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The first in the series to obtain the tensile strength directly would be you perform triaxialtest and I hope you can recognize this situation very easily if I perform the test, where Ido stress-strain relationship, for different types of samples and if I test them and whatI have to do is I have to develop the mohr envelopes All right. So, this line which youhave drawn is mohr- coulomb envelope and if I extend it up to the back and if I find outthe intersection of the mohr- coulomb envelope on the stress axis, normal stress axis thisis nothing but sigma t.So, it actual respect 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 they axis we have defined as apparent cohesion. So, apparent cohesion is the one where wedo not have any normal stress acting on the soil, but even then, the soil exhibit someshear resistance. So, this could be because of you know, the inter particle cohesion,which is because of maybe carbonates or sulfates 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 effect,you know, these are the two gear assemblies. So, in the case of the sands if the sandsare very irregular, and if they are highly compacted what happens you know, this is asort of a gear assembly which gets formed this itself might give you apparent cohesionin sands.You need not to have any shear strength sorry any normal stress, which is applied to getthis shear strength. So, we use this sigma t obtained from the triaxial response of theclays as the benchmark of the value tensile strength. Alright. And I am sure you musthave done triaxial test. So, you have to apply these membrane corrections and all to eliminatethe values which are coming because of the confinement.What we did is, we did some literature review, and we realized that tensile strength hasbeen attributed to the liquid limit of the soils. Why because, indirectly liquid limitconnotes to minerology, alright. Tensile strength has also been related with the plasticityindex. Again, the reason is simple, because PI is Indirect form of you know, understandor maybe the reflection of the minerology present in the soils.Then sigma t is also a function of cation exchange capacity again the same reason becauseof the minerology. The clay content, the clay content is the percentage fraction which isfiner than certain sized 2 microns. So, as the size decreases, cation exchange capacityincreases, surface area increases liquid limit increases, PI increases, all that series isstill 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 moisturecontent of the soil. So, higher the moisture content, lower the suction. correct and ACis the activity of the soil. So, there are several types of relationships which are availablein the literature. You will notice that tensile strength is a function of clay content. Morethe clay content more the tensile strength. Some people have correlated tensile strengthwith the OMC. Moisture content at OMC and the moisture content at a given point in thesoil mass.Liquid limited, Plasticity index, clay content, activity of the soil, moisture content ofthe soil, suction of the soil and so on. I would say that this is a sort of a, you knowjourney in terms of the evolution of the subject. So, suction came quite recently in the picturebefore that section was not included in defining the tensile strength, but people have realizedthat suction is the one which includes all of the parameters into it, because suctionof the soil is a parameter which talks about its physicochemical mineralogical response.So, if I measure the suction or if I measure the cation exchange capacity I can get sigmat values. This work was done by my two master students. Both of them are incidentally inDhar group, now. And they are doing extremely well. One was the Mr. Shinde, and anotherone is Ramana these guys have done fundamental studies related to tensile strength determinationand what we realized is that you know the relationships which are only single parameterrelationships cannot be much encouraged, because you cannot link directly clay content withthe sigma t and so on. So, this is a commentary which we created on the subject.So, generalized relationships of this type was developed sigma t is some function multipliedby clay content, CEC, and psi suction and I hope you are conversant with the symbolsby this time and this is how we validated this equation. Number one and number 2 equationdoes not consist suction in it and it deals with only clay content and Cation Exchangecapacity. What we have done is by using these equations, we have obtained the sigma t computedand this sigma t measured is from the triaxial test.And we have shown that there is a good relationship between the experimentally obtained resultsfrom the triaxial testing and both the equations yield good results. I am sure you will realizethat these equations require determination of two parameters which cannot be obtainedin every geotechnical in a laboratory. Is it not except for the clay content. Cationexchange 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 sakeof convenience of both parties, the suction measurement is being done and it is not beingdone or suction is known and/or not known. You can rely upon these equations and youcan go ahead with the design of the systems.So, I am sure you must realized these efforts were quite significant in obtaining the sigmat value of the geomaterial just based upon it is, I always read it like this physicaland chemical response. So, it is a physical, chemical and mineralogical and mineralogicaland physical. So, this is how you read this relationship. So, in short, we have the physicsof the material, the chemical state of the material and the mineralogical state of thematerial.These type of relationships become much more useful for designing the clay lines, and thetop covers for, you know, different types of disposal facilities. I am sure you canrealize one more advantage of having these equations particularly if the soils are contaminated.So, I can always be find out what is the level of contamination of the soils and how theseparameters get changed and hence how sigma t is going to get change.So, this is how the developmental work goes on. Sir here, by general specifications wehave 3 options to analysts analyze the tensile strength, three parameters, 2 parameters triaxialtest and in different cases we get different tensile strength. In these three methods weget different sigma t values, right now, we are preferring which case we are taking. No,I did not follow your question can you repeat it. Sir, here we are considering 3 parameters,2 parameter triaxial tests and in every case sigma t is different. No see, 3 parameterand 2 parameters are the equations.So, what you get is sigma t computed. So, sigma t computed you get from these two equationsand sigma t is the tensile strength test which you get from triaxial testing, if you matchthese two, then you realize that there is a significant match between the two. So, whatin first case you are considering a suction also and to two parameters, there is no suctionvalues. So, in case of that you will you will get something sigma t value something lower.I think, you missed the whole story. The whole story was that everybody is not capable ofmeasuring the suction value. Because it requires 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 CEC.So, cation exchange capacity has to be included. So, the choice is yours if you know the suctionvalue, you can substitute over there and if you do not have and then you can go aheadthat is what the whole idea is. Yes, So, what is the question, but this is the if we includethe suction value.So, we get more sigma t value this is the something concluded. It is basically rootof psi the way the mathematics and it is not so easy to decipher because it is a multiparameter system, so I am sure you will realize that these powers will take care of something.Alright?. So, truly speaking, this becomes a root of CEC into psi. This is how the mathematicalrepresentation is, as I said these empirical relations are ascribed, subscribed, you know,are basically these equation go in the name of the researchers who developed them.So, you never questioned that Casagrande’s equation to find out CEC value from the liquidlimit is that not. You always say point not not nine multiplied LL minus 20 is this correct?He was a person who obtained this relationship. So, these are empirical relationships whichmight be useful for designing the systems now your question should be that how basedon only 3 triaxial data you are generalizing the thing.So the answer would be this a philosophy. You are free to conduct your experiments Thenyou get the sigma t values. And to substantiate these, I think you should realize that ifyou look at this figure.As sigma t decreases, what is going to happen? Strength of the material is going to increase.Alright?. Su value is going to increase. So, simulating these type of things in the laboratorymight be having limitations. So you require different types of setups in particular, whereextremely low values of the stress and strains can be measured number one and you requirevery sensitive setups. Then only you can get extremely less values of sigma t’s and thenthis portion of the graph can be completed.So it is a hypothesis which is proven by some data points. Alright. 95% confidence bandis not a very poor band to convey the message that this relationships are working alright.Understand how the graphs are plotted. Graph is plotted by getting the computational valuesof sigma t by using these equations, which are derived earlier, "Professor - studentconversation starts" we got a particular value for sigma t from triaxial, then for that howdo you get the y value. for the same soil for the same soil, that means, I am sure youwill realize that CL, CEC are associated with the soil.So, that means for the same soil if I plot sigma t computed and sigma t which is fromthe triaxial testing. This is how they sit. Must be like for every triaxial test therewill be a particular computed value right. No, that will be very difficult because, youknow you cannot mold the soil sample with variable moisture contents. So, when you aredoing triaxial testing your sample is fixed that means the soil is fixed and the moisturecontent is fixed. In other words, the suction is also fixed alright. So, suppose if I saynumber one soil for which suction is known, that when moisture content is known, CEC isknown and CL is known.If I substitute the values over here, and if I do a triaxial test, the 2 data pointswherever they sit, this is the trend which emerges. So, the quick answer to your questionwould be that the sigma t values are for the same soils. No, sir. I did not understandfor a particular sigma t with respect to the y axis you got a value. Forget about sigmat. That is what I am saying is for the given soil, I have two values of sigma t 1 whichI get from computation and which I get from triaxial.I am plotting column number 2 and 3 for the same soil. That is it. Sir, yeah, then thischarge wont be there right. Which one? I thought for each triaxial test we will be like fora particular sample we will be computing the value numerically and then plotting. No, sothat is what I said this is all soil specific because for a given soil the CL is known,CEC is known and suction is known provided W is constant.So, if you are interpreting this graph in such a manner that is moisture content changeswhether I can use this relationship or not then this becomes interesting question becausepsi itself is a function of moisture content that means, for the same soil with same CL,same CEC, you might have to conduct several experiments by changing the moisture contentand measuring the suction then you will be getting several circles and then you willbe getting several sigma t values that is possible. "Professor - student conversationends"Otherwise, the simple way to look at this would be fix column number one and computesigma t by substituting these values and by conducting triaxial test might be computedwhy in Y axis, so why triaxial test that star mark result is coming that because for thatsigma t computed will not be there, if I plot x y z together on a scale this is a 3 dimensionalpart, which I will be getting.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 keepingthe first column constant and plotting for that value. Y versus Z? So, your sigma t mesmeasured is z, sigma t computed is one of the two values Y and for a given x I am plottingthese two rather than saying for a given sigma t. It is not that like that. For a given soilyou have two sigma t values are 3 sigma t values which you were plotting. So, you haveto look it like this for a given soil, if I use equation one if I use equation 2 andif I do triaxial test where the results would be and if you plot them this is what the picturewould be. You said that as undrained shear strength is increasing that tensile strengthof the soil is decreasing, undrained shear strength of the soil is increasing tensilestrength might be decreasing correct.So, what we observe in field is su sigma v prime is point 2 constant as a function oflet us say PI, yes. So, we can say that that soil which is below the certain depth willhave a lower tensile strength and soil above the means. So, all these are the limitationsof the Casagrande’s methods, please remember they are not talked about the tensile strengthas such, they are blind of these parameters.I hope before you interpret all those relationships, you should realize that the relationshipsare 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 comingin to the picture unless you relate OCR with the suction value. I hope now, this pointshould be clear your analogy is good, but try to understand the limitations of the existingrelationships. Now, beyond imagination would be a fact that you know, linking the tensilestrength which appears to be a mechanical property with the mineralogical, chemicaland physical properties is a very interesting philosophy. So, do not go by the terms onlyCL, CEC and psi this is a hunch of a researcher that he or she has used these parameters toobtain something which has a very wider application, Fine. Read the papers which have been writtenby Sudarshan Shinde and KV Ramana, Hanumantha Rao. These relationships were derived by thesethree guys. There is a lot of philosophy which we have discussed in the paper.
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