 Now, by this time you are aware of the thermal properties of geomaterials that is thermal resistivity, conductivity, diffusivity and specific heat. So, the parameters which influence these properties, the number one parameter is the effect of the type of the soil. So, it is a very random way of defining, but still quite difficult to state the quantitative value of the resistivity of any soil, mainly due to the fact that the type of the soil is not clearly defined in most of the situations. There are two things associated with type of the soil, one is the origin or the composition and the second one is when we use the word type of the soil, it is understood that we are talking about its size fraction. So, state of the art is not sufficient enough to address the origin of the soil and how it influences the thermal properties, but yes enough work has been done wherein people have talked about the grain size fraction distribution or effect of grain size on thermal properties. So, this is where actually most of the time the confusion arises when we say word clay, it is difficult to convert it to certain properties unless you are very particular, because clay could be because of the minerals or clay could be because of the size fraction. So, before you use this word, you should be careful that what is the connotation, whether the clay corresponds to the mineralogy or the clay work corresponds to the size fraction, but in short, if you look at this relationship, they should answer I think this Neha's question you are asking or someone else was asking in the previous lecture, what is the relative ranking of thermal resistivities of the soil, is it not? So, if you plot on y axis thermal resistivity, the units are degree centigrade centimeter per watt with respect to dry density. So, the first trend which is clear from this figure is that as dry density increases, the resistivity drops down is because of better contact between the grains, grain to grain contact increases because of good compaction or dry densities are high. Now, if you look at the trends, what you will notice here is that the finest grain material that is the black cotton soil shows maximum resistivity alright, followed by the fly ash which is a silty material. So, clays and cells mostly show very high resistivity followed by you will see that these two graphs or the trends are for sands, so core sands and the fine sands. So, this is how you can make out the influence of the size fraction of the soil on thermal resistivity, but most of the time you will notice that the natural soils which are available for construction purpose or industrial applications, they will constitute mostly clays and hence the resistivity will be very high. So, the biggest challenge is that how to drop or how to decrease the resistivity of the soil mass, so that you can do some construction related to either air conditioning ducts, buried pipelines, cables and so on. I hope this answers the question that what is the influence of type of the material or the fraction size on resistivities with respect to dry density. Now, some one of you should have asked this question that why these trends are not available beyond a certain limit of dry density, why this graph is hanging somewhere here only. The reason is it is very difficult to compact clays beyond 1.4 gram per cc. So, these are all experimental findings. So, in laboratory you cannot compact the material more than 1.4 gram per cc. However, you can extrapolate the trend and what you should observe here is that this graph will become asymptote after certain density. Now, it is a very interesting way of understanding how grain to grain contact influences the resistivity, because when you are plotting dry density it is understood that you are filtering out the effect of moisture content. And either this is the driest possible state of the material or even if you are studying the density total density you are normalizing the total density with respect to moisture content. So, your gamma t divided by 1 plus w term is nothing but gamma d. So, the tendency of the material is to achieve a constant thermal resistivity which is nothing but the resistivity of the minerals. Now, this concept can be utilized again for characterization of minerals not soils the minerals. And you think of a situation where the resistivities of individual minerals is known and then you can come up with a model to find out what is the mineralogical composition of the soil. So, that would be something very interesting and this is where actually people need to do research alright. The second major factor which influences thermal resistivity is moisture content. So, what is the philosophy behind this type of mechanism? Why moisture content controls the resistivity? So, heat conduction is mostly through the pores or the pore solution which is present in the in the soil mass or the porous media. The reason is resistivity of minerals is very high as compared to the pore solution. So, most of the thermal connection takes place either because of advection or because of advection convection. So, when you talk about the fluids the heat transfer is convective in nature. So, even if you are talking about partially saturated soils or fully saturated soils beyond a certain limit the conduction gets exchanged with convection convective currents alright. So, heat conduction through soil is largely electrolytic the quantity of water present in the soil mass will play a very important role. Now, why it is so? Why water is so important? The amount of water present is dependent on a number of factors that is the weather conditions, the climatic conditions, time of the year alright nature of the subsoil and the depth of the permanent water table fluctuation of the water table. So, this is why this study or you know this subject becomes very important in day to day life particularly in the scenarios where waste is being disposed and this takes as a component or the attribute associated with it as the temperature being very very high. So, in what way these temperatures are going to influence the geo environment of the geomaterial fundamental characteristics becomes a very important issue. Now, this is a logic that most of the time dry soils will depict low conductivity or very high resistivity it is mainly due to the presence of air which is a poor conductor and if you look at the value of the conductivity of the air resistivity sorry this will be 4000 degree centigrade centimeter per watt and this is separating the solid grains and the resistivity of the solid grains would be 4 degree centigrade centimeter per watt of the soil. Now, if the moisture content of water is assumed to be 165 degree centigrade centimeter per watt. So, as you increase the moisture in the dry soil what happen the resistivity will drop down and what you will notice is that beyond a certain point if you keep on varying the moisture content of the soil a situation comes beyond which the resistivity becomes constant or remains constant and that is the resistivity of the water as 165 degree centigrade centimeter per watt. A bit of explanation I had given in the previous lecture where I was talking about the influence of water and whatever is coming on the top is the influence of the matrix of the soil mass. So, that is the reason saturated soil will have high conductivity as compared to water because now there is a effect of water as well as the conduction through the grains. Now, this philosophy becomes very important for the people who are trying to study thermal impedance of the soils. In our country particularly people are not worked in this area, but the way you talk about electrical impedance is nothing but resistance of the circuit if you might be studying. Similarly, if you can find out the resistance offered by a soil mass for the passage of heat. So, this becomes thermal impedance. So, thermal impedance is becoming a very important parameter which most of the colleagues from power engineering or electrical engineering you know the subject as power they need this input from civil engineers. So, if they know the thermal impedance of the soil they can design their cables properly. So, I mean like you can understand this is a big challenge for the profession to give the feedback to electrical engineers who can then come in the picture as far as design of the cables and other things is concerned. So, the moisture content from where the rate of decrease or resistivity is less this is known as critical moisture content of the soil. I will just show you what is the significance of this. For a given soil if you conduct several tests corresponding to different dry densities by changing the moisture content this type of relationships will be getting. So, here you can see many things first of all the effect of density if density is more and this section density is less. So, as density increases what happens to thermal resistivity it drops down. So, the top most curve corresponds to very loose state of the material the bottom most part of the curve shows corresponds to dense state of the material. So, more density that means in this direction the gamma d is increasing. So, bottom most line corresponds to higher dry density as compared to top portion this is point number 1. The second thing is for a given by density what is the influence of moisture content. So, what you will notice is as moisture content increases the resistivity drops down and the logic is air is getting replaced by water which is having less thermal resistance. So, this drop is too high or very rapid up to a certain limit and beyond certain point you will notice let us say about 25 percent or so you will notice that more or less the R T value becomes constant. Can you correlate it to something else in geomechanics this magic number of 25 percent in terms of moisture content OMC. OMC of most of the soils is about 25 30 percent is it not silty soils and all. So, there is a philosophy that if you know this type of relationship you can again find out the OMC indirectly and I am sure you will agree that compaction process is not a very precise methodology to characterize the soil. However, this method happens to be a very precise method of characterization. So, there is a school of thought which proposes that thermal properties can also be used for compaction characteristics of a soil. Why it is so? One of the parameters is this gamma d and this is nothing, but the moisture content. So, truly speaking if you plot R T variation along the proctor compaction curve you got the point because this is nothing, but the gamma d versus moisture content for a given resistivity you will be getting the resistivity contours for the material in a three dimensional plane and that graph can be utilized for most of the problems related to your industrial design and applications. There is another interesting thing which comes out of this type of relationships that beyond this point where the drop in resistivity ceases and the resistivity becomes almost constant. Now, this is what is known as critical moisture content. So, this point somewhere close to 25 or somewhere close to OMC would be a critical moisture content point. Why do you say that this is a critical point? Now, this is the point beyond which the soil mass is going to exhibit a very high resistivity for a unit drop in moisture content. On the left hand side of this graph or this point sorry on the left hand side of this point unit drop in moisture content is going to get exhibited in increased resistivity alright. So, the issue is if you know this moisture content and if you can maintain this much amount of moisture content under in-situ conditions please understand what I am saying. If you know this point very precisely and if you can maintain the situation where the moisture content of soil does not go less than below this moisture content thermal instability will never occur. So, this is the best way of avoiding thermal instability otherwise what is going to happen? The resistivity will increase during summers because of the loss of moisture and that is the time when most of the cables may burn if they are buried in the soil mass. So, this is this looks like a very simple relationship, but the implications are several. Of course, these graphs are blind of the mineralogy. So, that requires more and intensive studies from researchers like all of us to make very comprehensive picture which can be utilized in the most precise manner is this ok. So, the soil has the greatest potential for induced instability when moisture content is below the critical moisture content this is what I have explained just now a soil that is better able to retain its moisture as well as is efficient to rewet when dried will have better thermal performance characteristics see this is the era of infrastructure everywhere in the country people are talking about infrastructure. So, infrastructure development is supported by not only soil most of the power plants development. So, about 80 power plants are being constructed in the country big power plants. So, the main issue is thermal instability you are generating power, but that power cannot be you know transported cannot be conveyed to different places why just because the local soil conditions are very poor. I mean can you imagine the extent of the problem if you are producing any other product you can always transported either by using railways or airways or transport of any type, but when you are transporting current electricity then it becomes very very crucial issue. So, this is where the concept of rewetting and drying of the soil comes into the picture and that is how this thought came in the mind that let us study the wetting and drying cycles which is Neha is going to educate us on by the end of this semester. So, what happens to the material when it gets dried up and then it becomes wet and the cycle goes on. So, what type of hysteresis comes into the picture what type of material property losses can be estimated and so on how material behaves how material is going to exhibit itself becomes a big question mark. So, in all these projects as I was telling you sometime back a term known as FTB is very important fluidized thermal bed. So, fluidized thermal bed is nothing but a artificial system by which the resistivity of the soil can be maintained below a certain value. So, that it does not shoot up because of change in moisture content. So, either by adding the different type of materials into the native soil you can design a FTB or by adding simply moisture in the soil mass you can create FTB depending upon the situation and the requirements. So, this is where I have written a soil that is better able to retain it moisture is very good because it is not losing the moisture. So, if it is not losing the moisture I hope you can appreciate the point there will not be any drop in the moisture and hence thermal instability will never take place. So, this calls for selection of fine-gain materials because fine-gain materials can only retain moisture, but the issue is if you are using fine-gain materials the resistivities are very very high. So, this problem becomes a design problem. So, a soil that is better able to retain its moisture as well as is efficient to rewet when dried will have better thermal performance characteristics. This is best accomplished with a well graded sand to fine gravel with a small percentage of fines that can be easily compacted to a high density. So, what do you require? Good possible densities very high moisture contents less fine contents. So, you add some coarse materials in the fine-gain material to create a good FTB material and then compacted better. So, for maximum density the smaller grains efficiently fill the spaces between the larger particles theory of compaction. So, a well graded soil can be compacted better as compared to a uniformly graded soil or a poorly graded soil and the fines enhance the moisture retention. So, it is a very interesting problem the moisture should not come out of the matrix at the same time heat conduction should be through the soil mass at a proper rate. Now, this again becomes a you know what you call it as a coupled phenomena. The heat migrates moisture does not migrate. So, you have to test the soil mass to understand what is the susceptibility of the material towards a thermal gradient and at what degree of compaction with moisture content thermal instability may occur. Is this part clear? So, basically we are talking about gamma d moisture content type of the soil and its compaction and the minerals. So, a sound mineral aggregate without organics and without porous particles ensures effective thermal condition. These are the philosophies based on which most of the time soils at power plants or the base facilities where thermal gradients are very high are designed. And this is the importance of the environmental geotechnics where you can select the materials you can talk about these attributes otherwise in classical geomechanics you cannot really consider these effects. Then comes the hysteresis effect not very clear to researchers how hysteresis can be you know correlated with the fundamental properties of the soils as on date. Still people are trying to study this the effect of moisture content on the thermal conductivity of some soils has been found to depend on whether the soil is in the process of drying or wetting and its understood that drying process will result in more thermal what resistivity or conductivity. So, during the drying process the thermal conductivity is decreased, but then this has to be studied properly what really happens at the microstructure to the soil mass. Another reason for studying this phenomena would be why cracking occurs in the fine-grained materials. So, why fine-grained materials crack. So, it is a very big issue in geotube engineering about the cracking and the tensile strength of the soils. So, if time permits I will introduce these concepts also in this course a little bit. I think there is a mistake during the drying process thermal conductivity should be yes. So, you should have told that. Then you should have pointed this out very clearly how can I go squat free. So, during the drying process thermal conductivity should be low. Then comes the effect of dissolved salts in water. What is your gut feeling if more dissolved salts are present what will happen to the resistivity? Why? Thermal gradient will not recognize currents. Let us see it has something to do with the pore solutions again. So, the amount of water which is present in the soil is a major factor in determining its resistivity alright. So, the resistivity of water is governed by the amount of salts which are dissolved in it with change electrical properties as well. So, this is where again the complex situation comes where the pore solution and the moment you add more salts into it its dielectric constant changes. So, if its dielectric constant changes its thermal properties will also change. Why do you add salt in ice? Yes you are quite close to the correct answer any other attempt why do you add salts in ice to lower the freezing point alright. So, if you lower the freezing point in what way it is going to help you sorry it will not melt very easily clear. So, when you are adding some water some salts in the pore solutions of the soil what is going to happen? Resistivity is going to change definitely now the question is whether it is going to be higher or lower. So, quite a small quantity of dissolved salt reduces the resistivity considerably you agree or no correct why simple logic is the density of fresh water is more or brain solution is more. So, that is the best possible answer. So, the moment you add salts to a solution water what happens to its density it increases a little bit and that is the reason the conductivity will increase and the resistivity will reduce this is what my logic is your logic is also correct, but then when you talk about the ionic interaction and the thermal effect mobility may increase that is true because of heating up. So, ionic conductivity increases because of elevated temperatures and hence resistivity drops down that is logic that logic is also correct. Now, the issue is that different type of salts will affect you know resistivity or conductivity in a different manner. So, different salts have different effects and this is probably the reason for the resistivity of similar soils, but from different localities is different considerably. So, if you take sand from the runoff catch or if you take sand from the central part of the India where do you expect resistivity will be less because you have more brain solution there correct salt water is there too much. These concepts can be utilized for thermography and then based on thermography you can you can estimate whether the soil mass is contaminated or not with the help of thermal cameras. So, nowadays thermal cameras are becoming very very you know potential tools particularly on the airports they are checking whether somebody is having sand flu or not you must have read in newspapers. So, you can identify in a crowd how many people are suffering with flu or temperatures or the fever and so on. So, same concept you can utilize for determining the extent of contamination of the soil by using thermal imagery or by using thermal cameras that they call these zones as the heat zones very high thermal zones. So, you can find out in the buildings where the leakage is taking place where the plaster is not intact by using thermal imagery. Now, another parameters which affect thermal properties would be particle size their distribution their packing closeness and the grains themselves yes. You have mentioned that quite a small quantity of salts than the thermal resistivity reduces what about the increase in the concentration of the salts. Any guess from the audience no if you keep on increasing the concentration there could be a situation where precipitation of salts may take place and the moment precipitation takes place the resistivities may go up again. It is a good question, but you have to study it. Yes, yes how it would be. So, what is your feeling? If you plot on y axis resistivity on x axis the concentration of salt how the curve should be? First it should decrease it should come up to a certain optimal point and beyond which again it should increase that is right. Most of the graphs in engineering practices are identical all right, but to my knowledge I have never come across any this type of study was a good idea. Somebody can consider this while examining the soils and coming up with some generalized relationships. So, grains anything else? So, we are talking about the effect of particle size distribution closeness of packing of the grains. So, this is where the grain size and distribution strongly affects the manner in which the moisture is held and hence it will be responsible for thermal properties of the soils. You have seen in the previous graph that if the grain size is more the resistivity is less and if grain size is less resistivity is very high. So, with large grains the pore space available will be higher due to the presence of air you cannot compact it. So, well resulting in higher resistivity or lower conductance for a well graded soil higher soil density can be achieved by compaction that is the space between the large grains gets occupied by the smaller ones and hence resistivity reduces. This is a simple concept all of you are aware of. If the size and shape of the grains are in such a way that they form a compact dense structure then the resistivity of the soil will decrease it is ok. Now comes the question what is the influence of soil fabric on the thermal properties of the soils. If you remember soil fabric is nothing, but arrangement of the grains. So, what is your feeling intuitive feeling? Loculated structure or dispersed structure which one out of the two will show you more resistivity and less resistivity. Why it is so? This has to be studied and if somebody studies this then he can easily correlate hydraulic conductivity with thermal resistivity. See basically the question is how to characterize porous media clear? You want to understand how porous media is behaving whether it is water flow, contaminant flow, heat flow, electricity flow, magnetism flow or radio activity flow. So, at the end of the day why people are studying all these things is so that these small small modules can be put in place to answer big issues. How water at elevated temperature having more contaminants in it? These contaminants are radioactive in nature and are active contaminants are going to flow from one point to another point or they are going to degrade the geo environment in what way. So, these are the biggest possible issues. So, in isolation you can study these parameters, but yes to start from somewhere you have to first isolate the issues, understand the behavior, put them together, make a modular structure and then see that what is the overall effect. So, my question to you was that how soil fabric influences the thermal response of the material? Well I am not sure about the answer, but I will go by your answer. Some of you are saying that dispersed structure will show you more conductivity, less conductivity and somebody is saying dispersed structure. Now, let me ask you a question as far as the dispersed structure is concerned and the flocculated structures are concerned. Which structure shows more viscosity in terms of water? Why? In dispersed structure, sir the grain to grain arrangement is laminar and they are having negative charges which is not allowing the water to flow from that as it is a dipolar liquid. Yes. So, which structure should be more susceptible to temperature change, flocculated structure or dispersed structure? If you change the temperature, flocculation may not take place. You agree with this or not? Yes sir. A simple example is when you make jellies in your home. Why do you keep it in the fridge overnight or so for few hours? A jelly which you take normally as a dessert, what it is? It is a dispersed structure or it is a flocculated structure? So, how many of you have heard about dispersed structure? Are you sure about it or you are guessing? Sir, sure about it sir. Actually, bentonite slurry also is the same case. When we make the bentonite slurry, it loses its strength but if we keep it for some time, it would gain strength which is called thixotropic. You are completely wrong. A dispersed structure is always because of compaction. The basic philosophy actually you are too much away from the basic concepts. Never lose the basics. You start from a flocculated structure, you keep on compacting the soil, you will attain a dispersed structure. See, this is the correct answer. So, all your logic is completely wrong. So, if you are not compacting any system, you just lose it and keep it in loose form in a water. Everything is in a flocculated way. Now, you start compressing it and then whatever the residue is, that would be a dispersed structure. Clear? Now, this process itself is the function of temperature. So, when I ask you the question soil fabric, in fact, I would like to study the influence of soil fabric on the thermal properties of soil. But then, this is a very big question. First of all, you have to talk about the mineralogy. Second, you have to talk about these parameters which are physical in nature. And by the time you reach to the soil fabric, the entire concentration of the study is over. So, it will take a lot of time for people to understand how soil fabric influences. In most of our papers which we submitted, the viewers were asking this question that why do not you study the effect of fabric structure of the soil? So, it is not so easy to answer as on date. I am sorry for that, but I thought let me talk to you and you may give me some ideas so that we can study our, we can conduct our research further. So, for the time do not bring the soil fabric structure into the picture. So, apart from fabric structure, this is how the grain structure is going to control the process. Effect of temperature. Now, what is going to affect the temperature maximum? Rise or drop in the temperature? Again, it is a pore fluid. You agree? Oh, no. Why? Whether it is gaseous form or whether it is liquid form, the changes will be much more. Why it is so? Coefficient of thermal expansions are very high for liquids as compared to minerals. Clear? So, a bit change in the temperature of the fluids which are present in the pore structure is going to alter the properties completely. So, soil resistivity is a function of pore fluid property. Clear? As said, the viscosity of pore fluid will get affected very easily and hence the soil resistivity will increase as the temperature gets reduced. This is at the macro level. So, you talk about the fluid where the densities are changing because of change in temperature. Clear? Now, see I am basically adding more and more complexity into the subject. This you must be realizing. So, the moment your fluid properties change, particularly the rheological properties. So, viscosity changes, its density changes. So, at elevated temperatures, they are definitely going to get reduced. And hence, what will happen to resistivity? It should be less. Now, comes your pore phase system of soils or the geomaterial where you have ice also into the picture. As I said, we are lucky that we do not have to deal with pore phase soils and geomaterials in our country in most of the part of the country except for maybe Himalayan ranges. So, for subzero temperature, the resistivity rises sharply. This may be attributed to the high resistivity associated with the ice. Ice is having more resistivity towards thermal flow or less. What floats on in water? Ice or water floats on ice? Ice. So, if you think about the crystals of ice, so that gives one idea about how the resistivity contrast would be in the same phase. Now, this is the important explanation. In the freezing process of the soil, ice cementation occurs and the adhesive forces increase as the temperature decreases. Is this part clear? This possibly leads to a better interfacial heat transfer with the consequent increase in thermal conductivity of the frozen ground. The subject which deals with ice mechanics in geotechnical engineering, there you have to take these concepts and put them in place to answer day to day life problems. Particularly, those of you who may get a chance to work in permafrost and heave and thaw process because of the permafrost formation, the temperature fluctuation and all. Did you have a question that we do not talk about the influence of environmental conditions on geomaterial response as such? You have been from, you might have heard that Indian military, they are posted at Kargil. Is it not? So, they also need shelter, basic amenities, infrastructure. So, we are not doing research in that direction. So, 6 months let us say it is frozen completely, again cycle comes, it is a thawing process. Correct? Most of the places and then this situation is much more worse than the western countries where the temperature fluctuations are too much, particularly Canadian continent, Scandinavian continent, Norwegian continent and so on. So, this is please. Sir, there is an increase in the thermal conductivity sir in the frozen state. This will occur in a sub 0 temperatures, but we are not considering the effect of temperature there itself, the temperature is getting reduced and reduced. So, I think there will be a. Temperature is getting reduced, where? Sub 0 temperatures, below 0 sir. So, there is, I think there will be a limit to that temperature, there will be a temperature limit where there will be, what to say that conductivity itself will not be there. Repeat your question again now. Of course, the thermal conductivity increases sir, but what will be the possibility of a presence of a, existence of a temperature, heat, presence of heat in that sub 0 temperatures. I think there will be a limit for that. No, there cannot be any limit. See, there is a process and there is a material which is exhibiting some property. So, it is a superimposition of a mechanism on a material property, that is it. Now, your question is, there could be a variation in temperature. Yes, there can be. Now, how heat flux is going to migrate from one point to another point, let us say within sub 0 temperatures itself. So, top surface is minus 40 and by the time you reach few meters below, the temperatures could be normal or they could be much more less than 0. So, there is a temperature gradient and this is because of the climatic conditions. Now, how heat is migrating into this type of a system? A good example of this, if you remember I had cited in the class, particularly in the extraction of gas hydrates. Remember, the biggest challenge is how to extract the gas hydrates which are at minus 40, minus 60, minus 80 degree centigrade. So, this is where you have to heat these hydrates. You have to provide certain amount of thermal energy in such a way that only certain amount of hydrates come out and you can trap them easily. If you apply the heat in a step function, what is going to happen? The entire thing will melt there only and you cannot extract anything. So, what you are saying is a very good example of this type of situation where the temperature variations are taking place and there is a thermal flux which is migrating into the porous media. I am not giving answer to your question, but I am just giving you a sort of analogy that where the question which you are asking can be implied directly. Sir, as temperature increases, water will dissipate, vaporize, then air will come. Water may not vaporize. So, let us say that state of the material alters, unless you go beyond, let us say, 100 degree centigrade. But sir, there will be some water and some air, but if the temperature increases, the air will come more air than water. Provided if you are allowing air to go out, there are a lot of ifs and buts and provided. There are a lot of constraints. So, we are not talking about all those constraints right now. We are just talking about how the parameters influence or they get influenced by a physical phenomenon. I know that there are a lot of ifs and buts. Alright. So, basically crystallization in what way it is going to influence the porous media characteristics in terms of resistivity. Now, if you can map this, you can locate where the gas hydrates are and this is where the roles of geotechnical engineers would be. Like when you are doing, let us say, in-sea to wind shear test and you think of a situation where your wind shear test is conducted along with temperature measurements. So, you have a thermal probe also attached to the wind shear. So, you are getting the shear strength parameters corresponding to a in-sea to temperature condition. And then let us talk about how undrained shear strength changes over a temperature change. So, these are more real life and practical problems for oil industry, for people who are more interested in gas hydrate studies and so on. Now, thermal conductivity of the frozen soil is greater than that of the unfrozen soils. Why it is so? The simple logic is there is no air. Clear? So, any other form of a fluid which is getting frozen and crystallized will show you lesser resistivity as compared to air. So, this is the simplest possible logic because ice has a conductivity value about 4 times that of the water. Now, this is another interesting thing. Basically, when we talk about porous media characterization, we are talking about porosity. So, there are two situations of porosity. One is porosity tending to 100 percent. What is the significance of this? Yes. Or the second situation would be porosity tending to 0. So, the first situation is for porosity 100 percent that is the 0 solid volume. The conductivity of saturated frozen soil may be expected to approach the value of the ice. While that of the unfrozen saturated soil approaches the conductivity of the water. Here you should, I do not know whether you could follow this fallacy or not. When we say 0 solid volume, why it is so? It is no more your skeletal soil which you are talking into or you are taking into account. Exactly. This is the crystallized form of the water which is present in the soil matrix. The whole idea of giving you this concept was that to maybe train your mind for going ahead with three phase to four phase to multi phase models for the soil system. I mean like these are the challenges in our profession. You should come up with now different phase systems and more reliable models which can be used for volume mass relationships. Like your G into W equal to S into E is valid only for a very, very ideal situation and you know the limitations. All right? Now, this is at the other extreme as the porosity decreases to 0, the conductivity should then towards to the solid particles. So, the skeleton comes into the picture. Seasonal variations very difficult to quantify. But in most of the projects you have to study the seasonal variation effect particularly where you are conveying a fluid from one point to another point or where you are conveying electricity from one point to another point. A good example is cross country pipelines for your gasoline or petroleum products. 75 percent part of the pipeline is in the deserts. Just imagine the temperatures where you are passing the crude oil. Is it not? And you are aware of the cavitation process. What is cavitation pipes? Not corrosion. There could be a pressure. Yes. The pressure of the flowing fluid will be if it becomes less than the vapor pressure of the fluid, then cavitation takes place. That is a cavitation process. So, these type of situations may occur because of very high temperatures. Clear? So, if cavitation takes place in the pipe somewhere, you cannot convey the fluid first of all. Pipes may also burst and so on. So, seasonal variations are also very important. Soil resistivity varies due to, have you ever seen that the pipelines are you know protected with some? Casing. Casing. They are not only the concrete casings, but they are protected with casings made up of some thermopolar particularly your air conditioning ducts. So, it is nothing but the insulation which you are doing for the pipelines. Soil resistivity varies due to changes in the moisture content and temperature which is nothing but the seasonal variation. High resistivity occurs during the periods when the moisture content is low and the ground temperatures are very high. So, resistivity survey should be done throughout the year, but it is difficult. So, the best possible values which you can use in your designs would be the most the worst values in fact, that is the driest possible state of the material. And then you may talk about the effect of wetting of the soil and how much resistivity will be dropped per unit you know intake of moisture into the system. Anisotropy. I think you were talking about anisotropy sometime back. So, in what way anisotropy influences the heat flow or the thermal properties of the soil mass? What is meant by anisotropy? Venil. Variation in the property of the like layered. Correct. Stratifications because of stratification the properties may not be same in all the directions. So, that is what is basically anisotropy due to soil anisotropy that is an stratification the resistivity may not be same in all the directions. Where do you think that this type of studies would be useful? Rocks. Kunal Singh you are from engineering geology. Can be possible sedimentary rocks. Why do you want to study stratification in subsoil? Flow of it stratification is a type of fracture. It can increase soil strength decreases sorry rock strength. So, my question is that why do you require anisotropy to be studied? Why it is so important? Strain depends on the anisotropy. Any mechanism for that matter see permeation you are right some of you were talking about the permeation of fluids let us say. Permeation strength you know they are bearing capacity in fact for that matter. Cere strength. Cere strength you talk about weak layer underlain by a hard layer or strong layer and vice versa and so on. So, anisotropy detection is also becoming very important unfortunately there is no way in classical geomechanics where you can define the anisotropy of the subsurface except for either utilizing the seismic studies or thermal studies or electric studies. So, this is where all the three studies will require properties of the geomaterials. So, that the modeling can be done properly. So, this is a good style of studying how much anisotropic the soil masses. The basic concept is parallel to the bedding the resistivity is always less. Resistivity is less conductivity is more and when you talk about the perpendicular to the bedding the resistivities are very high. So, if you understand this now you should be able to understand the effect of fabric structure on properties of the soil mass because fabric structure is nothing, but a sort of a stratification particularly when you talk about dispersed structure. So, if you study the anisotropy you can you know map the parameters which are getting from here into the soil fabric structure. A good way of doing this would be you define soil mass stratification index and this is nothing, but the ratio of the parallel resistivity to the ratio of to the normal resistivity. Another logic is that why normal resistivity is always more because the compaction densities will be more in the perpendicular to the bedding as compared to parallel to the bedding because you always compact or deposition takes place in the perpendicular to the bedding plane. So, these concepts can be utilized for tomography of the subsurface is it not or subsurface profiling. So, as I said there are three methods either by geophysical methods which again will use either thermal energy field or electrical energy field. So, if you know the thermal properties and electrical properties of the soil mass you can correlate your results in getting the stratification of the subsurface. This is part clear I will discuss a lot of basics today. Now, let me go through very quickly through the rest of the lectures. Determination of thermal properties in a geotechnical center which you have any doubts from the previous lectures or shall we go ahead and finish this off. The first question is why do you want to study this phenomena in a geotechnical center which when you have everything ready made that analytical tools are there numerical tools are there lot of the investigations are done in situ testing is done and so on. So, the answer is though several analytical and numerical models are available to model heat migration in geomaterials they lack simulation of the prototype conditions in terms of in situ stresses. I am not sure whether you are aware or not, but the biggest question is all your spent fuel which comes out of the atomic reactors where should be stored. So, that is where you go and go into deep into the subsurface in the rocks make tunnels over there and then charge them with atomic waste clear. Now, this is how the India is also adopting this strategy. Now, when you do this what is going to happen to the rock mass which is surrounding this waste there would be thermal stresses that is the right word is it not thermal stresses. Now, because of thermal stresses the mechanical stresses become insignificant the rocks are famous for arching action there not be any mechanical loading up to that point, but then thermal stresses become very important. So, then the question is if you if I give you a problem that below the ground let us say 50 meter what is the influence of let us say all these parameters which we have studied on overall transmission of heat from one point to another point. So, these are the problems which require either real life simulations where you have to really dig out a hole at a depth of 50 meter do some experiments these are known as hydrothermal mechanical models and do the probing of the area and see how heat is migrating from one point to another point and come up with the models is it not thermal behavior of the rocks whether the rocks can sustain this much temperature or not how heat is migrating from one point to another point and so on or you take the rock course bring them to the laboratory conduct centrifuge modeling you save time and you are more sure about what type of analysis and simulation you are doing. So, to overcome this type of difficulty people have done field studies, but then field studies are very expensive very time consuming and difficult to perform. So, what to do in order to overcome all this people have gone for centrifuge modeling. So, that at least you can you can simulate the stresses which are going to come on the system in the form of mechanical stresses or you are simulating the prototyping into stress conditions and how these stress conditions are influencing the heat migration in the geomaterial. Now, let me ask you a question because you are doing this course also. I am sure that you are aware of the scaling factors for length, void ratio, acceleration, force, stress strain, velocity, mass, time of diffusion, hydraulic conductivity and so on. Is it not? But do you have come across the scaling factors for thermal conductivity, thermal diffusivity, specific heat and heat flux? Why? Because if you are doing centrifuge modeling then you should be knowing the scaling factors for this phenomenon also. So, that is where the issue is before you take up centrifuge modeling of heat migration you have to understand what are the scaling factors for thermal properties of geomaterials. That means, thermal conductivity, thermal diffusivity and specific heat, how it gets modeled and what is your get feeling? You will get model or it will not get modeled? Yes, it should but unfortunately it so happens it will not get modeled and let us see how it can be ascertained. So, this is the question to a researcher that what really happens to the material when it goes into centrifuge. So, Dr. Krishnaya he was my PhD scholar. He did this work. He used this setup which has been developed by him. These are the buckets of the centrifuge where the entire setup is placed. You can see the thermal probe which we are discussing in the previous lecture and in this setup there are a lot of thermocouples which are embedded. So, these thermocouples will be measuring temperature in RZ domain. R is the radial distance from the center of the probe and Z is the depth below the sample surface. So, truly speaking what you are doing is you are doing temperature modeling in RZ T domain where T is the time. So, as a function of time at a given point in the radial direction and at a depth of Z what is the temperature value? But because this happens to be axisymmetric case your Z becomes insignificant. So, it is only R and T which are the important parameters and you are finding out temperatures associated with a radial distance at a given time. The counterweight was used as the batteries for supplying the power to the system and the beauty of this system is there was a switch and this switch when the bucket swings is not connected to the circuit, but in flight this switch gets connected to the bucket and the circuit gets complete. So, this was the simplest possible way of doing the experiments. We saved lot of money and the experiments performed like this. So, in flight this switch gets attached to the bucket, circuit gets completed, heat starts flowing into the thermal probe and you can measure the temperatures. Clear? A simple method and then we were data logging the temperatures over a period of time. Now, this is the whole assembly in the centrifuge where you have the data logger attached to this side is the batteries in the counter balance and this is the centrifuge setup and this is the switch which I have been showing you and the circuit is connected to this switch. So, the moment the bucket is in the flight it gets connected and then this current starts flowing. Now, this is how the flux modeling was done the voltage versus time in the centrifuge to show that the flux remains almost constant. So, the first question was what is the scaling law of a flux? There cannot be any scaling law for the flux because the flux is the form of energy it cannot be created it cannot be destroyed. So, this is what is getting done from here that the voltage remains constant practically over a period of time. A little bit of drop in voltage you are seeing because of the draining out of the batteries over a period of time. So, the best way of doing this was that you conduct experiments in less than 6 to 7 minutes time where the voltage remains practically constant and ignore this portion of the curve. So, if you are performing your experiment within 5 minutes 6 minutes there is no problem flux remains constant. Now, this is what I have been asking you if you conduct at different n values different test to obtain RT on different soils what you will notice is that RT remains practically constant. So, is the case with thermal diffusivity and so is the case with a specific heat. So, all these parameters remain almost same. This work was published in these two journal papers if you are more interested you can refer this the centrifuge modeling of heat migration in soils international journal of physical modeling in geomechanics 2004. Now, if you do this test and as I said that we are doing modeling in R and Z domain this is what the results would be on y axis you have temperature going up and x axis is time. So, for a given centrifuge effort at n equal to 150, 100 and 125 if you do the temperature profiling with respect to the radial distance R what you will notice is that this is how the temperature increases from the nearest point to the extreme point and you imagine temperature from this. So, these type of temperature profile you can obtain when you do centrifuge modeling and then the second thing would be how temperature is varying from this point to this point. So, if you plot it with respect to R variation in temperature the moment you go from center to the extreme out the temperatures will be dropping down. So, these are the basic raw results which you get from the centrifuge models. Now, utilizing these results you have to see what can be done. So, the answer is that I would like to do the modeling of time is it not. So, whether the same phenomenon can be observed after certain time or not. So, if you define on the y axis the increase percentage increase in temperature that is initial temperature minus final temperature divided by initial temperature with respect to R what you will notice is the maximum rise in temperature is near to the probe and as you move out of the probe the percentage increase in temperature is less. So, this is what time modeling is and for different n values you will see that the results fall perfectly on the unique curve that is what the modeling of models is for time. Now, this is the modeling of model exercise when you talk about the n value. So, for any n value or the centrifugation effort you will notice for different type of soils corresponding to different distance you will have a unique relationship. This shows that modeling of models is valid in heat migration analysis all right. Now, this was again another issue that these type of studies cannot be conducted in rocks and concrete of the steps step soils. The reason is you can insert the probe you can insert the thermocouples. So, what you should do? So, this is where the best way would be to go for numerical modeling using n-ces. So, this is the test setup is the top view this circle shows the probe and in the radial direction you have thermocouples embedded in the sample and then what you are trying to do is you are taking the one fourth or the one quadrant of this sample and then digitizing it or discretizing it. So, once you have developed the discretized model if you solve this by using n-ces you will get this type of thermal profile. So, close to the thermal probe the temperatures are going to be very high and as you go down the outer sides of the sample the temperatures would be quite less. So, 57.39 to almost 27.8 which is the room temperature. So, this type of thermal gradient has been imposed on the soil sample under in situ conditions. You can always debate the validity of the results, but the issue is at least these type of tests give you some values which are close to a physical phenomena which is going to happen in nature and then if you match the results of your n-ces with the experimental studies where you are putting on y-axis the heat temperature and on the x-axis the time. So, for different radial differences distances you will notice that the experimental results and the n-ces results they will be matching in each other. So, this gives more confidence in the type of exercise which is being done. So, what is remaining now is that we have answered two questions where the properties remain same. So, there is no modeling of models of the properties and the thermal flux, but still one question is that what about the physical time of the heat migration. So, that is where actually very intelligently you can take help of numerical models and you can scale them for time. So, this is what is known as time scale factors for the mechanism that is prototype and model if you put like this. So, tp by tm equal to n to the power x where x is unknown scaling law. So, if you take the log on both the sides x will be log of tp by tm and divide by log of n. Now, this table summarizes the entire study. So, if you have initial temperatures which are known you do the finite element analysis for a distance of rp and t this is nothing but the prototype and then you have the models in the centrifuge. So, essentially the logic is that because on rocks, concretes and strips wise you cannot do this type of studies. So, we want to generate confidence in the NCIS models. So, once NCIS model has been validated with respect to field conditions using NCIS you can validate centrifuge results and hence you can find out the time scale factors clear. So, if you know the centrifuge test times which are known you can put this in the equation and then you can get the x parameter. So, how would you read this expression now tp by tm equal to n to the power 2 all right 1.8, 1.8, 1.9 is nothing but 2. So, do you agree with this law tp upon tm equal to n square what is the meaning of this hydraulic conductivity gets model n times because it is a advective flow and this is a diffusive flow it gets model n square times clear. So, even if you do a consolidation test in the centrifuge what should be the scaling law for consolidation process consolidation time intact it should be n times or n square times it should be n square time because that is a diffusive process for water or the pore pressures. So, these type of studies can be done and the whole idea was to show NC2 modeling with you know mathematical modeling and the mathematical modeling is of is the laboratory experiments and centrifuges. So, with this I will close the discussion on thermal properties.