 So, today I will discuss about analysis and design of heel slab for a cantilever retaining wall, learning outcomes. At the end of this session learners will be able to analyze and design heel slab of a cantilever retaining wall, introduction. The soil reaction varies linearly with more pressure on toe and less pressure on heel slab. This is because of earth pressure on the stem slab as shown in figure 1. This is figure 1. So, here you will find P by A plus M by Z, this is P by A minus M by Z, where M is created by the lateral pressure acting on the stem slab of a retaining wall. So, which the design principle of cantilever retaining wall is to see that the pressure at the end of the heel is never negative. Since soil cannot apply negative pressure, earth pressure. If the earth pressure is negative, the stability of the structure itself will be in doubt. Apart from soil pressure, direct weight of the backfill and the surcharge on the heel slab are to be considered in the design. So, these loadings are shown in figure number 2. So, here this is the earth pressure. So, this earth pressure will create a force pH. So, this pH will try to overturn this particular retaining wall. So, therefore, due to that effect, we will find a maximum pressure on this side, which is P by A minus M by Z and a minimum pressure on this side P by A minus M by Z and this loading it is the weight of this particular earth fill and surcharge if any on this. So, this is greater than this particular pressure. Here it is P by A minus M by Z that is why the pressure ordinate is less and here also it is less. So, this will be more than that. So, hence this will deform, this will have a sagging bending moment. So, now let us see the analysis of heel slab. Where is the maximum bending moment in a heel slab? We have just seen. Can you guess? The maximum bending moment in a heel slab will be at the inner face of the stem slab. So, if I have, so I will just show you here. So, this is the inner face of stem slab. So, at this location, so this is going to deform like this. So, therefore, at the inner face of the stem slab, we get maximum bending. So, we are supposed to find out the maximum bending which is sagging bending moment. The bending moment about the face of the stem slab is equal to W into L2 square by 2. W is the pressure from the earth downwards minus P2 into L2 square by 2 that is again UDL upwards then P6 into L2 by 3. So, that will be the bending moment at the face of the stem slab, inner face of stem slab. So, that is maximum bending moment in the heel slab. So, Mu will be equal to 1.5 times M. So, now E is the eccentricity which is B by 2 minus sum of stabilizing moment minus overturning moment divided by sum of all downward roots. P1 is sigma W by B into 1 plus 6 E by B which should be less than SBCF soil. P2 is again sigma W by B into 1 minus 6 E by B which should be greater than 0 or equal to 0. P5 it is the P by 2 plus P1 minus P2 by B into B minus L by 2 and P6 is one half L2 into P5 minus P2. I will just show you all these loads in first figure. So, now this is P1, this is P2 then we will find this is P5. P5 is the pressure ordinate just at the face of the stem slab. Then P6 is at the CG of this triangular portion and W is acting downwards which is uniform distributed load and this P2 is uniform up to here. So, that we have taken moment then P6 we have taken moment about face design of heel slab. Now for the design of heel slab MU limit should be equated to MU. So, the MU limit is 0.148 fckbd square if you use mild steel, 0.138 fckbd square if we use fe415 steel, 0.133 fckbd square if we use the fe500 h wise debars. Find the effective depth required and compare it with effective depth provided in the preliminary dimensions. Now, for the preliminary dimensions and stability analysis please go through my own video on stability analysis of cantilever retaining walls. So, after stability analysis only we are supposed to do for analysis and design of each particular component that is stem slab, toe slab and heel slab. So, which shall be greater than or equal to effective depth required. That means required we are going to calculate by this equation and provided we have already done by approximation earlier and we should see that the provided depth should be more than required depth. Determine area of steel required by using equation g 0.1.1 b because it is under reinforced section. So, MU is equal to 0.87 fy astd into 1 minus ast fy upon bd fck. So, minimum steel is 0.12 by 100 into b into d. So, b considered is always 1 meter. Provide design steel at the at the top not bottom it should be actually top at the top and the minimum steel as distribution steel perpendicular to it as shown in figure number 3. So, it is at top because this is having sagging minimum this is this is going to bend like this. So, therefore, design reinforcement should be at top it is a cantilever. So, therefore, distribution steel just below this. So, here you find minimum main steel that is the horizontal bars at top and the distribution steel perpendicular to it. So, this distribution steel is 0.12 percent distribution steel is 0.12 percent and design steel as per this particular calculation. So, this is how we are supposed to design the cantilever portion of a heel slab. So, it is a it is actually a all the slabs the specialty of this cantilever retaining wall is each slab is a cantilever stem slab is a cantilever toe slab is a cantilever and the heel slab is also a cantilever. So, this is how we are supposed to design the heel slab of a cantilever retaining wall. So, this shows the reinforcement arrangement in the heel slab this is heel slab from face of the stem to this. So, here we find this particular main reinforcement then below that we find distribution steel and this main reinforcement should have development length on this side. So, minimum development length you are supposed to provide here. So, this this is this finishes the design of heel slab. So, the references used are these things. Thank you very much.