 The most important parameter is frequency as we seen in the previous slides. What happens because of frequency? We talk about three components of a geomaterial that is capacitance, inductance and resistance. And that is why the instrument which is used and which I had shown you sometime back is known as LCR meter. So, L is nothing but inductance, C is nothing but capacitance, R is nothing but resistance. So, a system or a device which measures LCR components that is capacitance, inductance and resistance is known as LCR meter. And these parameters will strongly depend upon frequency of the current which is being input. Simple example which we have just discussed, higher the frequency of AC what happens to resistance component it disappears. And then these two components come to the picture clear. What is capacitance? Capacitance is the property of an electric circuit that opposes any change in voltage and is dependent on the frequency. Basically the charge storage capacity of a system or a circuit. Water due to its dipole nature in the pores is largely responsible for the residual high frequency capacitance. Can you correlate this phenomena to something which most of the geologists are doing? If water has this fundamental property, what is the geologists do? They try to map water table is it not or water reserves. So, more charge carrying capacity should also correspond to more water in the aquifer. Why? Because water itself is a dipole material, so its charge carrying capacity should be more. So, if you apply this concept in day to day life, the aquifers where water is more should be having very high capacitance in terms of electrical resistivity measurement. So, this is how using one component of the material in terms of its electrical or property, you can identify its characteristics, this is what clear. So, basically it varies from a high value at low frequency to a low value at high frequency. If you remember in your physics, you must have talked about 1 upon j omega c. Do you remember or you have forgotten? The resistance offered by a capacitor, remember R plus j 1 upon j omega c is a total impedance of the resistance of the circuit. I will talk about these things later on. So, 1 upon j omega c terms at very high frequency what is going to happen? This term becomes negligible, at lower frequency this becomes very high. So, capacitance value at high frequency correspond to the background capacitance of water in the medium. And using this concept you can use TDR probes or the FDR probes for finding out the amount of water which is present in the pore volume. And inductor what is inductor which shows inductance for that matter, I am sure you must be knowing how a inductor is depicted, a coil. So, an inductor is an electronic component that stores energy in the form of a magnetic field. Inductance is the property of an electric circuit that opposes current, Lange's law. If you move two current captors carrying inductor stores to each other what happens? Either current can be produced if there is electromagnetic effect or vice versa, if there is electromagnetic effect then current can be produced. This is how you do the coupling of the transformers. However in most of the geomaterials unless they contain iron this component is not significant. So, this becomes another important tool to differentiate ordinary soils with the electric soils. Electric soils will have more iron component. So, the inductance is going to be much more as compared to ordinary inorganic soils which will not have any iron component. What is resistance? Resistance is the opposition to the flow of current in an electric circuit and it decreases rapidly with increase in frequency of current. So, that is how actually frequency plays a very important role and what researchers are trying to do is they are trying to look into the response of the geomaterial in a complete frequency range starting from very low frequencies like 100 hertz to gigahertz. And this is what is known as again frequency spectroscopy. You are seeing the spectrum of the material how it properties change because of the frequency effect. So, the type of current used in the analysis plays an important role DC and low frequency currents less than 100 AC are employed for determination of soil resistivity. So, most of your resistivity surveys they are not very expensive all right they will use low AC current or DC current for frequencies more than 100 hertz the conductivity is noticed to increase with applied frequency. On the other hand high frequency that is 1 mega hertz dielectric response of geomaterials can be employed to characterize the soil fabric structure. When you talk about soil fabric structure these are the three issues particle shape size and orientation and porosity this is what switch it is doing is using high frequency AC current more than 1 mega hertz and then is trying to study the particle shape effect size effect orientation of the grains and their porosity. These studies highlight the presence of water the dielectric constant 81 in increasing the dielectric constant of the wet soil as compared to the dry state of the soil for dry state of the soil dielectric constant would be 3 to 5. The dielectric constant is noticed to remain constant only if the applied frequency is more than 50 hertz mega hertz. Now, TDR and FDR devices that is a capacitance probe and a TDR probe they are employed for finding the dielectric constant of the geomaterials based on which their characterization can be alright. So, they work all in this based on these concepts just quickly to take you through the methods which are normally used the simplest possible method is known as two electrode method. Take a sample of a geomaterial put it between two metal electrodes apply power supply and measure the voltage across this clear. So, depending upon the voltage and the current which is passing through the circuit you can find out its resistance. You know the area of cross section of the sample you know the H 2 S difference between the electrodes and you can use the classical equation rho equal to R into L by A to get the resistivity of the material. Unfortunately, the two electrode method has a problem associated with electrode polarization whenever you are applying voltage across two electrodes what happens the electrodes themselves become charged and hence the material is going to material which is in contact with the electrodes is going to be oppositely charged. Now, this is what is known as electrode polarization and because of this what will happen slowly and slowly the current will not migrate into the material or there could be a reverse current which is flowing through the material into the electrode which is not possible. So, to overcome that what people have done is they have gone for four electrode method. So, take the sample apply current across the two external electrodes and measure the voltage in between. Now, can you tell me this concept is used somewhere else in engineering where else you use this concept the resistivity profiling Schmertzmann method Schlumberger method correct that is right. So, it is nothing, but the Schlumberger method what do you do resistivity profiling. So, you apply the current to the outer electrodes and measure the voltage in between. So, if you know the voltage across two points if you know their distance you have a relationship with which you can find out the resistivity of the system. So, that is the field method and you can change the spacing of the electrodes. Here this is a laboratory method what you can do is you can measure the voltage in the sample across two points when some electric field is applied across and by measuring this voltage you can work out its resistivity. So, this is known as four electrode method because there are two electrodes which are outer and the another two which are inside the material. Now, this method is better than the two electrode method why because electrode polarization is not possible in this case electrode polarization will always take place at the electrodes, but what you are doing is you are measuring the voltage in the material and hence there will not be any polarization. Now, this is a technique by which you can measure the electrical properties by using 4 probe resistivity cells. You think of a situation where this cell corresponds to the odometer cell alright and this odometer cell is fitted with 8 electrodes 1, 2, 3, 4, 5, 6, 7, 8 clear and then you are measuring voltage across two points where 4 and 1 correspond to the current electrodes. So, because of the application of the current across 1 and 4 I can measure voltage across 2 and 3 it is nothing, but the equivalent of the previous method. So, in this way by changing the location of the current and voltage electrodes you can profile the entire sample. So, next round 3 and 8 can be taken you apply current across 3 and 8 measure voltage across 1 and 2 clear. So, the material anisotropic can be studied very easily by using this type of concept. What people have done is they have done consolidation studies by implementing this type of a cell. So, what you get is Eversa log sigma prime in the relationship at the same time you get sigma prime versus the resistivity and dielectric constant of the material clear. So, it is an interesting way to find out how material anisotropy and its volumetric deformations can be linked with each other. I would like to show you some of the in house developments which are done by my students. This is a two electrode method where we took two plate electrodes in a cubical fashion which forms a 100 mm cube. So, there are two electrodes one is on the front phase another one is on the backside phase and then this is the electrode point through which you can apply the voltage across this end and this phase and fill up the material in between clear. So, you know the volume of the soil mass you know the area of cross section you can divide this box in different parts by shifting this plate electrode to another distance. So, what you are doing is you are changing the distance between the electrodes for non conducting materials and then by using simple equation rho equal to delta v upon i into a by l where a is the area of cross section l is the length between two electrodes you can work out the resistivity. Delta v upon i is nothing, but the resistance a by l is the geometrical properties of the electrode and rho is the resistivity. So, this is the way we started our studies on characterization of geomaterials later on these plate electrodes were changed to point electrodes because plate electrodes are their own problems associated with them. So, this was again a cube of 12 centimeter embedded with point electrodes on all the phases we wanted to study the material in isotropy due to compaction. So, we are measuring electro resistivity in the x plane y plane z plane and then we wanted to see what type of structure of the soil can be created just by compaction it. However, you will notice that here it is very difficult to define the area of cross section of the point electrodes because these are the points. So, what is the property of a point area of cross section tends to 0 is it not. So, there is another way of doing this analysis if you use this equation rho equal to r into a by l if I replace this term a by l with small a where a happens to be some coefficient shape factor. So, what I need to do is I can fill up some liquid in this box and this liquid will be having known resistivity value I can measure the resistance across 2 electrodes across each other and I can get the parameter area. So, this is how you can calibrate these box I will show you how calibration was done. This work was done by Reshma one of my master's students she developed this probe also and the box this probe works on the principle of four electrode method. We imagine a shaft made up of ebonite where the copper electrodes are fitted 1, 2, 3 and 4. So, the motivation behind developing this probe was again the four electrode method where we use copper electrodes in such a way that the ebonite rings are placed in between two sets of electrodes these are the rings and these rings are connected to external circuit. You can apply current across the external electrodes and measure the voltage in between all right. So, this was a probe which can be inserted in the soil mass and then you can do resistivity profiling. The calibration can be done in this way as I said you fill the box with a solution of sodium chloride of known resistivity what you will see is that the current and applied voltage they will be varying in the linear fashion. Similarly, the probe can be dipped in a column of sodium chloride solution. You can draw a relationship between applied voltage and the current and then if you know the resistivity of the solution and if you know the resistance which has been measured by using the box S 2 D box you can draw a relationship like this rho E R B is known that is the solution specific solution which you are using its conductivity is known or resistivity is known. Resistance using the box can be measured you can obtain the slope of this line and this slope of the line will give you relationship between resistivity and resistance. So, once you have done this calibration you can go ahead with geomaterial characterization fill up the box with the geomaterial of your interest you have this calibration with you what you are measuring is resistance between the 2 electrodes multiplied by this factor and you get the resistivity of the material. Similarly for the case of the probe you can do this calibration and again you will get this relationship where if you measure the resistance across the 2 copper rings multiplied by this factor it will give you the resistivity. So, first you insert this probe in a sodium chloride solution calibrate it and the same probe can be inserted in a geomaterial. The parameter multiplication factor remains same. So, if you measure the resistance multiplied by this parameter it will give you the resistivity. Now, based on this we got the results for resistivity box the 2 extreme soils which were tested silty soil and the white clay what they show you is that resistivity drops down as saturation increases. Remember these are all DC measurements at low AC current alright say 10 to 20 hertz we have used. The same trend you are observing for thermal resistivity also thermal resistivity with respect to dry density and moisture content, but here when we talk about saturation it takes into account volumetric moisture content also that means the resistivity which you are obtaining from the box test can directly be related to saturation or in terms of porosity or volumetric moisture clear and what it indicates is more the saturation as the resistivity that is true. Then why did we say that thermal resistivity is inversely proportional to electrical resistivity that question still remains you should understand that this question is incorrect. If you remember we were talking about the biggest loophole in thermal conductivity measurements is that effect of mineralogy cannot be incorporated. However, when you talk about electrical resistivity that limitation is also overcome here clear. So, though it appears that the relationships between the 2 parameters is inverse it is not correct because the thermal resistivity does not include as such the mineralogical aspects which are included in electrical measurements. So, electrical measurements are much more versatile than thermal measurements and that is why people are working in this area much more. Now, this shows that how probes can be utilized for finding out the in situ saturation conditions where again as the saturation increases what you will notice is the resistivity drops. And it so happens that because the probe is being inserted in the to the soil mass the influence of soil mass does not get highlighted so much except for the scatter while when you are placing the material in the box you know the compaction and the matrix structure cannot be replicated. And hence the conclusion is that the probes are much better than the electrical resistivity boxes and that is the reason why probes are being used and not you take the sample from the field and the undisturbed form place it in a box and test it that will give you misleading results. Now, if you compare both the results that is the box and the probe what you will notice is that the box gives higher resistivity as compared to the probe or the same saturation why it is so any reason. Now, this is where the contact problem comes in the picture when you are burying the when you are filling the soil in the box compacting it there is always a thin layer of air between the electrodes and the material. However, when you are inserting the probe into the soil mass the chances are that this layer would be minimal. So, basically because of the air pocket formation between the soil sample and the electrodes in case of the box its resistivities are not so reliable as compared to the probes that is one of the reasons again that why people would like to use probes rather than the boxes. Now, we wanted to see for wide clays what happens in case of clays the results are very very misleading because as I said when you are using the probe the entire volume of the soil is not conducting the current it is again a contact area problem these are a small rings of the probes all right which are contributing to the area of cross section of the flux which is much less. And hence you will notice that if you compare the results they do not compare well. Now, based on these studies some relationships were developed for determining electrical resistivity. So, this is a generalized form of the relationship where electrical resistivity is a function of saturation then the relationship between electrical resistivity and thermal resistivity this is how this relationship was developed what it indicates is that both the resistivities are equivalent to each other except for some multiplication factor all right. So, here this is term known as C R where C R is a coefficient correlation coefficient which depends again upon saturation. And A and B and C are the parameters which will depend upon the soil type how to define soil type. So, A B and C will be functions of fine contents. So, this is where you can say that these are the relationships which can be utilized for a given soil if you know they are fine content fine contents are nothing, but the clay contents or silt contents sometimes. So, combination of the two is also fine content you can obtain A B and C if the nomograms are given. Using these nomograms you can get the value of C R for a given saturation and using this C R if R T is known you can compute electrical resistivity or if electrical conductivity is known resistivity is known then you can compute thermal resistivity. Now, my question before I wind up is which one you like to compute if this equation is to be utilized you would like to determine electrical resistivity or thermal resistivity which one is more easily predictable and precisely predictable electrical. So, this equation is normally used to determine the thermal resistivity. And what is the beauty of this determination of R T value from electrical measurements it will also include the influence of mineralogy which could not be included otherwise into the study. So, that is one of the reasons that why electrical measurements and electrical properties are considered to be having a very wide scope as compared to thermal properties. Another issue is maintaining thermal flux is very difficult as compared to electrical flux. So, under in situ conditions you can easily obtain rho value electrical resistivity. And if you know the C R values for different type of soil conditions and their degree of wetness then you can compare the you can compute the thermal resistivity. So, this is a good application which was published by Reshma and my other students and this equation is widely being used by the people who are mostly in pipeline industries either the oil or air conditioning or even the thermal resistivities due to the buried cables.