 Hello, this is Dr. Mahesh Kalyanshti, Associate Professor, Department of Civil Engineering, Valchan Institute of Technology. In this session, we will discuss regarding determination of indices of soil consistency. The learning outcome of this session will be, at the end of the session, students will be able to determine various indices of soil consistency. Let us take a quick review of the utterable limits which we already discussed in the earlier presentations. With the help of this sketch, we can very easily define the various utterable limits as it is shown here. First one is the liquid limit, second one is a plastic limit and third one is shrinkage limit. Now, with respect to these utterable limits, now we have to define various indices of consistency. The first index is the plasticity index which is been briefly denoted by P i and plasticity index is given by liquid limit minus plastic limit. So, L L means liquid limit and P L means plastic limit. So, it is a difference between the liquid limit and plastic limit. This index provides a measure of a soil plasticity which is the amount of the water that must be added to change a soil from its plastic limit to its liquid limit. So, as it is shown here in the numerical equation, so we can see it is a difference between the liquid limit and plastic limit. Or other words, we can say that it is the amount of water that must be added to change a soil from plastic limit to liquid limit. The plasticity index is useful in engineering classification of fine-grained soil and many engineering properties have been found to correlate with plasticity index. So, P i is one of the very important indices of soil consistency which describes the plasticity of the soil. Now, based on the plasticity index, we can define the types of soil here. So, you can see various descriptions here for different P i values. Now, P i is zero means what liquid limit and plastic limits are same. In that case, it is called as a non-plastic soil. Then from 1 to 5, it is a slightly plastic. 5 to 10, it is low plasticity. 10 to 20, it is medium plasticity. 20 to 40, high plasticity. And even for greater than 40, it is very high plasticity. So, with the increase in the plasticity index P i, the plasticity of the soil goes on increasing. So, this is how we can get an idea regarding the plasticity of the soil from the index called plasticity index. The another index is the liquidity index which has been denoted by L i. The relative consistency of a cohesive soil in the natural state can be defined by a ratio called liquidity index which is given by this equation. So, liquidity index is nothing but it is a ratio of difference between natural water content minus plasticity limit divided by liquid limit minus plastic limit. So, the liquidity index gives us an idea about the natural state of consistency of the soil. This index provides a clue as the condition of the in situ soil. This index helps us to know if our sample was likely to behave as a plastic brittle or liquid. So, as I told earlier that liquidity index gives us an idea regarding the natural state of consistency of the soil. And from this we can we can get an idea about whether the soil is in a plastic state or whether it is in a brittle state or whether it is in a liquid state. Now, if you look at this diagram, so this is plasticity plastic limit and this is liquid limit. And as per this equation liquidity index, if suppose the natural water content is equal to plastic limit, then naturally the index becomes zero. So, this is that case. And another case is that if the natural water content is equal to liquid limit, then both the numerator and denominator becomes same and it becomes one here. So, these are the two distinguished points here we get. Now, this point represents the natural water content equal to plastic limit. This point represents the natural water content equal to liquid limit. And based on the liquidity index value, now if Li is less than zero, it indicates that the soil is in a brittle state. So, you can see in this zone here. So, if liquidity index is less than zero. If liquidity index is in between zero to one, so it means this range. So, if it is in between zero to one, then this is in a plastic state. The soil mass is in a plastic state. And if Li is greater than one, the soil is very viscous. So, greater than one means this zone, it means liquid limit and higher water content. Naturally, the soil is in a liquid state. So, in this way, we get an idea about the natural state of consistency of the soil based on the liquidity index. Another is the consistency index. This also index helps us to describe the natural state of consistency as that of liquidity index. So, here there is a little change in the equation. Now, in the numerator, you can see it is liquid limit minus natural water content divided by liquid limit minus plasticity index. So, based on this equation, we can get the consistency index. And the liquidity index and consistency index are one and same with different significance, because both the indices indicate the natural state of consistency. Then the flow index, flow index is nothing but it is a slope of the flow curve. Now, in the earlier presentation, we discussed the liquid limit determination. In that case, we have to draw a similar graph paper wherein on x axis, the log scale is there and on y axis, there is a number of loads. And in the laboratory, we developed this kind of line there. So, that line we call it as a flow curve. And the slope of this flow curve is nothing but flow index. So, this equation gives us the flow index. You can see here the numerator is w1 minus w2. And denominator is log n0 2 minus log n1. Of course, you can see if I want to get the slope here. So, the ratio of difference between the water content and difference between the log of the number of loads, this gives me slope that is called flow index. The next one is the toughness index. Now, toughness index describes regarding the toughness of the soil. And it is given by equation P i divided by i f. P i means plasticity index divided by flow index. So, plasticity index at the beginning we discussed. And flow index just now we discussed here. So, the ratio of these two gives us toughness index. So, all these indices basically gives us a state of consistency and behavior of the soil. Now, let us take a look at the example. So, we will take one small example and we will see how to get the indices. So, the following data were obtained from the liquid and plastic limit test for a soil. Now, liquid limit test data is given. Plastic limit test, the plastic limit is obtained as 21.3 it is given. And in situ motion content it is natural water content is given as 25.7. So, what you are supposed to find is find liquid limit, plasticity index, liquidity index and flow index. Now, let us go first of all for the liquid limit. So, for liquid limit as we know that we have to plot the graph water content versus number of blues. So, this table we have to refer. So, on x axis there is a number of blues on log scale and on y axis there is a water content in percentage. So, all these four points we plotted here. And once you get the points you have to join it by a straight line this is called as a flow curve. But we want the liquid limit. So, liquid limit is the water content at 25 blues. Therefore, at 25 blues let us draw a line and the corresponding water content gives you liquid limit. So, this liquid limit comes out to be 37 percent are most you can see here. Then next is a plasticity index. So, plasticity index is nothing but the difference between liquid limit and plastic plastic limit. So, liquid limit is obtained as from this graph 37 minus plasticity index is already given here 21.3. So, it comes out to be 15.7. Next is the liquidity index. So, this equation we discussed earlier. So, in this natural water content is given to us 25.7 plasticity index is 21.3 liquid limit and plastic limit is substituted here and we get the value as 0.28. Third one is a flow index that is it is a ratio of the flow curve. So, as already we discussed so, such kind of flow curve that we developed earlier. So, the slope of this line gives me flow index. So, for this slope you can consider the any two points. So, 0.362 minus 0.341. So, these are the water content. So, that is 36 percent and 34 percent. So, we can just see here this point and this two points. So, in between these two points you can get a line and you can get the slope that comes out to be 0.284. So, this is a summary. So, these are the answers we got liquid limit 37 percent plasticity index 15.7, liquidity index 0.28, flow index 0.284. So, these are the references which are used for this presentation. Thank you.