 So, this is Dr. Mahesh Kalyanshti, Associate Professor, Department of Civil Engineering, Valjan Institute of Technology, Solapur. In this session, we will discuss about shear strength of soil. The learning outcome will be, at the end of this session, students will be able to describe the theory of development of shear strength of soil. Let us discuss regarding the strength of different materials, especially which are used in the civil engineering field. For example, if you take a steel material, so the strength of the steel is basically a tensile strength. As we know that the steel is very strong in tension and very weak in compression. Therefore, primarily the strength of the steel is nothing but tensile strength of the steel. In the same way, if you look at the concrete as another material, so concrete also the strength of the concrete is nothing but compressive strength. Since we know that the concrete is very strong in compression, therefore the strength of the concrete is compressive strength only. In the same way, if you take an example of a soil, in case of the soil, the strength of the soil is nothing but the shear strength because the soil is strong in shear. However, the evaluation of shear strength is not a simple thing since it involves a lot of complexity. As we know that the soil basically is a three-phase system, therefore the strength of the soil depends on so many factors. So presence of pore water is one of the biggest complicity present which affects on the shear strength of the soil. So therefore, the behavior of the soil is supposed to be a very, very complex. Therefore in case of the soil, the evaluation of shear strength and determination of shear strength is basically a very complex process as compared to other building materials. Now, what is shear strength? Shear strength in soil is the resistance to movement between the particles. As we know that the soil comprises of the solid particles as well as air and water. So if I consider the solid particles, then the resistance to movement between the particle is the shear strength and this resistance is developed because of a physical bond. So from number one, the particle interlocking. So this is one of the reason. Second one is atoms sharing electrons at surface contact point. So this we can call it as a cohesion. So because of the atoms which are sharing the electrons at the surface contact points. And the third one is the chemical bonds that is called as a cementation such as crystallized calcium carbonate. So these are the three factors which are responsible for the physical bond, development of the physical bond and due to presence of this physical bond, there exists resistance to the movement between the particle and this resistance to movement between the particle is called as shear strength of soil. Now soil failure usually occurs in the form of sharing along internal surface within the soil as we already discussed here. Therefore the structural strength is primary a function of shear strength. So the strength of the soil is nothing but it is a shear strength only and shear strength is a soil's ability to resist sliding along internal surface within the soil mass. Now which are the factors influencing the shear strength? So these are the soil composition, this is a major factor which is influencing the shear strength of soil. So the soil composition means it is a mineralogy that is present in the soil mass, then grain size and grain size distribution in the soil mass, shape of the particles, pore, fluid type and content. So these are the factors which comes under the soil composition and the soil composition is one of the important parameter which affects on the shear strength. The another factor which is influencing the shear strength is the initial state. So the state can be described by terms such as loose soil, dense soil, over consolidated soil, normally consolidated, stiff, soft, etc. So based on the initial state of presence of the soil in a natural condition the shear strength of the soil also goes on varying. The third factor is a structure which refers to the arrangement of particles within the soil mass, the manner in which the particles are packed or distributed. So this also affects on the shear strength. So these are the three major influencing factors which affects on the shear strength. One is soil composition, another is initial state and third one is structure. Now let us take a look at the examples of the shear failure. Now as we already discussed that the soil generally fails in shear because the shear strength is a primary strength of the soil. So some examples we will see here and we will see the mechanism of the failure of the soil. For example say if we are considering one footing which is rested on a soil mass. So as the load is applied on this footing naturally some portion of the soil mass will have a tendency to move away from the footing and there is a bulging phenomena. So because of the movement now you can see this arrow this indicates the movement of this soil mass and the soil is likely to fail along one particular plane. So this particular red line shows the failure plane. So the soil is about to fail along this particular plane and this much quantity of the soil will have a tendency to move away from the soil mass. At the same time along the failure plane there is a resistance offered by the soil. You can see here these arrows show the resistance. So this resistance offered is called as a shear strength of the soil. Once the stress crosses that value then the failure takes place and we observe that the soil mass slides along this failure plane. Another example is an embankment. So in case of the embankment also you can see here the self-heat of the soil mass which will have a tendency to move away from the backfill or away from the embankment. So therefore again here also one failure plane is developed and along this plane the soil is about to fail and again you can see the resistance is offered which is opposite to the movement of the soil mass. So here also the shear strength is been developed. Now if I look at the mechanism so what happens along the failure plane we can see here there is a resistance offered by the soil and if I just take a enlarged view of the failure plane so on the failure plane there exists a normal stress. So here this particular soil mass will exert a normal stress here and then based on this normal stress the shear stress is also produced here. So along the failure plane you can see here this is what is the shear stress produced. So this shear stress produced it depends upon the normal stress. Therefore we can say that the shear strength of the soil is a function of the normal stress. So based on these discussions let us have some review questions for options given tensile strength, comparison strength, shear strength and axial strength. The second question is unleash the factors influencing the shear strength of soil. So take a pause answer these questions and resume the video. Welcome back. So let us look at the answers. The first question was which kind of strength is governed in case of soil. So naturally it is a shear strength. So in the earlier slides we discussed that the shear strength is a major strength possessed by the soil. So answer is C and second question was unleash the factors influencing the shear strength of soil. So these are the factors which affects the shear strength. First one is soil composition. Second one is initial state and third one is structure. Let us move ahead. Now once we understand the mechanism of the shear failure then we can write this phenomenon mathematically. For example now in the earlier slides we have seen an example of the embankment where the soil mass will have a tendency to move away from the backfill. So along the surface now if you just look at this particular failure plane there exists a normal stress and based on the normal stress the shear stress is developed. So therefore we can say that the normal stress is a function of the shear stress. So if you increase the normal stress shear stress will go on increasing. The same thing mathematically has been represented by a scientist called Mohr Coulomb. So Mohr and Coulomb together have developed one equation which describes this particular behavior where they have made an attempt to correlate the normal stress and shear stress. And this equation is given by tau f that means the shear strength tau is nothing but the shear stress which is based on the normal stress tau f is nothing but the maximum shear stress produced along that particular plane. So shear strength is nothing but C plus sigma tan phi. Now this mathematical equation can be graphically represented here. So on x axis the normal stress is plotted on y axis the shear stress is plotted and you can see here normal stress and shear stress has been correlated with the help of this particular line. Therefore the equation of this line is nothing but tau f equal to C plus sigma tan phi and this line is called as failure envelope. So once you get this failure envelope then the intercept of this failure envelope on the y axis is called as cohesion. This is one of the strength parameter of the soil and the inclination of this inclined line with horizontal is called phi that is called as friction angle. So in this way the two major strength parameters can be determined from this particular failure envelope that is cohesion and friction angle. Now in that particular equation now basically you can see here the two parameters are playing very important rule for the shear strength. One is the cohesion component. So you can see here this total is the tau f you can see tau f this is the total shear strength for this particular given normal stress. Now this total shear strength comprises two components one is C and there is sigma f tan phi. C is nothing but it is a cohesion component and sigma tan phi is the friction component. So cohesion component and friction component taken together we get the shear strength. These are the references which are used for the presentation. Thank you.