 Now, let us discuss the second methodology which is MIP, mercury intrusion porosimetry. So, why you need to conduct MIP, what is the requirement? So, basic understanding is all the geomaterials which are composed of wide range of particles, their sizes, shapes and the pores or the material is porous in media. So, this way of the knowledge of pore structure of these materials is important as it can give insight into both microstructure and the performance. See, there was a time when people used to talk about particle size distribution. Now, particle size distribution is very well understood and its limitations are also very well known. So, present-day geomechanics you know entails MIP analysis to understand what type of pores are present in the soil mass and what is their distribution in terms of diameter, radius and so on and frequency. So, rather than measuring the porosity it becomes more informative if the manner in which volume is distributed with respect to the pore size. So, lot of people you will find are working in this area where they are trying to develop equivalent seepage models for soil mass, where there is a very serious you know doubt or question being raised whether your Heisen-Polsley equation is correct, whether Darcy's law is correct you know. So, these type of studies people are trying to do because these equations do not consider the overall porosity of the system. And in the subsequent slides I will try to show you that when we talk about the porosity I think we are only taking into account hardly 20 to 40 percent of the porosity of the system which you call as the bulk porosity it is not the total porosity. Now for that matter if you look grain of the soil and the pores how they are you know associated with each other. So, there could be some pores which are closed, there could be some pores which are dead ends. So, it is just like driving a vehicle in a lane which ultimately ends up in a dead end. So, you think of water molecules entering the system, but then there have no way out to come out of the system. So, in what way the overall hydraulic conductivity is going to get affected if you have not included dead ends which are present in the pores of the soil mass. Similarly, for that matter you can see some of the pores are interconnected. So, the moment water comes over here gets distributed in two parts and both of them end up in dead ends. So, those who are working into the micro mechanics of the system they require these type of analysis much more and this is where the energy concepts are becoming very important in geomechanics because using the energy concepts particularly the law of thermodynamics you can analyze what is happening inside the porous material. Now most of the time we talk about the pores which are through and through like these are the pores you know these are the passing pores. So, any water which enters into this simply comes out of the system and we call it as a short circuiting effect. That means, the water has tendency to short circuit the sample itself it is not entering to the sample it is passing through the pore through and through without taking into account the complete porosity of the material. So, this is where most of the time people have given a thought that how total porosity of the system can be measured and that is where mercury intrusion porosimetry becomes quite important. In western countries they do not use it because of the reason that it deals with mercury and they are too much scared of you know mercury as a poisonous and toxic material, but anyway we continue over study using these things. So, whatever porosities you have till now talked about look at this grain there is another grain like this of the sand or the clay or whatever there is a agglomeration of the grains, suspension and there is another grain like this. So, if you want to understand what is meant by porosity the first type of the solid is known as a non porous solid it will not have any tendency towards fluid no attraction clear nothing can pass through this. So, this is extremely low surface area most of the sands will show you this type of a porosity this is where we talk about their surface porosity. How about this system these are the porous solids they have high surface high pore volume and high dimensions because of all these protrusions and the interest which are present in the system. Now, this is a particulate structure where you have particle size and the surface area which are quite high and this is a very interesting type of a porous material which is sometimes also named as catalyst. So, on the particle you will see that lot of ions cations or the foreign bodies have a tendency to get bugged. Now, this process we will discuss later on under sorption desorption capacity of the material. So, basically these are the activated sites on porous systems which are normally present in powders or very fine-grained materials. So, we talk about the porosity the whole idea is to distinguish between this to this to this to this type of grain which are present in the soil mass. These are the shapes of the poles which are present in the soils they are cylindrical in nature they are the slits. So, a material will pass through like this it will come over here again pass through like this and so on. This is slate structure conical pores spherical or ink bottle type of pores you have. So, enough permission can take place through this ultimately there is a dead end in this form and everything gets accumulated over here and sometimes you have interstitial interlinking of different types of pores. So, these are the basic models which people have come up with when they talk about the porosity of the system. Now, how would you identify a pore is a million dollar question. So, that again is a very intricate thing. How would you differentiate between these type of pores? Versus of MIP and its results are required to be from that basically we can understand which are the of course. Yeah one of the examples I will show you how to differentiate between the two types of pores at least. Any question doubts? That is what I said these are the assumptions these are the people have assumed that these type of pores will exist and they have done mathematical modeling and they try to collaborate the results from the experimental results and then they show whether this type of system has cylindrical pores or slit type of pores or ink bottle type of pores or interstitial diseases and so on. Lot of research is going on in this area and not believe this, but this is the micro analysis of the soil samples and for understanding the interaction which we have been talking about you have to understand these type of phenomena and the mechanisms. Then only you can talk about how the contaminants are getting you know interacted with the soil mass. So, when you start talking about interaction then you have to go into the micro mechanism. So, roughly if you characterize or if you classify the pore sizes and the parameters which you can obtain from this type of analysis there are three types of pores micro pores, meso pores and micro pores. I think now you can understand in which zone you normally talk about when you do classical geomechanics. These are all in nanometers range. So, when you talk about micro pores they are less than 2 nanometers. Most of the zeolites, carbon, silica fumes they will have this type of pores. Meso pores they are from 2 to 50 nanometers, alumina, polymers, catalysts they will exhibit this type of pores. And micro pores are the pores which normally you talk about when you do your porosity test to obtain the porosity and that is where I say you only you know talk about one third or one fourth of the porosity of the total system ignoring the micro porosity and meso porosity for which you require either helium gas or mercury. So, that under pressure these fluids will enter and they will reach up to these pores water molecule cannot reach up to this pores. So, that is the difference why you require some non-wetting fluids like mercury and helium gas to do pore structure analysis. Now these are the parameters which normally one will look for from the analysis bulk property apparent and real density, percentage porosity, pore volume pore size distribution that is the pore volume versus pore size. So, rather than particle size pore size is more important this is what I am trying to emphasize over here is the pore volume versus pore size not the particle size. The total pore volume in total volume divided by per unit weight of the material average pore size a specific surface area of the material and particle size distribution that is relative percentage versus particle size. So, this information you should be getting from a typical mercury intrusion porochymetry. Anything else Sneha which you can think of getting from this test or this is a complete system. In your hydraulic conductivity models what are the parameters you have used to define k hydraulic conductivity normally you say k is proportional to e upon 1 plus e or e square upon 1 plus e or e cube by 1 plus e, but there are lot of coefficients which get multiplied to this. What are those coefficients shape factor tortuosity factor sorry diameter that is for coarse grain materials yes. So, shape factor tortuosity these are the two important things. So, we have been always assuming or ignoring these factors we never talk about shape factor and tortuosity, but slowly and slowly when you go to the modeling of contaminant transport you will notice that the tortuosity factor becomes much more important. So, you can still use these techniques to obtain shape factor c parameter and tau parameter this is the tortuosity. I hope you understand what is meant by tortuosity factor that is effective length divided by physical length of the sample square of that. So, that is why tortuosity factor could be much much higher than 1 and hence your hydraulic conductivity gets affected because of tortuosity of the particles. So, there is a lot of scope of doing research in this area. Then comes the characterization schemes and here I am going to just introduce a bit of gas adsorption because later half of the lecture is going to be associated with the gas adsorption techniques for finding out surface area and so on. So, MIP basically gives you course as distribution, particle as distribution, bulk density, apparent density, total porosity, pore area distribution. You require gas adsorption also sometimes because of finding out let us say surface properties. So, if you are interested in finding out low high specific surface area then gas adsorption is a good technique. Micro mesopore distribution that means, further differentiation between the pores which are present in the system, micro mesopores which are in the total volume and of course, helium gas spectrometry which will give you the real density of the system. This is part clear. So, we have discussed about MIP quite in detail. Helium gas technometry instrument you must have seen in the lab where you can pass helium gas and you can get the real density. About gas adsorption I will show you what is the application and how these techniques are used for characterization of the geomaterials. A bit of the MIP details. So, mercury intrusion porosimetry is regarded as the standard method for macro and mesopore distribution analysis and since this technique is conceptually much simpler it is experimentally much faster and this is unique because of its ability to evaluate a much wider range of pore sizes than the alternate methods like gas option, calorimetry, scanning electron microscope and thermoporometry. How much heat gets diffused in the soil mass from one place to another place? This is what is known as thermoporometry and this technique is used not only to determine the distribution of pores in various materials of the soils, but is also to find out the changes which a system undergoes during loading conditions. One example is that compaction process. So, from dry to wet of optimum when you compact the soil how your pore structure is changing can be captured by this technique. This is the basic concept of porosimetry. A typical wetting fluid will show you this type of meniscus and the angle or the tangent between the surface and the meniscus will be theta value which is going to be lesser than a non-wetting fluid. So, in case of non-wetting fluid because of the surface tension this is how the fluid will sit each drop of the fluid. Now, using this concept I can pass it through a pore of size d by applying certain pressure without breaking the drop clear. So, if you think that this is a tube which is nothing, but your capillary tube you have done this analysis that if this is a surface tension force. So, T times multiplied by cos theta into the area of cross section is the uplift force. T sin theta component gets nullified and this force is lifting the fluid in the capillary that is the volume multiplied by density. So, from there you can get the equation which governs the law of mercury porofimetry is known as Washburn equation I will show you slightly later. So, the characteristics which you use are mercury is a non-wetting fluid for many solids and it is forced to penetrate into the pores and penetration pressure is related to the pore size. So, this is the pore size the amount of pressure which you are applying from outside they are correlated with each other that means, a certain pressure will take care of a certain pore size. So, I will show you a typical MIT result which will be self-explanatory and to show you how this type of analysis can be done and you can achieve some conclusive results. Another interesting thing is that the volume of mercury which is going into the pore is directly related to the pore volume. So, here we are showing a pore in this way this pore could be cylindrical ink bottle type slit type or anything as per the previous models. Now, this is what happens when you are trying to intrude mercury into a pore because imagine as if you are parking a mercury droplet into a pore by applying some external pressure and the condition is that this mercury drop should not break clear due to the external pressure. So, it is a basically synergy between the between the pore and the fluid which is trying to enter into it. So, the more pressure you apply here what will happen either the pores will change or the droplet will change. So, this type of contradictions will come sometimes when you do this type of analysis. So, I would like to show you one trigger. Now, this is the basic model which is used to understand a wetting and a non wetting fluid. If you have a system of particles where the pores are you know concealed by a layer of the liquid what happens mercury will not be able to enter into this. However, there could be a system where if you apply more pressure what will happen this mercury has to enter into this. So, this is the basic concept of choosing a pressure and how this pressure is going to result in intrusion of mercury into the pores of the system. So, basically this becomes a interesting phenomena what pressure should be applied for a given pore. So, that these pores of a certain diameter get built up. So, this equation you can derive easily by the mass balance that is a subsistension T cos theta r is the radius of the pore or the capillary and P happens to the pressure. So, this is how you have computed suction pressure also in the soil mass by using the same equation and theta is the contact angle. Now, this is what is known as Washburn equation. So, T is known for mercury and theta is known for a soil mercury system 130 to 140 degree and T is 0.48 dimes per centimeter I suppose. What it leads to is a typical mercury intrusion porosimetry characteristic curve. So, if you look at this curve what you will notice is on the y axis is volume of mercury which is getting entered into the system or coming out of the system with respect to pressure on the x axis. So, how would you read this graph is if you increase the pressure what will happen the mercury it has a tendency to go into the pore. So, this becomes an intrusion curve. So, the black one is intrusion curve as you increase the pressure applied the more and more volume of mercury goes into the pore of the soil mass. So, this way you can complete all the pores by applying a very high pressure. Now, what is going to happen when mercury is entering into the pores of the soil mass can you speculate something it may it may break the pores itself. So, there could be a collapse of pores. So, now, this is what you are going to see here it is just like your consolidation graph you know where this is known as intrusion curve the mercury goes into the pore and if I retreat back the mercury by applying suction. So, what is the graph which I get this is what is known as extrusion graph that means, if I can extrude the mercury which has entered into the system by decreasing the pressure or by applying some vacuum this is where you end up. So, some volume of the mercury remains in the soil mass this could be because of the destruction of the pores and this phenomena is normally known as hysteresis. Now, hysteresis is becoming a very big question mark in geomechanics everywhere we talk about hysteresis. If you remember in your electromagnetic courses there you talk about hysteresis and based on hysteresis you have classified the material you agree or no a material which stores more of the magnetism has more hysteresis. Now, this concept can be utilized in geomechanics also in characterizing the materials and differentiating between two types of materials and the type of pore structure which is existing in the system is this part ok. So, this is what Sneha is trying to study and she will be presenting a seminar on wetting and drying curve where she will be talking about hysteresis associated with wetting and drying. Now, that again is a capillary action that is what you are trying to study. That is what Seema is trying to answer in her thesis and she talks about soil water characteristic curves during wetting and drying. So, why they are different or why they are similar? So, these are three examples of hysteresis which normally we talk about. Now, NC2-OC response in classical geomechanics is also nothing, but hysteresis. So, how do you define hysteresis? There is nothing, but the amount of energy which gets stored into the system. Here what is happening? The amount of mercury which is getting stored into the pores. So, there must be some force which is capturing all the mercury into the pores or this mercury cannot come out because of several reasons. One of the reasons could be collapse of capillaries. So, Sneha this is the challenge. Later on maybe when I talk about hysteresis in drying and shrinking phenomena, there you can notice that your proctor compaction curve in wetting cycle will be different than the proctor compaction curve which you obtain in the drying cycle. So, these are the you know effects of environment which are causing drying and wetting of the material when moisture goes into it or comes out of it. So, these type of tests which we are discussing like MIP are nothing, but a good simulation of a natural phenomena in terms of quantification of its pore structure and the alteration in the pore structure because of some process. Is this part clear? If pores were perfectly elastic, what would have happened? Come out exactly. So, the red line and the black line would have got superimposed perfectly over each other. That is right. So, no loss of mercury, no loss of pores and so on. That is what I said. The way you characterize your ferromagnetic material, nonferrous materials, nonferromagnetic materials, what is the differentiation? It is just based on the amount of magnetic energy which they store. Exactly that is what we are doing. That is what we are trying to do and that was the reason of telling you that the consolidation theory should be revisited by using energy concepts. Just by applying mechanical loads, you cannot find out the volumetric deformation to a precise limit. You are ignoring lot of mechanisms which are going on in the sample and you are just measuring something which is not very accurate. I think now you can correlate it better. So, similarly somebody may ask you to develop a model based on energy model for stress strain relationship of materials. Why you get peaks in OC material? Why you do not get peak in NC material? Why do you get a peak in heavily compacted sands and you do not get any peak at the time of shearing in loose sands? So, everywhere you are finding this is the packing of the grains which is getting affected by the particle arrangement. So, lot of things are going on inside the particle which we are not capturing to the many test details. And that is where this type of thinking and philosophies you know is going to be quite helpful in answering the mechanisms which are very close to the nature. Good. So, since that today they have followed things. Is this okay? Any other suggestion? No doubt. One more additional this thing means about the cisterosis. Another reason could be you know this entrapped mercury it is because of the pore shapes which sir has already shown. For example that ink bottle type. So, while including it will get entered but while extruding it is not possible to come out all that mercury because it got entrapped into that bottle shape. So, that could be another reason means even if the pore structure is intact but because of the pore shapes it is possible that mercury will get entrapped and it is not possible to come out. Or in another word it means what you can say it is soil contaminant interaction how it going to affect the pore structure. Correct. That we can understand from this. The degradation of the pore porous media because of interaction it becomes a reverse problem. You got it it is a very good thought which you are giving that is right. So, you can see the after effect and then you can back trace the effect. This is also known as back analysis. So, degradation of the material, materials response to external disturbances you can study easily. I have included one slide what he was talking about and I hope it should be clear when I show you that slide. So, what is the information which you get from this type of a relationship. So, basically what you are doing here is you are developing a incidentally the way you look at it is nothing but your consolidation curve is it not your pressure sigma prime versus void ratio e versus sigma prime curve. So, e is nothing but there you talk about the compression of the grains sorry compression of the pore structure void ratio void ratio keep on changing. So, the same graph what information you will get from is this the pore size distribution surface area equivalent pore size critical pore diameter distribution of total porosity and free porosity under trap porosity. This trap porosity which it was discussing. Now, this is a typical intrusion curve which we got for one of the samples which we had analyzed. So, where you have pore diameter versus applied volume normalized volume. So, the more the pore diameter what happens more and more volume of mercury is going to get intrusion system. Now, could you answer this question that you find here one bench what is the reason for this bench formation. That means, the normalized volume does not increase with the pore diameter clear mercury is a non compressible fluid. So, there will not be any time lag it shows the porous structure property that the pore diameter of this range are quite prominent. So, it is just like please free flow of fluid into the system. So, with a with no even increment in the pressure the entire mercury goes and sits into the pore spaces, but then I just just wait a minute please and then if you want to further overcome the resistance offered by the force you have to apply more pressure. So, truly speaking as the pressure increases you know the normalized volume keeps on increasing which is being mapped over the pore diameter. So, this is a good way to see what type of distribution of the pores you have in the material and how easily the pores are getting filled up with the mercury because of certain pressure. So, this type of diagnosis you may do by looking at this type of graph yeah what you are saying because of the type of the pores that means, from pore sizes of let us say 2 to 0.2 the most of the resistance is not coming in the picture. So, these are the pores which are good enough for mercury to flow just like this very easily you do not require any external pressure. So, if in other words there is a predominance of the pores of this size in the sample this is the resistance offered by the system and this is the resistance offered by the system. So, you can very easily make out that this is the range in which the pores are present in the soil mass or a porous system. So, this is how you can diagnose what type of pores and their frequency and their magnitude and their diameters are present in this system. Present day MIPs have softwares which are included in them. So, they analyze everything for you based on the curves which normally you get by doing an experiment. Those of you who are interested in learning MIP they can contact switch it and whenever he is doing his experiment next time you can come and sit with him it takes time. So, you please fix up with him and you can demonstrate to them how it works. Now, this is another interesting relationship which you will get out of this exercise mean pore diameter as a function of void ratio alright. So, as the void ratio increases the mean pore diameter also increases that is understood. So, but this void ratio is the total void ratio which we are talking about which includes all sorts of pores micro meso macro which otherwise you would not be able to obtain. That means, the material and the grain porosity also you are considering into the analysis. Now, this answers your second part of the question when you are talking that how these studies can be employed for soil contaminant interaction. You will notice in the subsequent lectures when sorption desorption takes place there is a lot of parking of the cations which is taking place on the grains of the clays. So, unless you know exactly how much is the surface area which is exposed to the environment or the contaminant you will not be able to estimate how much interaction is going to occur. Now, this is what actually such it was trying to explain. You may have a system where the mercury gets entrapped inside and there are both the ends which are choked. So, less orifice on both the end, but more cross-section which is available for mercury to get filled up. Now, other way of understanding this would be there is no difference between this type of pore and this type of pore. So, truly this is a limitation of MIP. You cannot really map the pore structure because this is equivalent to this. All the mercury which is entrapped in this portion can be you know drawn an equivalent with this type of a analogy. So, two systems which will present almost the same response, but it is very difficult to differentiate between two type of pores. You have to think of something new for differentiating between these two type of pores. For civil engineers this may not be very important at this moment, but those who are working in synthetic polymers, synthetic zeolites catalyst for them these studies are very very important particularly those who are may I came across a sponge iron sample where people wanted to do MIP. I hope you can appreciate why MIP should be done on a sponge iron. How much amount of energy is required to melt it? For that pore structure is required to be studied and lot of raisins, polymers, catalysts which are being fabricated by the industries require these type of studies and they contact us for doing this test for them. Some more interpretation on the results which you get from mercury intrusion porosimetry with this is the complete tomography of the sample. You cannot come across things better than this. This work was done by my another PhD scholar Dr. Vibhuti Das and we studied here the concrete specimens. Like in your particular distribution curve you use lot of terms as C C, C U, D 15, D 85, D 30, D 60, is it not what for, for what purpose. So, that you can characterize the material better. Where do you use C C and C U term in classification of the soil coarse grain materials? For fine-grained materials you have another classification scheme, liquid limit, plastic limit, plastic D index, Atterberg limits and so on and then drawing the A line. So, the question is that after doing MIP how I am going to differentiate the materials? How I am going to use the parameters to differentiate between one material and one material? So, if you look at the first relationship which is the volume of mercury which is intruded in the sample as a function of the pore diameter alright. So, as the pore diameter increases what you will notice is that the volume of mercury dropped down. Now, if you do a bit of construction now this type of construction you have done to find out the creep and T 90 if you remember 90 percent consolidation in the soil. So, the mechanism remains same. So, this is the pore diameter versus volume of mercury graph will give you a parameter which is known as DT. So, DT is nothing, but this pore size you know there will be a sudden increase in number and the cumulative volume of the pore. So, this parameter becomes very important characterizing the geomaterials. If you plot percentage volume intruded of the mercury versus pore diameter there is something known as mean pore diameter Dm which corresponds to 50 percent of the pore volume. So, if you consider 50 percent of pore volume if you obtain Dm this becomes another parameter which can be used for characterizing the geomaterials. And the last parameter is DC this is known as continuous pore diameter. This is what I was talking about in the previous slide that therefore, which are continuously staggered or continuously present in the system. So, this is the term which is known as DVH that is increase in volume of the mercury divided by differential changes in the log of the pore diameter. So, if you plot this index with respect to pore diameter wherever you get a maxima. Now, this maxima corresponds to DC. So, this is the continuous pore diameter the maxima of the curve which corresponds to the group of the largest fraction of the interconnected pores. So, this gives to the answer to the point which you are raising that when the pores are interconnected you do not require much pressure to push them from one pore to another pore to another pore conductivity is very simple. So, based on DT, Dm and DC they are your equivalent terms to D50, D30, D60 and D85 and D15 and then you can try to see what is happening to the material. I thought of showing you this relationship which you will appreciate which shows that how curing of the concrete can be checked you know by using these three parameters. What you want concrete to become after 28 days much more durable that means, the pore sizes should be as small as possible. So, if you plot DT, Dm and DC with respect to days of curing what you will notice is as days increase there is a decrease in pore diameter and that is what you wanted clear. So, it is a very simple application of MIT in checking the pore media characteristics clear. So, this is how you can go for synthetic concrete as well by using different type of pozzolonic materials and making a good grade of concrete. In the next class I will discuss the specific surface area determination.