that can be an issue So I will include a lot a night mode in the update if you guys want that And lastly for those of you who want this on Android, I do know what you I do acknowledge that That's obviously a lot of you that want it on Android. It is coming. I promise But it's just it's just a case of how to find the funds to go from here to there It's gonna cost me a fair amount to have it developed on Android and also the updates and the fees and things associated with that So although I do really appreciate you guys donating on on patreon I think a couple of you have donated like a dollar a month or something on on patreon Sadly, that isn't enough for me to then hire a developer to make it an Android version I really do need like a bigger response from you guys in terms of like a patreon donation or something Maybe like go on to my website and buy a few of my books or like by the bootcamp or something something that would help me then be able to get from here to there and As soon as that happens, I can I can make it happen a lot faster And I am I am trying to save up for the developer and everything and get it up and running sooner But it's just there are roadblocks. There's developments I've got to pay for the updates of this app on the iPhone and stuff like that as well as various other business-related costs for keeping the website going and things like that But overall, thank you guys very much for all of your comments and support with this app If you have got it on iPhone, please leave a review on the iced the ice store the app store That would be greatly appreciated and I'll see you next time Don't thanks for watching guys this video and this channel was supported by my patreon followers Please consider giving just a dollar a month to support this channel or just click the links in the description You'll find links to various lucid ring products articles techniques and tutorials if you did enjoy this video Please click the notification bell and subscribe and I'll see you next time Why are you still watching that you should have clicked one of my related videos by now right or subscribed or gone onto my website or something like that