 The first in the series to obtain the tensile strength directly would be you perform triaxial test and I hope you can recognize this situation very easily. If I perform the test where I do stress strain relationship for different types of samples and if I test them and what I have to do is I have to develop the more envelopes alright. So, this line which you have drawn is more coulomb envelope and if I extend it up to the back and if I find out the intersection of the more coulomb envelope on the stress axis normal stress axis this is nothing but sigma t. So, a triaxial response can be utilized to obtain the tensile strength of the soils provided you have done the test very, very precisely. For your quick review the intercept on the y axis we have defined as apparent cohesion. So, apparent cohesion is the one where we do not have any normal stress acting on the soil but even then the soil exhibits some shear persistence. So, this could be because of you know the inter particle cohesion which is because of maybe carbonates or sulphates which are present in the soils. It could be because of the angularity of the grains of the sands and because of the angularity there could be a sort of a normally what we call it as a gear assembly sort of a effect you know these are the two gear assemblies. So, in the case of the sands if the sands are very irregular and if they are highly compacted what happens you know this is a sort of a gear assembly which gets formed and this itself might give you apparent cohesion in sands you need not to have any shear strength sorry any normal stress which is applied to get the shear strength. So, we use this sigma t obtained from the triaxial response of the clays as the benchmark of the value tensile strength alright and I am sure you must have done triaxial test. So, you have to apply these membrane corrections and all to eliminate the values which are coming because of the confinement. What we did is we did some literature review and we realized that tensile strength has been attributed to the liquid limit of the soils why because indirectly liquid limit connotes to mineralogy alright tensile strength has also been related with the plasticity index again the reason is simple because P i is indirect form of you know understood or maybe the reflection of the mineralogy present in the soils. Then sigma t is also a function of cation exchange capacity again the same reason because of the mineralogy the clay content the clay content is the percentage fraction which is finer than certain size 2 microns. So, as the size decreases cation exchange capacity increases surface area increases liquid limit increases P i increases all that series is still valid and the suction. So, psi corresponds to the suction value and one interesting thing here to see is that the suction includes in it the state of moisture content of the soil. So, higher the moisture content lower the suction correct and AC is the activity of the soil. So, there are several types of relationships which are available in the literature you will notice that tensile strength is a function of clay content more the clay content more the tensile strength. Some people have correlated tensile strength with the WOMC moisture content at OMC and the moisture content at a given point in the soil mass liquid limit plasticity index clay content activity of the soil moisture content of the soil suction of the soil and so on. I would say that this is a sort of a you know journey in terms of the evolution of the subject. So, suction came quite recently in the picture before that suction was not included in defining the tensile strength, but people have realized that suction is the one which includes all of the parameters into it because suction of the soil is a parameter which talks about it is physico-chemico mineralogical response. So, if I measure the suction or if I measure the cation exchange capacity, I can get sigma t values. This work was done by my two master's students. Both of them are incidentally in dark group now and they are doing extremely well. One was the Mr. Shinde and another one is Ramanna. These guys have done fundamental studies related to tensile strength determination. And what we realize is that you know the relationships which are only single parameter relationships cannot be much encouraged because you cannot link directly clay content with the sigma t and so on. So, this is the commentary which we created on the subject. So, generalized relationships of this type was developed. Sigma t is some function multiplied by clay content C, C and psi suction and I hope you are conversant with the symbols by this time and this is how we validated this equation. Number one and number two equation does not consist suction in it and it deals with only clay content and cation exchange capacity. So, what we have done is by using these equations, we have obtained the sigma t computed and this sigma t measured is from the triaxial test and we have shown that there is a good relationship between the experimentally obtained results from the triaxial testing and both the equations yield good results. I am sure you will realize that these equations require determination of two parameters which cannot be obtained in every geotechnical engineering laboratory is it not except for the clay content. Cation exchange capacity requires some basic paraphernalia in the laboratory. You know how it is done, we have discussed about this. So, and of course, suction measurement. So, suction measurement is still not many people are doing, alright. So, for the sake of convenience of both the parties where the suction measurement is being done and it is not being done or suction is known and not known, you can rely upon these equations and you can go ahead with the design of the systems. So, I am sure you must have realized these efforts were quite significant in obtaining the sigma t value of the geomaterial just based upon its I always read it like this physical and chemical response. So, it is a physical, chemical and mineralogical and mineralogical and physical. So, this is how you read this relationship. So, in short, we have the physics of the material, the chemical state of the material and the mineralogical state of the material. These type of relationships become much more useful for designing the clay liners and the top covers for different types of disposal facilities. I am sure you can realize one more advantage of having these equations particularly if the soils are contaminated. So, I can always find out what is the level of contamination of the soils and how these parameters get changed and hence how sigma t is going to get changed. So, this is how the developmental work goes on. Sir, here by general specifications, we have three options to analyze the tensile strength, three parameters, two parameters to actual test and in different cases, we get different tensile strength. In these three methods, we get different sigma t values. Right now, we are referring which caves we are taking. I did not follow your question. Can you repeat it? Sir, here we are considering three parameters, two parameters to actual test and in every case sigma t is different. No, no, no. See, three parameters and two parameters are the equations. So, what you get is sigma t computed. So, sigma t computed you get from these two equations and sigma t is the tensile strength which you get from triaxial testing. If you match these two, then you realize that there is a significant match between the two. So, what in first case you are considering a section also and two parameters, there is no sectional values. So, in case of that, you will get something sigma t values something lower. I think you miss the whole story. The whole story was that everybody is not capable of measuring the suction value. Because it requires a lot of gadgets. So, idea was to give two equations. If you can measure suction, that is also good. Unfortunately, you cannot get rid of Cc. So, cation exchange capacity has to be included. So, the choice is yours. If you know the suction value, you can substitute over there and if you do not have even then you can go ahead. That is what the whole idea is. Yes, what is the question? This is the, if we include suction value, so we get more sigma t value. This is the something concluded. It is basically root of psi the way the mathematics is and it is not so easy to decipher because a multi parameter system. So, I am sure you will realize that these powers will take care of something. All right. So, truly speaking, this becomes under root of Cc into psi. This is how the mathematical representation is. As I said, these empirical relations are abscribed, you know, are basically these equations go in the name of the researchers who develop them. So, you never question that Casagrande's equation to find out Cc value from the liquid limit. Is it not? You always say 0.009 multiplied by LL minus 20. This is correct. He was the person who obtained this relationship. So, these are empirical relationships which might be useful for designing the systems. Now your question should be that how based on only three triaxial data you are generalizing the thing. So, the answer would be this is a philosophy. You are free to conduct your experiments and then you get the sigma t values and to substantiate this I think you should realize that if you look at this figure as sigma t decreases what is going to happen? Strength of the material is going to increase. All right. Su value is going to increase. So, simulating these type of things in the laboratory might be having limitations. So, you require different types of setups in particular where extremely low values of the stress and strains can be measured number one and you require very sensitive setups. Then only you can get extremely less values of sigma t's and then this portion of the graph can be completed. So, it is a hypothesis which is proven by some data points. All right. 95% confidence band is not a very poor band to convey the message that these relationships are working all right. Understand how the graph was plotted. No, no. Graph is plotted by getting the computational values of sigma t by using these equations which were derived earlier. We got a particular value for sigma t from triaxial then for that how do you get the y value? For the same soil, for the same soil that means I am sure you will realize that cl, c, c are associated with the soil. So, that means for the same soil if I plot sigma t computed and sigma t which is from the triaxial testing this is how they sit. Must be like for every triaxial test there will be a particular computed value right? No, that will be very difficult because you know you can not mold the soil sample with variable moisture contents. So, when you are doing triaxial testing your sample is fixed that means the soil is fixed and the moisture content is fixed. In other words the suction is also fixed all right. So, suppose if I say number one soil for which suction is known that means moisture content is known, cc is known and cl is known if I substitute the values over here and if I do a triaxial test the two data points wherever they sit this is the trend which emerges. So, the quick answer to your question would be that the sigma t values are for the same soils. I did not understand for a particular sigma t with respect to the y axis you got a value. Forget about sigma t that is what I am saying is for the given soil I have two values of sigma t one which I get from computation and which I get from triaxial. I am plotting column number 2 and 3 for the same soil that is it. So, yeah. Then the stars would not be there right. Which one? The star mark 3 test triaxial. I thought for each triaxial test we will be like for a particular sample we will be computing the value numerically and then plot. No, so that is what I said this is all soil specific because for a given soil the cl is known cc is known and suction is known provided w is constant. So, if you are interpreting this graph in such a manner that if moisture content changes whether I can use this relationship or not then this becomes interesting question because psi itself is a function of moisture content. That means for the same soil with same cl same cc you might have to conduct several experiments by changing the moisture content and measuring the suction. Then you will be getting several circles and then you will be getting several sigma t values that is possible. Otherwise the simple way to look at this would be fix column number 1 and compute sigma t's by substituting these values and by conducting a triaxial test. Multi computed in y axis. So, y triaxial test that star mark result is coming that because for that sigma t computed will not be there. If I plot x, y, z together on a scale this is a 3-dimensional plot which I will be getting and if I want to convert a 3-dimensional plot to a 2-dimensional plot what I will be doing I will be keeping one column constant that is it as simple as that. So, I am keeping the first column constant and plotting for that value y versus z. So, your sigma t me s measured is z sigma t computed is one of the two values y and for a given x I am plotting these two rather than saying for a given sigma t is not that for a given soil you have two sigma t values or three sigma t values which you are plotting. So, you have to look it like this for a given soil if I use equation 1 if I use equation 2 and if I do triaxial test where the results would be and if you plot them this is what the picture would be. You said that as undrained shear strength is increasing that tensile strength of the soil is decreasing. Sorry, undrained shear strength of the soil is increasing tensile strength might be decreasing correct. So, what we observe in field is SU by sigma v prime is 0.2. Constant. Yes. What is the function of let us say P i. Yes. So, we can say that soil which is below the certain depth will have a lower tensile strength and soil above the things. So, all these are the limitations of the Casagrandes and Schmerzmann methods. Please remember they are not talked about the tensile strength as such. They are blind of these parameters. I hope before you interpret all those relationships you should realize that those relationships are blind of these parameters. They cannot be employed here. Their domain is totally different. There you are using one term you know OCR value also clear. So, that OCR is not coming to the picture unless you relate OCR with the suction value. I hope now this point should be clear your analogy is good but try to understand the limitations of the existing relationships. Now beyond imagination would be a fact that you know linking the tensile strength which appears to be a mechanical property with the mineralogical, chemical and physical properties is a very interesting philosophy. So, do not go by the terms only C L C C and Psi. This is a you know hunch of a researcher that he or she has used these parameters to obtain something which has a very wider application. Fine. Read the papers which have been written by Sudarshan Shinde and K V Ramanna, Anwant Rao. These relationships were derived by these three guys. There is a lot of philosophy which you have discussed in the paper.