 So, let us discuss now the first mechanism which is advection or sometimes is also known as convection. So, you consider a control volume at time t word there is a solute which is available in the control volume. As time t naught becomes t 1 and from t 1 to t 2 this whole control volume of the contaminants gets a place shift or it moves from one point to another point. So, this is how it shifts from one point to another point to another point. Now, this is the phenomena which is known as advection that means, the solute or the contaminant gets transported because of what? Because of the seepage or the seepage velocity along with the flowing fluid which could be water in response to a gradient and this gradient is nothing, but hydraulic gradient. So, if this is the case you are talking about advection or convection normally this type of mechanisms are defined by v s equal to k into i by porosity. What is v s here and what is eta or porosity? So, if you divide v by porosity v is the discharge velocity divided by the porosity it becomes your seepage velocity. So, which velocity will be more discharge velocity or seepage velocity seepage velocity. So, seepage velocity is higher than discharge velocity. Now, if a mass of solute and please note that this solute happens to be non-reactive. What is the significance of non-reactive? It has no affinity towards porous system clear. It has no affinity towards porous system. So, it simply migrates through it without stopping anywhere without changing its own form. Better word would be without changing its own form. So, form includes concentration also clear. So, if a mass of solute which is non-reactive it is a passive contaminant of a concentration C is placed at one end of a pipe or a control volume then in a given time it will travel a certain distance as a plug. Now, this is what is known as a plug let me without losing its entity or identity or the control volume of the surfaces it simply keeps on migrating from one place to another place to another place due to advection process. So, these are the attributes of the advection mechanisms. Now, the challenge is to find out the transit time. How much time it will take to move from one place to another place to another place that means, how do you obtain T 1 and T 2 and so on. So, the transit time required for a non-reactive solute to migrate through a saturated soil of thickness L would be what L upon V s. So, if you know the distance if you know the V s it can simply work out it is time is this part clear. Now, suppose if I change the word the transit time required for a non-reactive solute to migrate through a unsaturated soil then what is going to happen that means, your in your logic the unsaturated hydraulic conductivity will be more or saturated hydraulic conductivity will be more why it is so that is right. So, you are correct for unsaturated soils the value of k would be much smaller. So, if value of k is much smaller what happens for time the time becomes much more what is the meaning of this. This is useful for engineers or not useful for engineers when you are dealing with unsaturated soils. Suppose the contaminant transmits itself from point A to point B when the aquifer happens to be saturated the time taken is less and saturated when this system happens to be unsaturated time taken from 1.1 is a point moment is much much higher clear. Now, this is where I had told you sometime back that if you are dealing with unsaturated soils you need not to go for barrier systems provided you have characterized your soil mass very precisely and you know what is the hydraulic conductivity of unsaturated state of the soil mass and that is where most of us are trying to study unsaturated hydraulic conductivity of the soil mass ok. So, this is where the deviation is from classical geomechanics to unsaturated soil mechanics because most of the deposits most of the aquifers in nature are unsaturated what are tables are pretty deep. So, most of the contaminant transport is going to take place in unsaturated soils not in the saturated soils. This is part clear exactly because hydraulic conductivity of unsaturated soils is much much less. So, that means, the contaminant transport from one place to another place would be very slow because hydraulic conductivity itself is very slow, but suppose if you are not using the correct hydraulic conductivity which is unsaturated hydraulic conductivity what is going to happen you are going to over predict the phenomena which is not going to take place in nature ever. So, that is the reason people are now shifting from classical geomechanics to unsaturated soils where they want to establish all the properties to most precise state of the material which happens to be unsaturated clear. Now, a very long thinking here would be if your waste has enough energy thermal energy and if this migration is taking place through the porous system what is going to happen a saturated porous media may get altered into unsaturated state of the material. Now, this is what is known as a coupled phenomena that means, heat is migrating moisture is migrating even vapors may also be there. So, a lot of coupled mechanisms are going to take place simultaneously and I always like to give an example of the people who are working in the field of petroleum engineering where they try to take out petroleum from the deposits clear. Now, these deposits are mostly saturated in nature water saturated. So, that means, you think of a situation where the flow of gas is taking place and a fluid of different density is taking place through water saturated porous media. Till now you have been talking about only seepage through saturated soil mass consolidation through only saturated soil mass compressibility of saturated soils and so on, but then when you talk about the natural processes or more complicated processes where coupled mechanisms become essential for consideration. This is partly did you follow or not. So, you think of doing a consolidation test where the gas permittivity should be obtained from saturated clays. How easily gas is going to migrate through the saturated clay deposit alright. Now, my question to you is where you are going to do this type of an equation in real life modeling. Can you think of a situation where by simply obtaining B as porosity of the material if you know the k value what wonders you can do for the society just by using this equation. Ultimately what is the whole idea of studying the transport mechanisms at a given distance l after certain time t how much contaminant is going to get migrated which happens to be non reactive in nature. So, by using simple equations I can give the answer that down the line in terms of time or in terms of distance what type of environmental deteriorations are going to take place because of some industrial activity. Now, this is where what you have studied in your undergraduate can I model k layers of soil mass either in parallel or series. So, I can find out k equivalent of the ground or the sub soil I can use this in this model and I can work out the time or distance regarding a given situation. Of course, the condition is that the contaminant is transport is taking place just because of advection flow of water and contaminants happen to be non reactive they are not going to lose their entity. So, the scope of even advection analysis is also quite big. Now, this is what the real modeling is what a hydro geologist will be doing is there any way of measuring V s how would you measure V s under in situ conditions you cannot you cannot measure why do not measure it then you do not require to measure it you can get the equivalent porosity you can get the equivalent permeability you know what type of hydraulic gradients are acting and then you can find out the time for a solute to travel a distance L or vice versa is this partly. So, you need not to talk about or determine V s as such because V s gets nullified. So, V s is not a very important parameter there, but suppose if somebody is after you and he says no you have to find out V s how would you obtain under in situ conditions under in situ condition how would you obtain V s can you obtain K under in situ condition yes or no in situ hydraulic conductivity how would you measure how would you measure which test should be done Packers test Packers yes. So, you perform a simple Packers test and you can get the K value now if you know the K value if you know the hydraulic gradient you know the porosity you can work out V s that is right clear. So, either pumping in or pumping out test you can do to get the Packers permeability ok good. So, though it seems to be very simple, but applications and implications are tremendous is this part clear it is used for any deposit under in situ conditions of course, then by bore logging you should find out whether you have obtained the hydraulic conductivity or the discharge for a subsystem which contains soils or rocks. So, it depends upon if you can characterize the substrate the values which are going to get are nothing, but corresponding to that. Now, just to give you an idea about the representative values for effective porosities all soils clear would show you a very wide range of porosity 0.2 to 0.01 that is 1 percent to 20 percent approximately do you agree with this data or you think that this is not very correct. So, I think you can understand what is G C G P G M G S as W S P S M and S C M L M H what about this C L O L C H O H P T. What is P T? Peats O H organic soils of high high plus T index. So, as you transform from this to this state of the material what happens to the porosity this answers your point that there could be some dead ends and all in the materials which are fine grained. So, what is the meaning of this? It indicates that for these type of soils definitely you have to do micro structure analysis otherwise your porosities and the permeabilities may not be very correct because you have already studied that there will be meso micro and macro pores micro macro and meso pores in the fine grained material. Now, for rocks if you talk about the non fractured rocks and the fractured rocks there could be a situations where you can find out this type of range. The fractured rocks minus fractures highly fractured material. However, non fractured materials can also give you 15 percent of porosity. What is the porosity of basalt? Approximately granite, granite would be of the order of 8 to 10 percent basalt can be 15 to 20 percent, chocks would be 15 to 30 percent, sedimentary rocks will show you high porosities 25 to 40 percent and so on. So, this is a sort of a very rough indication of the state of the material and the corresponding porosity. Yes please I told you minus fractures minus fracture that means, though it is very fractured rock mass, but when you talk about see that is what actually I have been trying to tell you all the time. When you talk about the porosity if you include the fracture that becomes fracture porosity you are not talking about fracture porosity as at all. Most of the fractured rock masses will be very very less pervious, their porosities will be very less because of the weathering process alright. So, because of the weathering process what you will find is there will be fractures in the system which may attribute to overall porosity, but not at the micro level. So, this is a chart which is normally used for obtaining the effective porosities of the materials. Now, the question is how would you obtain the advective flux? So, it is very easy advective flux would not be J which is the mass of a fluid which is flowing through a unit cross sectional area in a unit time and this is nothing, but the discharge velocity multiplied by the concentration, where else you use this type of equation apart from geomechanics. Have you ever used this mass balance equation for determining something apart from geotechnical engineering v 1 into C 1 equal to v 2 into C 2 sorry cleared fluid mechanics exactly that is right, but v 1 into C 1 equal to v 2 into C 2 you have used in fluid mechanics for determining what for finding out the discharge through open channels. So, if you want to find out the discharge in an open channel what you do you take some salt put it here and down the stream at a distance you must measure the concentration if you know the concentration you know the v 1 v 2 and you can work out the discharge. So, that is the utility and you know beauty of this equation symbol equation. So, it is nothing, but the mass balance. So, velocity multiplied by concentration will give you now in geomechanics how we can extend this further we can use v equal to k into i and k into i into C is nothing, but your total mass flux. So, from one point to another point if your mass flux is moving what is the significance of this you think of a situation where your falling head test is replaced by a solution of sodium chloride which is permeating through the soil mass is this clear. Now, what I want to ask you is after certain time at the middle of the sample what is the concentration of sodium chloride it is not less or more what I am saying is if I want to ask if I want to determine how would I find it out. So, you have k into i into C you know what is the hydraulic gradient acting between the first half and the second half of the sample is this clear what is unknown is C. So, till now you have been plotting I variation with this sample you agree or no delta H upon L the variation is linear. Similarly, you can plot the variation of concentration within the soil sample the one end is exposed to 100 percent concentration of sodium chloride which is permeating into the soil sample. So, my question to you was what is the concentration variation of sodium chloride within the soil sample of length L is this clear you know hydraulic conductivity the same test which we have been doing to obtain k can be done just by replacing ordinary water with sodium chloride solution. You can take out the sample of the soil mass or the porous media you can slice it and find out the concentration of chloride ions at different depths and then you can do the profiling you need not to do this even if you use mass balance k into i into C at first point equal to second point equal to third point. You know the variation of hydraulic conductivity you know the variation of i you know the C values from the boundary conditions and you can draw the variation of concentration. Is this part clear most of the problems which are encountered in day to day life are being modeled by using these simple equations impact analysis of certain in activity on the environment.