Alison's New App is now available on iOS and Android! Download Now
Video 1: Ohmic Conduction and Electrical Impedance
A bit of the idea on what is the state of the art on the subject because this is a researcharea, which is open for research and people should contribute, lot of things are to beanswered, I am sure that state of the art tells you that you need not to conduct anyof the conventional experiments in the laboratory in today’s world, because people have notime and look at the size of the infrastructure which is being developed.You know, thousands of acres, thousands of kilometers and also gone are the days andpeople used to take out the samples and bring them to the laboratory and test them thencontemporary thought process is that I should be getting in-situ properties and which aremore reliable and this is the fashion.So, all this started since 1736 when Coulomb came out with the theory which is known asCoulomb’s Law.Maxwell, Frick and Archie.So, Archie’s factor that is formation factor is a function of porosity is what is beingused by the guys who are in the realm of geotechnical engineering and those who are geophysicist.So, this formation factor basically tells you what is the contrast of the electricalconductivity perpendicular to the plane of the deposit and parallel to the plane of depositsyour KH upon KV.This concept is being utilized in understanding how the formations were created and whetherthese formations should be bearing minerals petroleum or not.So, if you if you get a chance to work in the petroleum geophysics, you will find thatformation factor is utilized there a lot which is the electrical resistivity of the saturatedsoils divided by the electrical resistivity of its pore fluid.And this is a function of the porosity, there are people who have done a lot of studiessince 1933, it has picked up this subject people have worked in the frequency rangesof hundred to 10 megahertz, kilohertz to megahertz, megahertz range 20 megahertz, 1 gigahertzrange and the soil properties which have been determined of water content, soil structure,particularly orientation, electrolyte defect, determination of water content, relative density,and soil liquefaction.So, this motivated us to take research in this area.And if you further look at the list, you will try to see that you will you might find thatpeople have been very ambitious and they have been talking about the clay fraction directlyas a function of electoral property, porosity, conductivity of the clay, what is the electricaldispersion and soils for different applications.And even some people have worked on the permeability of the soil.Having a relook at the electrical properties of geomaterials, as we discussed the conductivityand dielectric constant are the two major parameters which are used for defining thestate of the material and conductivity comes because of the movement of the charges.Alright?.A dielectric constant is a measure of the capacity of the material to reduce the strengthof an electric field and to behave like an insulator.So, here we talk about the variation of the electrical properties as a function of frequencyof AC and this is what is known as dispersion of electrical properties or delicate dispersionin the material.So, this part I have already discussed that the electrical conduction in the moist geomaterialsis more you know and we have talked about the polarization also when you apply the voltageacross the sample in a electrodes, they get a positively charged we used here the conceptof lossy dielectric material.We treat soil as a lossy dielectric material that means there are some losses of the storageof the charges takes this to the soils.So, dielectric constant of the permittivity is a function of frequency and we define kas C into d upon A into epsilon not capacitances k into A into epsilon upon d.So, what about the dielectric constant?So, dielectric constant is epsilon upon epsilon not, this is the material permittivity earlierI use this term with Es that was for the soils, epsilon could be any material and epsilonnot as the permittivity of the free space, we can represent k in 2 parts that is thereal and imaginary.So, k is the real part -j into imaginary part of the dielectric constant.So, this is where the interpretation of the measurement of electrical properties startsimpedance analysis starts.So, if I define the dielectric constant as a combination of real part of dielectric constantand imaginary part of the dielectric constant, this is the composite function, what we dois we plot many times real against the imaginary part to decipher the information.I will show you how.So, before we go into that, a bit on the ohmic conduction of geomaterials, all of you knowthat the flow of current follows the ohm’s law, which is because of the ionic movement.And we define current equal to resistivity into V clear.So, we write sometimes as v equal to I into R where r is one upon sigma.So this becomes the resistivity or resistance is R, so, these are the factors which influencethe electrical conduction.Void ration, degree of saturation, shape, size and orientation, pore structure and natureof the fluid and its conductivity.As I said earlier, unless the grains are charged, the surface conductivity is ignored.What you will realize is that ohmic conduction through pore solution is very easy.But ohmic conduction through the soils and the grains is going to be very complicated.And very soon you will realize this.The reason is when we deal with the fine grain soils there are double layer formation DDLwe call it as diffused double layer and that is a consortium of different types of ionson the clay platelets.So, there is a lot of interference which takes place when you measure the electrical propertiesof the geomaterials, particularly when they are fine-grained, because of double layerformation.So these are the basics of the impedance.That when we measure the resistance, by using DC current we call it as a resistance.However, when we measure the resistance by using AC current is becomes impudence.And I can define impedance that as V as a function of time upon I as a function of time.Which is nothing but V cos of omega t upon I cos of omega t minus delta.This is the lag behind between the voltage and the current.So, when you plot voltage and current together there is a time lag we can define this termas r minus J x in the complex form.Alright?.So, r becomes the real part of the resistance and x becomes the imaginary part of resistance.So, whenever we measure the impedance of the samples, this impedance can be representedin combination of real and imaginary parts and then these real and imaginary parts canbe utilized to decipher a lot of information from the geomaterials.So, these are the basic models which we use, you have studied this RC circuits and all.In your engineering, soil can be represented as a RC material, a material which shows resistanceand capacitance.So, this is the equivalence between the geomaterial or the soils and their electrical circuitsalright?.So, these are the components of resistance, inductance, and capacitance which can be utilizedfor defining their impedance, remember impedance is the resistance and admittances the conductanceor inverse of the impedance.So, you must have come across these terms, when you deal with the resisters the impedanceis R when you deal with the inductors, this is G omega L. And when you really the capacitorsthis is - 1 upon G omega c.So, these components can be fitted to describe the state of the soils.And I hope you can realize that if I want to find out the total impedance, I can sumup the resistances and when I do for parallels then I have to sum up all the admittance of the material.
Video 2: Determination of Electrical Properties of Soil
So, one of my master’s students started working in these complicated topic.His name is Azaz Masood Bhat, and he published 2 very impactful papers on electrical characterizationof geomaterials, which have become landmark papers.He has created this impedance and the concept is simple you take a small cylindrical, youknow, rectangular box and this box is standing on a base plate and there are 2 electrodes.Which are plate electrodes which are fitted inside and this box can be used for findingout the impedance of the sands.And when you are dealing with the liquids then you can use this type of a setup wherethe liquid can be contained in the cell and there is a top cover and there are two electrodeswhich are embedded inside the cell.So, both systems can be utilized.And this is how the setup looks like.What we are doing here is we are measuring the volumetric moisture content of the samplealso along with its impedance.So, this is the impedance cell, we are measuring the impedance of the sand and the moisturecontent.This is the setup which is used for obtaining the impedance of the samples this is whatis known as impedance analyzer.One interesting thing is that the sample itself can be modeled as a combination of RC.Alright.So, if I consider this specimen and these 2 electrodes, I can develop an equivalentcircuit like this so, the central portion is of the specimen which is represented asa combination of capacitance and resistance and the two plates of the electrodes are representedas again RC circuit.If you plot them on a scale which is known as the Nyquist plot, there are different waysof plotting this data.The complex electronic circuits.So, if you see here this is that z prime is the real part of the resistance and this imaginarypart of the resistance, when you plot the results that you get from this, you can getcircles and these circles describe the state of the material.So, as the frequency increases, it tends to infinity very high gigahertz values if youare using the resistance offered by the sample would be less.So, this is the very state of the art thing which we are doing right now.And we are trying to capture the response of geomaterials and the mechanisms which happenedin them by capturing these type of results and showing that how the phases are gettingformed and disappear.We did a lot of experiments on soils of different type is sands.And just to show you how the results vary the real part versus imaginary part.I am not going into the details of how the analysis of the results is done.Just my intention is to show you how these results can be utilized for characterizingthe geomaterials.We use the Z-view software.And the best way to analyze a soil mass would be to create a simple RC circuit.So, what it shows here is, if I include the response of theoretical models, on the experimentalresults, these are the experimentally obtained results of the soil sample which we were analyzing.And if I fit an equivalence circuit to this.A simple RC will give you a lot of deviation from the experimental results.That means you need to refine your circuits.I hope you will find it very useful.And this is a very complicated process where you keep on generating the equivalent circuitsof the soils and the materials and keep on mapping them over here.So starting from a simple RC circuit what we have done is we have added resistance tothe RC circuit and with this, what has happened is the results are at least bound by the experimentalresults.We were not very happy with that.So, we have included one constant phase element, I do not know whether you remember or notin your electronics course, they must have talked about the CPEs constant phase elements,which maintain the phase of the system constant.So, by introducing a constant phase element, we realized that the results are quite matchable.And then we did further manipulation to come out with an equivalent circuit for the soilswhich looks like this.So this is the electrode this is the electrode in which the sample is encased.So, that means the soil sample has been represented by two resistances and one capacitor of whatis known as CPE constant phase element.Now you can reply or get the answers to the type of question that you have been askingany process which happens in the soil mass will get reflected, if I measure R2, R4 andCP2.And that is how I can say that what is changing over a period of time.So, all the properties of the soils has been now imbibed with time.And that is the art, so, here we have shown how the resistance of the soils changes asfar as the grain resistance is concerned, the grain boundary two grains sitting nextto each other, there is a boundary getting created and two grains sitting together willalso create a sort of a capacitance effect because of the pore solution inside.So, we did this type of modeling a lot.And then we came out with the analogy of how current flows through the geomaterials allthis done by my students, Azaz and Dr. Hanumantha Rao.So, you can read their papers which have been published.Now if you look at the possibilities of current, which is passing through the dry materials,there are three possibilities is a dry soil, so voids have only air, one of the possibilitiesis that from grain to air to grain to air, this is one of the possibilities.The second possibility is of the current passing is grain to grain, grain to air, grain tograin to grain and so on.And third one would be through the voids only, I hope you can realize that, deciphering thisinformation from mathematical models is not going to be easy, but we are into it and weare trying to develop models which will help you in defining the state of contaminationof the soils, we would also try to develop models where you can differentiate betweenthe fine grained soils and coarse grained soils including their shapes is quite intricateR and D differentiating between the saturated state of the material and the unsaturatedstate of the material is very easy that you can do very quickly by doing this type ofmodeling.So, this is the micro mechanics of how the current flows through the porous media.So, A to A is the surface of the soil again which is mainly due to the presence of surfacecharges If you remember, we were talking about what is the difference between the coarse-grainedparticles and the fine grained particles.Coarse grained particles do not have surface charges, Fine grained particles have surfacecharge.So, this is one of the differences.And we can utilize this concept in differentiating the material without any sieve analysis, becauseyou know the sieve analysis and the hydrometer analysis has its own limitations and the problems.The BB part is the soil cluster, where in the soil grains are in contact with each otherand the current may flow through the interconnected grains, this type of possibilities are goingto be more in case of fine grained materials as compared to coarse grained materials.The third possibility is partly through the soils grains and partly through the air whichis present in the voids, which is the least likely part due to his high resistance whichis offered by the air.So, once you enter into the micro mechanisms of this type, it becomes quite complicated.Presently what we are trying to do is we are trying to model the gaseous phases into thesoil mass and the bacterial activity into the soil mass.So, for us the bacteria itself becomes a particle and gas molecules would be present into thepores.And if I apply pressure and temperature conditions, what is going to happen?.Either the gases which are present in the voids would get dissolved in the pore solutionclear or there could be crystallization of the water in the form of the ice.So, this becomes a very complicated matrix.The second possibility is when we deal with the partially saturated soils.So, the concepts remain same only thing is we have created a void which is water filled.So, you have the grains of the soils in between there is a void which is full of water.To me It appears like a several capacitors which are arranged within the soil mass eitherin the parallel or series.So, once I do the impedance analysis, I come out with a equivalent circuits and they arein a equivalent circuits.Then again I have a model what type of combinations of the resistances, capacitance can be possiblewhich would give you the response of a material.So, there are the possibilities of current passing through this AA prime, interconnectedpores, these are all interconnected pores, the easiest way for conduction of the current.Clear?.Particularly, if the ionic solution is present in the pores.The B is interconnected soil grains only then CC prime is the partly through the connectedsoil grains and sometimes through the interconnected pores and DD is the grain through the voids,which might contain air and the pore solution.The third possibility would be when we have saturated soils.So, I hope you realize now we are trying to attempt characterization of geomaterials basedon their saturation which is the genesis of unsaturated soils.So, one of the possibilities is the pore solution continuous pore solution which is presentin the soils.The easiest way for current to pass through, no resistance is being offered much.B prime double prime is interconnected soil grains provided the soil grains have goodconductivity like fine grained materials.Third is the sandwich of the two, we have the interconnected soil grains and partlythrough the pore fluid.So, these type of micro mechanisms have to be studied and they should be developed inthe future "Professor - student conversation starts" Sir, microorganisms like when theyare present you said the current passing capacity will decrease drastically.Say it again.The microorganism is if present in any phase around the soil grains, then organic matterwill hinder the process at that time I was about to ask that.Very complicated situation.The aim is to use these models to determine how degradation in the material is going on.And not only the degradation, but upgradation also.If we need to find the impedance of the fine-grained soils or the properties of fine grained soilsthen what we will do.He employed for sands impedance of sands he found.So, if we need to found the impedance of clays or fine grained soils, so, what change willoccur.What change will occur?.How will we do interference will come.A quick answer to your question is nothing of this sort is going to happen.Measurements can be done.It is like a generating a lot of ECGs but if the doctor or the person does not knowhow to decode the ECGs, what is ECGs are going to do.I hope you can understand my point.So, measurement of the properties is not an issue.You can just pack the sample in the cell and then you can measure something.The million dollar question is how to create a mechanism out of it and how to decipherthe results so that these results can be utilized by people who are in the field of monitoringinstrumentation and micro mechanisms.
Log in to save your progress and obtain a certificate in Alison’s free Understanding Cracking, Electrical and Magnetic Characteristics of Geomechanics online course
Sign up to save your progress and obtain a certificate in Alison’s free Understanding Cracking, Electrical and Magnetic Characteristics of Geomechanics online course
Please enter you email address and we will mail you a link to reset your password.