 Until now we have discussed about the characteristics of soils and we have tried to characterize them. We also talked about their classification scheme, we talked about the compaction characteristics and henceforth we will be trying to use these concepts in answering most of the real life problems which as a geotechnical engineer or as a civil engineer one has to face. I would be talking about seepage characteristics which are quantified by using a mathematical parameter permeability of soils. Sometimes people use the term hydraulic conductivity also for this but in wider application if I replace flow of water through the porous media or the soil mass this could be any example which can be set as a flow of hydrocarbons, flow of chemicals and so on. So hydraulic conductivity is a mesonomer, we will be talking about then flow of ground water is a very important discussion which has to be done at undergraduate level to understand what are the consequences of not understanding how the flow of water influences the stability of the soil mass and the structures which are sitting on the top of this. Now from this point onwards I will also be trying to emphasize on the concepts of soil water interaction in the form of let us say kinetic process where the movement of the water is occurring through the porous media. So these type of studies become very very contemporary and useful for the profession where we try to understand how the movement of the ground water is influencing the overall structures and their stability. I intend to talk about 3 major topics from this point onwards. This topic should be covered in other 3 to 4 lectures followed by I will be discussing quite in details the compressibility of the geomaterials and the soil mass and to understand the compressibility characteristics of soils, one has to understand how the stresses get distributed in the soils. So these are the 3 major topics I will be covering henceforth and with that I will be winding up the course. So to begin with the permeability of soils and the flow of ground water to make life simple we assume that the soils are saturated. So this is assumption number 1 if you do not assume the soils to be saturated this becomes a completely different discussion which falls under the realm of unsaturated soil mechanics. So at undergraduate level I will not be discussing unsaturated state of the material because the flow of water is going to be extremely complicated and cumbersome and I will restrict my discussion on the permeability of the saturated soils or the flow of water through the saturated soils. You have enough exposure of what capillary action does, what the unsaturated state of the material does, what the dry state of the soil does and so on. So the best way to understand this whole process would be you must have studied the Bernoulli's theorem in your fluid mechanics course. Suppose if I take a glass tube and if I allow glass tube can also be considered as a control volume or this could be a pipe even through which the flow is occurring. Now suppose if I assume that this glass tube pipe or the control volume is frictionless in your hydraulics course when you deal with the flow through conduits and the pipes you apply the friction factor as C factor alright but here for the sake of simplicity we are assuming that there is no friction which is induced from the glass tube or the pipe or the control volume and at this point the velocity is V1 and at this point the velocity is 2, V2 alright. If I know the area of cross section here as A1, area of cross section here as A2 what we are trying to do is we are trying to find out what causes flow of water between point 1 and 2. I am sure you must have done this exercise if I consider a datum somewhere here I know what are the heads which are acting at the point 1 and 2 and the head difference is going to cause the flow to occur. So if I say at point number 1 the height of point 1 is let us say Z1. Now Z1 is defined as the location head, Z is defined as the elevation head in meters or centimeters or whatever. So point 2 is located let us say here at a elevation head of Z2. Now suppose if I say that the pressure head at this point which I am defining as P1 and pressure head at point 2 I am defining as P2. So P corresponds to the pressure head and the units will be the pressure units. If I divide this by the density of the fluid this becomes the height of the fluid and the pressure can be converted into the height also alright. So we have elevation head, we have pressure head and the third one I am sure you must have studied is what is known as the velocity head normally this is defined as V square upon 2g alright put together that is 1 plus 2 plus 3 is known as the total alright. So if I say that the total head if I say the th the total head at point 1 is greater than total head at point 2 the direction of the flow is going to be from 1 to 2 is this okay. However if I reverse the situation and if I say that th2 is less than th1 greater than th1 the flow is going to get reverted it will be from 2 to 1. So what we are trying to analyze from here is a situation where we can establish the direction of the flow in a glass tube is this alright this is nothing but your Bernoulli's theorem. Now Mosul time when we use this concepts in cases like soils or the porous media what is going to change suppose if I want to extend this to porous media alright. So porous media means yeah you have some doubts yes please total head said I have the general situation okay so your objection but I have given a1 and a2 alright area of cross sections are different so v2 is different than v1 I think this is okay yeah so I will come to this point just keep this mind alright. So for the time being there are no frictional effects we are ignoring it and we are trying to see whether the total energy concept can be utilized to establish the direction of the flow alright total head always total head velocity also has to be included elevation has to be included pressure also has to be included always remember yeah I will come to that but unless you have created a context what you are saying is not correct so now let me create the context and that is what I was trying to do here so the moment you extend this theorem to the porous media now what you are saying is going to be correct so that means what I have to do is I have to introduce an element of a porous media somewhere in between alright. So suppose if this is a compacted soil mass so what I have done is I have taken some soil in the loose form and I have compacted it within this tube to create this state of the compacted soil mass so when you say compacted soil mass the attribute of this control volume are going to be porosity agreed void ratio Yamadhi so this is a state of compaction saturation okay moisture content and what else the material is this correct so material is represented by let us say a specific gravity particle size distribution what is the best way to depict particle size distribution here the entire graph cannot be fitted sorry better than that sorry very nice good so let us say D10 or DX for that matter clear normally D10 is used to define the material and hence we call this D10 as the characteristic dimension of the porous media choice is yours you can take here DX also but when you say standard terminology this is D10 normally we use to define the material so look what we have done we started from Bernoulli's theorem and we are now you know extrapolating it to the porous media by including a porous media over here fine and hence forth now we will be discussing about the flow through porous media is this part okay everybody has followed this any question fine so now coming to so we have defined now the porous media in the form of its compaction state and the material now what is going to prevail the flow one is definitely the total energy and the second would be the Reynolds number alright so we have to define the Reynolds number you remember what is Reynolds number we define it as RE so truly is being the ratio of viscous forces to the inertial forces two things you should remember never get confused what will be this D term characteristic length or the diameter correct you are right so I can say this is D10 and we happens to be the velocity so whatever we have been talking about was always discharge velocity discharge velocity is divide of the porous media I repeat discharge velocity is divide of the porous media as a porous media does not exist what are the possibilities when porous media will not exist the only possibility is what we call as preferential flow that means what is going to happen the water the porous media provides the resistance to the flow of water clear everybody wants easy life so what see page has done what discharge has done it has short circuited the sample itself now this is what is known as a preferential flow preferential flow is at the at the interface of two materials mostly chances are when you are compacting the sample the contact between the glass tube the pipe or the control volume and the soil mass is not perfect and hence whatever discharge is taking place this might take place through the preferential flow however if I curtail this preferential flow you will ask why how so I may put a rubber gasket over here or I may put some different types of raisins or I may put different type of what you call a lubricants or sealants so what I will be doing I will be cutting up the preferential flow and now I am making this sure that the discharge is going to occur through the porous media only is this story clear is this fine yes please okay so now I am forcing the discharge to occur through the porous media okay so what I have done by doing this whole thing by manipulation I might have created a laminar flow situation or a turbulent flow condition okay so you are aware of what are the laminar flow condition what are the turbulent flow conditions if I zoom a certain portion of the sample alright and if I show it over here this is how the pores are distributed in compacted soils okay so these are the pores and this is the soil matrix as long as the flow of the fluid is parallel to all the flow paths including the bends or including the distortions the chances are the flow might occur like this there is a bend over here again there is a bend and if you take the next layer you know these 2 are almost parallel to each other so as long as I ensure that the laminar the flow conditions are as if the flow paths are parallel to each other including the bends this is what gets followed in the laminar flow condition the another characteristic of this type of a flow would be so this is the first condition the second condition would be the velocity of fluid is proportional to I and this is what is known as Darcy's law so Darcy's law is used normally for defining the flow through the porous media alright it is a linearity V is proportional to I and if I say in generalized form I to the power n this becomes a turbulent or non-linear non-laminar flow so I will use this I here this is Darcy's law V is proportional to I if I say that turbulent flow is or non-laminar flow is where this condition gets violated this condition can be written as I to the power n alright where n could be equal to 2 this becomes your non-laminar situation the quantification of all this is done with the help of RE so in case of soils what we say is RE is less than 1 in your pipe flow or the flow through the conduits you have taken laminar flow condition up to 100 is it not RE is less than 100 is the laminar flow so what I have done remember see we started from a pipe conduit and then I have stuffed this with the porous media and I have created a situation where I have forced fluid to flow through the porous media and not to get short circuited clear under all these circumstances these are the assumptions or the laws which are used to define the flow through a porous system so there are several ways of doing this what you have to establish is you have to just say that RE is less than 1 or not density of the fluid is known rho is the density of the fluid mu is the viscosity that you know for the fluid d10 you know why because you know the material characteristics the specific gravity and d10 from the particles as distribution curve and at what stage you have compacted it so stage of compaction is gamma w moisture content if gamma w is known porosity white dishes are known and saturation is known so state of compaction and the material is getting depicted over here what fluid is passing through this is getting reflected by 1 2 and 3 clear so in other words what we are studying is we are studying the interaction between the porous media and the fluid flow now this concept can be utilized by chemical engineers civil engineers hydraulics guys petroleum geophysicists and so on their fluids are going to be different fluid of hydro carbons flow of hydro carbons through the sediments one case flow of sludges through filters clear another case for a biotechnologist a solution having all sorts of bacterial activity microbes in it and I am trying to filter it and I want to create a clean solution for various applications clear the concepts remain same yes we call this as the characteristic length of the porous media d10 is known as the characteristic length you see we never talk about the third dimension because all these tubes are going to be infinite in the length you agree so it depends upon how long the porous media has been created I am not interested in that what I am interested in is at this point what's happening and if I am doing a very precise modeling by using some supercomputer or something I will try to see how d10 is changing all along but imagine you have a compacted soil mass and you have to see and realize and measure how the velocities and the pressures are dropping within the sample it is going to be extremely difficult we will discuss these things today so for the time being we are not interested in lengths of these things we are just interested in the characteristic diameter which is going to cause the flow of fluid to the porous system and hence d10 is good enough for me why because d10 is going to define that's a good question so now suppose if I say that this is a particle arrangement all right what is the d10 here through which the fluid will flow yes you are right so this is the open space and this space is going to depend upon the particle diameter so these are the complications I hope now you are realizing that the flow through porous media is not a very simple subject so now you are heading towards complications so now your next question would be what is the relationship between d and this clear another question would be what about the shape of the particles another question would be how about the tortuous lens and so on so this is the ever green topic to work on fine it has lot of commercial value okay for the time being is fine yes please anything else okay so let's go ahead if I say that th1 is equal to z1 plus p1 and th2 is equal to z2 plus p2 all right and if I put a condition that delta th is positive so it's inbuilt that z1 plus p1 is greater than z2 plus p2 fine even if I rotate it and if I keep it on the horizontal plane in such a manner that z1 becomes equal to z2 what I have got rid of is the elevation hats agreed so that means under this circumstances when z1 is equal to z2 what I am saying is p1 is greater than p2 the pressure head is causing the flow of water to occur through the porous media clear and the easy way to understand this is by using a term which is known as I the hydraulic gradient so what is I I is equal to delta p all right divided by length of the sample and length of the sample is let us say L now how would I read this one of the ways of reading this would be even is acting at this point or total head is acting this point total head is acting at this point we have done some mathematical manipulation to get rid of z2 doesn't matter even if I include z2 as long as the flow is taking place from this to this point clear energy at this point is higher than energy at this point the dissipation of the energy is taking place per unit length of the sample clear so hydraulic gradient is the term which is defined to show how pressure is getting dissipated over a certain length of the sample now your question is why it is not negative okay so what we have understood until now is the discharge is going to be equal to no let us say not discharge let us say v is equal to k into I sometimes k is also known as Darcy velocity or Darcy's permeability Darcy's coefficient also we call it as we also call this as hydraulic so I normally do not use this word coefficient of hydraulic conductivity sometimes people also call this as a coefficient of permeability it has different names this is the proportionality constant what we have done is v proportional to I we have changed to be into k into I now suppose if I say it is I to the power n I cannot be negative because what is the flux which is acting across the two points a1 into v1 correct so it is the flux which is getting dissipated at in length l this is another interpretation so flux has to be positive gradient agreed as long as the saturated soil is concerned remember the moment this becomes unsaturated it is a different case all together we are not talking about that situation so as long as delta p is positive getting dissipated along l your velocity of the flow is going to be proportional to the hydraulic gradient agreed it cannot be reverse of that what it says is if I increase the hydraulic gradient the velocities are going to be more and vice versa and that is true so this term we now we have agreed that I will be one positive I can write another expression that q is the discharge and this is equal to velocity into area area of cross section so q will be equal to k into I into a all right and for your quick reference if I say q upon a what is q upon a the small q so small q is nothing but the flux fine now in today's world how these equations are being manipulated please understand in two minutes we are talking about here all fluid flow clear what I have to do is I have to apply a flux gradient to cause the flow of something is this correct so the guys who are working in the field of electromagnetism what they will be doing they will be applying electric field gradient across the sample to pass current chemical engineers what they will be doing they will be applying concentration difference across the two points to create a diffusive current agreed C1 concentration of chemicals C2 concentration of chemicals delta C upon L is nothing but the driving force which is equivalent to the concentration gradient and I can compute everything like this only thing which is going to change is k so here k was Darcy's coefficient hydraulic coefficient permeability coefficient their k will become diffusion coefficient is this part okay this is in market right now everybody is trying to do extrapolation of these things in different energy field concepts to cause the chain in the total head yes yes yes how can I manipulate the total head tell me one of the ways would be I can lift this up but it is not going to help why as long as datum remains same I am not going to achieve anything then pressurize the points pressurize apply the same problem number four so there is a atmospheric pressure or some gas pressure which is acting over here now what's going to happen this pressure gets added to this unfortunately this pressure will not get delegated up to this point why because there is a shock absorber pressure absorber clear so now you have to do an experiment to find out how much pressure is getting delegated at this point which is definitely going to be less than this so what I have done I have done one manipulation to create a different type of total head at this point as compared to this point and that is my requirement is this fundamental here what could be another way suppose if I rotate the whole system now what's going to happen that's a trick are you getting this point so suppose if I rotate the whole thing so this point always sits above this point agreed head at this point elevation itself is going to be higher than elevation at this point so the discharge going to take place on this place with this place another manipulation imagine now hundreds of situations like this and go ahead with the engineering there is another good application of D10 which you might come across in some books you know there are people who tend to find out k now the question is how would I get the k value so let's discuss this a bit so determination of k please make sure that you write a small k because later on I will be using capital k intentionally for something else so right now I am dealing with all small k's alright don't mix up small k with the capital k there are different tests which you can do some are the laboratory tests which you will be conducting in the laboratory and they are known as you know constant head test and falling head test these are the two most prevalent and prevalent tests anybody is doing centrifuge modeling here as a BTP or whatever no centrifuges are also utilized to get the hydraulic conductivity we have done a lot of work in this field so you can check the thesis and the papers written by AK Gupta myself and some of your seniors who were doing BTP with me Anup Ramchandra Rao he is the guy who has done a lot of work he was my B.Tech student I will show you what he has done and so you may use the centrifuge centrifuge modeling also what essentially these tests are the first test is a constant head test number 2 is falling head test number 3 centrifuge test in a centrifuge I can do both the test 1 and 2 so in the first one what we do is that is known as constant head test normally this is performed over granular materials granular why because the permeability is so much that if I make a control volume alright just now I was talking about rotating the whole setup by certain angle so that it becomes like this so suppose this is my porous media or the sample which I have prepared this is the soil mass compacted soil mass now what we do is the principle is like this that we allow flow of water to occur by maintaining the head constant here so head remains constant and then I was explaining to you why porous media has to be granular when you conduct constant head test because the permeability is so high that unless you maintain the constant head the hydraulic conductivity values are going to be incorrect fine so what we do normally is we connect it to a reservoir you know there will be something like this which is connected to a reservoir and this reservoir will supply the constant pressure head at this point and the discharge takes place here and we measure this over a period of time and then from here we can compute k value is this okay if you measure q hydraulic gradient can be obtained area of cross section is known alright velocity can be obtained or k can be obtained directly simple test used normally for granular materials because of very high their high permeability the more challenging is the one the second one which is falling head test this is normally done on the materials of the soils which are fine grained high because the permeability of the fine grained compacted materials are going to be extremely low so you need not to maintain the pressure always alright constant head so here what we do is we will expose this system this is the control volume of the soil which I have taken which I have made and this will be connected to a tube glass tube which is graduated so here you have graduations we fill it up with the full water after compacting the sample to a certain moisture content gamma d and we wait for this water to drop over a period of time and we measure q value so this q is also the function of time one thing you can appreciate here is that the total head which is causing the fluid flow is decreasing is it not you agree so delta H is negative so this is the experiment which will be doing in the lab so if the area of cross section of this tube is known let us say small a if the area of cross section of the sample is known as capital A you can do the continuity equation this is nothing but a continuity is it not so continuity equation will be this q which is dropping down or the discharge is taking place is entering into the soil sample and hence q in the tube will be equal to the q in the sample is this okay q in the tube is not a porous media so this is only the area of cross section multiplied by the velocity what is the velocity in the tube of the falling water level del H by del t is this okay negative sign why negative sign because H is decreasing clear so this has to be equal to q of sample permeability of the soil mass multiplied by I what is causing I H the hydraulic gradient at a given time so what I am assuming is that the head difference across this point is H though H is decreasing and that is what I am getting reflected it over here multiplied by K into H upon L L is the length of the sample physical dimension of the sample all right so K into I into A solve this expression and get the value of K you understood in this expression because I am doing experiment I can find out at the function of time how H is changing I can record the values and I can measure the discharge so H is known for a given instance L is known area of cross sections are known you solve this thing this comes out of a log function do you remember the function 2.3 something I mean you can solve this this will be D H upon this will be del H upon H equal to K A upon L into A into DT and then integrate it from 0 to H capital H or whatever fine so this becomes a log function log of H equal to K into L into T time you are measuring at a given time what is the value of the head substituted and solve this this is okay remember the dimensions of the K are going to be velocity dimension I hope you can realize this because in this expression V is equal to K into I so I is a non dimensional term pressure can be equivalent to the height elevation is height clear so this is the height normally we deal with heights only similarly at this point divided by L of the sample which is a height so I is a non dimensional term hence K is mostly in meter per second unless specified is this okay so what we have done is we have obtained the K value in laboratory setup you are assuming that whatever head is dropping over here delta H alright that is this value so velocity is delta H upon delta T multiplied by area of cross section this is the discharge and this discharge goes into the sample continuity that is it H is the head H is the head so I will introduce this concept slightly later alright so if the head is causing the flow to take place this is the equation now what I can do is I can make miniature models of these setups install them in the centrifuge and do the test so that is what most of the Japanese Koreans and Americans are doing yes this is your K into I what is causing the hydraulic gradient the head across the sample I can I can do a manipulation I can keep the datum over here everything becomes 0 at this point total head total head at this point is H this becomes H upon L so another way of finding out K is what some people are using particularly consulting people they use a equation 100 times d 10 square this is an centimeter per second you will find this type of equation unfortunately these equations are valid only for the granular materials though they are extending it to the fine-gain materials also because d 10 is being used so let us remove d 10 from here make it as d square so let us take a simple case so that you can follow and get rid of all your doubts suppose if I take a case like this suppose there is a vessel and in this vessel water is filled up up to this point I give you two points let us say one is here another one is here show me what is the direction of the flow so the best formula to understand these type of things is fix a datum here compute the point number one point number two let us say elevation head what is elevation head at point two what is the elevation head at point number one make life simple let us make it at atmospheric surface itself piezometric surface you remember piezometric surface so where the atmospheric pressure temperature conditions are acting what about point one elevation is z at this point elevation is 0 what about the pressure head at point one atmospheric is acting here also by the way 0 you are right what about the pressure head at point two are you sure why take a piezometer here install it up to where the water level will go heights at simple rule always put the piezometer or a tensiometer clear up to what height it goes clear what is the total at what is the pressure what is the hydraulic gradient followed so I is 0 what is the meaning of this this is a case of hydro static problem agreed I can do different types of manipulations over here clear the real fun is the moment porous media comes in the picture because as long porous media does not come into the picture there is no fun hydro static case I will induce flow through the porous media by remember that to which I had plotted and just tilt it a bit so this is the case a and now let us talk about the case b this is the porous media this is the water level and this is kept in the water bath so here I am showing this as the free water surface this is the free water surface now how do I maintain is my headache I can connect this to a reservoir up to stream and the downstream I can connect it to another reservoir does not matter this is all redundant long as I have the pressure conditions over here now let us say point number 1 and point number 2 do the same analysis suppose if I say L is the length of the sample area of cross section is known material properties are known this is the height h and at this point suppose this is h1 let us do 1 by 1 what is the elevation head of point 1 so select 1 datum correct datum is normally we to eliminate all this what I can do is I can put the datum here itself this elevation and all agreed it is your choice you can put the datum here also but then becomes more complicated at point 2 what is happening what is the elevation head 0.1 this is L what is the pressure head at point 1 how do you compute pressure head please understand this do it in your notebooks so use the piezometer a small tube fix it over here up to where this will go point h height what about this point h plus you are right but why have you understood this or through the guess why that is interesting thing so until now whatever you have studied saturation partial saturation variably saturation case remember tutorial number 3 where I have created s as a function of depth and I have specified saturation limits as long as this happens over here your answer is wrong correct however the moment you assume the whole thing is saturated after a steady state has been achieved clear now if you put a piezometer over here you have 2 options what are 2 options this is atmospheric this is also atmospheric are you getting the point this point is connected to atmosphere is it not so let us do in simple way if I shift my datum over here what is the position head at this point this much if I put a piezometer here where it will go this is what you have to understand it can never drop even if I put a piezometer here what is going to happen is going to go up to this level it will never drop down so please do not get confused ever with this that could be the capillary action when you have negative tension zone getting developed in the system then only the pressure at this point will try to get nullified with the atmospheric pressure as long as this pressure and this pressure are atmospheric the only possibility is that if you put a piezometer over here it will go up to this plus this is this funda clear so your answer was correct but have you understood the thing hello this okay what everything is under positive pressures so there is no reason that the pressure will drop from here because the entire thing is exposed to the atmosphere this surface is same as the surface as far as the pressure conditions are concerned these are basically isopressure points there is no capillary remember this is the glass tube this is the soil I am just talking about this is the water body in which the glass tube is dipped complication I have done is I have raised this level a bit so that here also you have water but truly speaking the pressure at this point and this point is all atmospheric what I have to do either I have to reduce the size so much make it a capillary tube number one these are finite dimensions these are not in finite SML is small in dimension clear so capillary it does not come into the picture second thing is we have assumed that the system gets saturated over a period of time so this soil is completely saturated clear now you are connecting the whole system like this so what I am trying to expose you to the concept is try to understand what are the pressures which are acting across samples so this is C easy somebody said atmospheric one of you atmospheric is acting here also atmosphere acting here also that gets nullified now what is over here is the elevation head plus pressure head because of this water column it is okay this fellow said elevation is whatever depends upon the datum so elevation is 0 here and what is the total head this plus this because of the pore the pressures so let us write here the pressure would be H plus L so what happens to the total pressures see again I have created a situation where the flow is not going to take place through the system why because he said that at this point what is the total head he said H plus L so one of the ways to come out of the whole situation would be if this whole thing is placed in a water bath like this what's the total pressure at this point so this is the L yes so what I can do is I can assume this water column of delta H very infinitesimal volume and I can assume that this is the head over acting at this point which is variable so now it is alright so as your H changes this is the velocity which through which the water is getting discharged in this tube area into velocity of water this H remains universal this H is also acting on the sample this remains H what is causing flow to take place H so H upon L is the hydraulic gradient area is the cross section I have generalized the whole thing I do not care what is the pressure acting at what point I am simply saying as far as this is the datum I am assuming everything from this point to H which I can measure alright and at this the moment H is measured H is generalized so rate of change of H in the glass tube is nothing but the velocity of water discharge multiplied by area of cross section clear and this H is also causing discharge to take place through the sample so this becomes your H by L I into K into area of cross section H by L H is the hydraulic gradient which is causing the flow to occur because delta H of H is causing the flow to take place a small change in the height of the water column is your velocity component that it small change in the H is also causing the hydraulic gradient which is acting on the sample all the time so now your question is what repeat it integration choice is mine I might be doing this experiment to measure H1 and H2 and fall in H1 to H2 is in a given time T that is it got it so basically this is going to be from H1 to H2 in a time 0 to T okay now the rule of the game is normally we do not allow significant changes in the head to take place why because we are talking in terms of the infinitesimal changes delta H so truly speaking delta H should not become a meter because by the time the entire water passes through what is going to happen H is getting drastically changed so if you look at this expression discharge in the tube though it remains same as I discharge the sample but truly speaking H is decreasing and when H is decreasing what happens to K is decreasing so you are doing a test where the hydraulic conductivity or the parameter which you wanted to obtain is a function of time or a function of head not a very good thing truly speaking this should have been a constant parameter so normally we do not allow delta S to become more than few centimeters 5 centimeter clear so the moment one test is over again you fill it up to the top again go for 7 centimeter drop 3 centimeter drop because it is going to take time is a fine-grained material this is okay now let us restart this business now using all these concepts you know where these concepts are being used number one and what type of questions are being answered I am just trying to show you concentrate a bit we will answer that sand boiling phenomena also if you remember first lecture you had sent a movie correct so now you are going to get the answers to all those questions what seepage does to the soils so if you type on net sand boiling all right this is what happens when earthquake strikes and if you really want to do the analysis of these type of situations what we are studying here is a static case though this is a hydrostatic case and I am trying to convert this problem into a flow through the porous media case a real dynamic case will come when earthquake strikes the deposits or the soils and tries to liquefies I hope you can see that this is what is going to happen these are beautiful sand boils which you can see on the beaches and that is why the warnings are given don't go to the beaches when it rains and the whole thing has liquefied you know this is a beautiful example of what seepage does to the sandy soils you are seeing a boil and the entire soil has got lifted up and it is flowing like if this is what is known as liquefaction another beautiful example you can see over here there is a huge crater getting formed because of the liquefaction of the soil and this video very nicely describes as if this is a volcano volcanic eruption which is taking place the sand comes along with the water and these type of systems are very difficult to deal with in a real life there are several examples you can think of look at the sizes of the craters and so on this is the sand boiling phenomena I will prove how sand boiling occurs if you see this video this interesting video where the influence of seepage and the concept of effective stresses is demonstrated this is something which you can go through whenever you get time how the effective stresses come in the picture and how the boiling of sands might occur the beautiful example of how the pore-water pressure rises and how it gets changed when the water table changes another interesting PPT on levees which are founded on the peats and organic soils this is a big headache for geotechnical engineers it is an interesting slide if you read through what you will observe is that most of the levees which have been designed embankments have failed they have liquefied so this is what the land subsidence is we have been talking about land subsidence in the very first lecture so the more and more water you draw for irrigation purpose or for commercial purpose the whole thing might subside and ultimately the failures might occur so the embankments have failed because of the subsidence of the ground remember we were talking about the delta formation sedimentary deposits and whether they liquefy or not because of the earthquake though PT soils are cohesive soils they are also bound to liquefaction there is a lot of research which is being conducted in this context and here the question has been that does the delta have seismic hazard and the answer is yes because they have done the seismic hazard mapping and they have shown that it fails so this is the influence of the earthquake which they are studying on the soil mass and this is how the modeling has been done so before the earthquake you know the whole condition is like this of the embankment and after the soil liquefies what happens there is a sort of a subsidence and there is a failure so all these problems can be modeled easily by using the concepts which we are going to discuss we have to define few terms like what are the hydraulic gradients and what is the seepage force which is acting on the system there is interesting paper you should go through those of you who are interested in 2011 when the earthquake occurred at in Japan house and boiling characteristics were modeled everything comes from the basic principles like liquefaction sand boiling grain size distribution and permeability so intentionally I am showing you this paper because many people think that R&D is something you know very extraordinary but truly speaking R&D is also simple concepts which you pick up from third year onwards and then you just build on them to answer the questions which society is asking so this is how you will see the moment you raise the height of the R&D level which is not in the particular light of the radiance which is the condition and extra value which is valid at the moment use on the bottom something known as piping piping also get from these type of models the moment you open you can see the we will be talking about the piping this is an urban embankment which is holding water and then we want to see how the embankment will become unstable because of the excessive seepage force this is the piping which is getting generated I will just show you one minute this is the pipe which gets generated in the sand bed because of the gradients and then the whole thing liquefies watch this video so this is a dam which is being modeled and this is retaining water now if you increase the height of the dam retention look at how the whole system is about to fail concentrate at this point so when you are increasing the height of the water column the entire sample might yield and that is happening at the critical hydraulic gradient so look at the soil this has kept in look at this because of the boiling process loss of strength so imagine the building in which you are living and because of geomorphological alterations it is a big world in today's context alright geomorphological alteration could be how many under underground structures are being constructed in bombasticity any idea right now let us find it out and what could be the impact of that we have discussed this lowering of water table alright mathematically we have obtained a solution and we have shown the sigma prime increases and ultimately what happens so these are the models which you can go through so a hydrostatic case has got converted into a seepage case and seepage is causing all this to happen