 class, I have discussed about the different types of settlement that immediate settlement and primary consolidation settlement and secondary compression settlement. Now, in this lecture I will discuss how to calculate these different types of settlement that is immediate settlement and consolidation settlement for different types of soil. Now, first I will go for this settlement calculation. This is settlement calculation. So, first expression that I will give for the immediate settlement calculation. So, immediate settlement calculation. So, by theory of elasticity approach, this immediate settlement can be determined by q b by e to 1 by mu square into i f. Using this expression, we can calculate the immediate settlement of the soil, where q is equal to net foundation pressure. So, this is q is the net foundation pressure. So, this is the net. Next mu is equal to Poisson's ratio of the soil, p is equal to the Young's modulus of the soil and i f is equal to mu influence factor. So, this q is the net foundation pressure, mu is the Poisson's ratio and u is the Young's modulus of the soil. So, these are the soil properties and this is the foundation pressure and b is the width of the foundation and b is equal to width of the foundation. Now, e i f is the influence factor or this factor we can calculate for different types of footing that is for the square footing, circular footing and for the rectangular footing and for different types of foundation, because this we can have the, we have this flexible type of foundation and or the rigid type of foundation or matte foundation. So, flexible type of foundation is generally the isolated footing and the rigid type of foundation is the rap foundation or the matte foundation. So, depending upon the type of foundation whether it is the rigid and the flexible or the safe of the foundation will get the influence factor. Now, this influence factor when you calculate this influence factor. So, first if we want to draw the settlement response of the foundation after the application of loading and the different foundation types. So, suppose this is the application of load through the foundation this is q 0 and this is the depth of the foundation. Now, for the settlement profile, so this is the b into l say. Now, the settlement profile suppose if it is the center then the settlement profile would be only this type of if it is a flexible type of foundation. So, we can say that the settlement variation at the corner of the footing this is the corner of the footing and the settlement variation at this corner of the footing or settlement value at this corner of the footing and settlement value at the center of the footing both are not same for flexible type of foundation. Flexible type of foundation means if it is isolated footing. So, that is the example of flexible type of foundation. So, here you can see the settlement at the center is more compared to the edges or the corner of the foundation. So, and for the rigid type of foundation this value is more or less same. And here we will get this pattern. So, this is for the rigid foundation. Now, rigid type of foundation is matte or wrap foundation. Here in the rigid type of foundation you can see that settlement is throughout the uniform whether it is the corner or the center of the foundation. So, here the influence factor will be 1 because here this settlement where variation is nil. That means it is uniform. So, whether it is the corner or center this value is same. But whereas for the flexible type of foundation the influence factor value you can calculate the center or you can calculate at the corner. Both are not same and then you can consider the average one also. So, that means the corner and this, but at the center it is observed that we can say that the foundation rigid foundation settlement is less compared to the flexible type of foundation. So, that means the influence factor also is at the center if I consider this is the less compared to the flexible foundation. So, that means influence factor of the rigid foundation is less as compared to the flexible type of foundation at the center of the loaded region or the foundation. So, now if we want to calculate the influence factor. So, we will get this influence factor same for the rigid foundation whether it is corner or center. Then it will get the different influence factor for the flexible type of foundation at the center and the corner. Then you can consider the average some influence factor factor for the influence type, a flexible type of foundation. So, on chart that table we can consider this is a table where by using this table we can calculate the influence factor for the flexible foundation and for the rigid type of foundation. As I have mentioned the rigid type of foundation this value is same whether it is a corner or center. So, this is the same different types of foundation this is a circle a square then the rectangle. So, rectangle is a different L by B value if L by B equal to 1.52510 to 100 and this is. So, as I have mentioned for the flexible type of foundation we can calculate the influence factor at the center corner and this is the average value for the flexible type of foundation and for the rigid type of mat or wrap foundation this value is same for the corner or the center. Now, for the circle is 1.64 for the corner and average is 0.85 and in case of rigid 0.86 and for square this center influence factor for the flexible foundation if it is square putting is 1.12 but where is for the rigid foundation is 0.82 and for the rectangle L by B equal to 1 is 1.36 for the rigid 1.06 and for L by 2 is 1.52 for the rigid is 1.2 there is 2.1 this is 1.7 this is 2.52 this is 2.1 and this for the L by B equal to 100 this value at the center is 3.38 whereas, this value is for the rigid foundation more or less 3.4. Now, for the most of the cases it is observed that the influence factor at the center for the flexible type of foundation and the influence if we compare this center influence factor for the flexible foundation and the influence factor for the rigid foundation is it observed that the influence factor for rigid foundation is 0.8 times with the influence factor of the flexible foundation at the center because it is almost 0.8 times. So, that is why when we calculate the settlement for this rigid type of foundation then one option that we can directly use the influence factor for the rigid foundation case whether it is L by B is different value or square or this is circle or if it is a rough foundation then it is better to calculate the influence factor for the flexible foundation at the center. Then multiply it by 0.8 times then you will get the settlement of the rigid foundation that means the first we calculate the settlement considering the influence factor of the flexible foundation at the center then if it is the rigid foundation then we will multiply that settlement calculation by 0.8 then we will get the settlement of the rigid foundation. That means first we calculate the flexible foundation considering the flexible foundation at the center then multiply it by 0.8 then we will get the rigid foundation settlement. So, that 0.8 is the rigidity correction that we will apply. So, that one correction is the rigidity correction if it is the rigid type of foundation that is 0.8. So, now next we will go for the consolidation settlement calculation that how to calculate the consolidation settlement. So, this is consolidation settlement by consolidation. So, for the first class I will explain that how to calculate this consolidation settlement. So, this is 1 plus E 0 into H is the thickness of the layer locked in then del P 0 a P 0 bar by plus del P into by P 0 bar or we can calculate that S c by M v into H into del P. So, here P 0 bar is the initial effective over burden pressure before applying foundation load and del P is equal to vertical stress at the center d 2 applied E 0 is the initial wire ratio then H is the thickness soil layer and C c is equal to compression index. So, either we can use this expression to calculate the consolidation settlement or we can use this expression to calculate the consolidation settlement where M v is equal to compressibility of the soil T of the soil. So, here also H is the thickness of the soil layer and del P is the vertical stress at the center due to applied load. So, if it is the single layer then we can calculate this way or if it is a multi layer then we can calculate the this settlement at different point then we can sum this all the settlement then you will get the total settlement of the soil layer. Now, that means using this expression these two expression we can calculate the consolidation settlement as well as the and the immediate settlement. The next one that will apply the E value or the corrections. So, what are the different corrections that will apply? The first one as I have mentioned that if it is a rigid foundation then we will apply the rigidity correction. So, S rigid is equal to 0.8 times into S center flexible. So, I have as I have mentioned that the settlement of the rigid foundation is first we calculate the center settlement of the flexible foundation then we will multiply it by 0.8 then you will get the settlement of the rigid foundation that means this 0.8 is the correction factor. So, next one and this correction will apply only for the rigid foundation. Next one we will calculate the depth correction. So, this depth correction is the corrections factor or depth factor that is equal to settlement at embedded then settlement at surface. That means the settlement that we are calculating that we considering this is that means at the if it is a embedded settlement then that means first we calculate the settlement that is the surface settlement and then we will apply the correction factor for the depth then we will get the settlement for the embedded condition. Actually we will place the footing at below the foundation depth. So, that is in the embedded condition, but the settlement that we are calculating by using those expressions that will give us the surface settlement. So, as the footing is placed at the depth below the ground surface though that means we have to apply some depth corrections. So, that correction factor is embedded by a surface. So, that means we will first calculate the surface footing, surface calculation of the surface then settlement placing the footing at the surface and then we will calculate the settlement then we will apply the corrections factor then we will get the settlement at the embedded condition. The next correction factor is the correction for the effect of 3D consolidation because the consolidation expression that we are using that is for 1D consolidation theory. Now actually in the field there will be the 3 directional consolidation. So, the x, y, z, but here we consider only the z direction consolidation, but it will go for the x and y direction also. So, that means to incorporate the 3D consolidation effect you have to apply some consolidation correction factor. So, that means the sc consolidation for 3D is equal to the correction factor mu into xc for 1D where mu is the correction factor. So, that means here we will get the consolidation so that corrections also. So, these two corrections this here we will this correction factor is pointed, but what will be the correction factor for depth and consolidation. So, and it is noted that this consolidation correction will apply only for the consolidation settlement not for immediate settlement, but for the rigidity correction and depth correction these two corrections will apply. So, these two corrections for A and B will apply for the immediate settlement calculation, but this consolidation correction factor will apply for the consolidation settlement calculation. That means A, B, C these three will apply for calculation of consolidation settlement, but for calculation of immediate settlement will apply only A and B these two corrections. Now, next we will solve one problem then we will get how to calculate this consolidation correction factor. So, this is the example 11.1. So, a raft foundation so this is a raft foundation where loading that is coming is 50 kilo Newton per meter square meter square. So, this is ground surface so this is plus 0 meter level. Now, what a table is placed at the base of the foundation so that means this is minus 2.5 meter. So, what a table is placed at minus 2.5 meter so that means this depth is 2.5 meter. So, one layer depth is minus 7 meter minus means in the below the ground surface and another layer is minus 19 meter. So, the depth of this second layer so this is layer 1, this is layer 2 and the position of ground water table this is ground water table which is 2.5 meter below the ground and that is the position of the footing base also. So, that means d f is 2.5 meter and the dimension of the raft that is the raft dimension whose dimension is 10 meter cross 15 meter. So, that means the width of this raft foundation is 10 meter and length of the foundation is 15 meter. So, now we have to calculate the total settlement and what will be the total settlement. Now, first we will consider that means the this total layer first layer 1 is 7 meter thickness and layer 2 is 12 meter thickness. So, this is 19 minus 7 that is 12 meter and the properties that we will get this for the layer 1 gamma is 18 kilo Newton per meter cube. C u is 35 kilo Newton per meter square and C c 1 plus e 0 for the layer 1 is 0.06. And for the layer 2 this gamma is 17 kilo Newton per meter cube C u is 20 kilo Newton per meter square and C c 1 plus e 0 that is 0.15. So, this is a soft clay this is layer. So, this means we can say this is layer 1 and this is layer 2. Now, as I have mentioned that for the settlement calculation we will go for. So, that means the thickness of this here this one is the heart stator or the rock. So, that means this soil so that means the influence zone for the settlement calculation is twice B and B is here is 10 meter. So, influence zone will be 20 meter, but below the base of the foundation. So, base of the foundation this total thickness of the soil layer is 16.5. So, this total thickness of the soil layer from the base of the foundation this is 16.5. So, that means here the base of the foundation and the influence zone is 20 meter. So, that means we will consider this total soil layer. Now, if influence zone is within that. So, suppose this width of the foundation is 4 meter then the influence zone for the settlement calculation would be 8 meter. So, that means up to 8 meter soil you have to consider if the width was 4 meter, but here width is 10 meter. So, 20 meter as this portion is heart stator. So, we will neglect the settlement calculation for this portion we will consider only this two layers settlement contribution because as this total thickness 16.5 which is less than the 20 meter. So, we will consider the total if this 16.5 which is more than the influence zone then you have to consider only that influence zone. Suppose if it is 4 meter then only 8 meter you have to consider to calculate the settlement. So, here we will consider the total soil and here as we will consider the approximate method to calculate the stress due to this footing load. So, now we will consider one point at the center of this first layer below that is center of this portion below the footing. So, this portion is 4.5 meter and another point we will consider at b point at the center of this second layer. So, as if we consider more points then we will get further accurate result, but for this calculation we will consider only the one point and that is sufficient to calculate this total settlement. So, that means this b is 6 meter from the top of the second layer and a point is at the depth of 2.25 meter from the base of the footing. So, there we will consider the two points one is a and b here these two points will calculate the consolidation settlement and this four this a point is 2.25 meter from the base of the footing and b point is 6 meter from the top of the second layer or 10.5 meter from the base of the footing 6.4 meter this base of the footing to this top layer top of the second layer and from the top of the second layer is 6 meter. So, the total will be 10.5 meter from the base of the footing. So, first we will calculate the immediate settlement, then we will calculate the other settlement. So, first we will calculate the immediate settlement of this foundation, then we will calculate the consolidation settlement and then the correction. So, first we will calculate the immediate settlement. So, as the immediate settlement calculation expression minus q n into b divided by e 1 by mu square into i b. So, in this question it is also given that, e for this layer 1 and layer 2 is equal to 700 c u, because we will get various relation in terms of e and c u. That means, we will get the, if we know the c u cohesion, undrained cohesion of the soil, then we can calculate the e for the case. So, for this particular problem, it is mentioned that e is 700 c u. Now that means, from q n is equal to 50 kilo Newton per meter square for this particular condition, b is equal to 10 meter, mu consider for the clay, it is 5 meter 0.5. So, mu is also considered as 0.5 and now we will calculate the influence factor. So, we will calculate the, consider the flexible foundation influence factor at the center, then we apply the multiple correction factor 0.8 for the rigid foundation. As it is a wrap foundation, so it is a rigid foundation. Now for this l by b, this value is 15 divided by 10. So, this is 1.5. So, if it is a, so from this table we can see that for the rectangular footing, if l by b is equal to 0.5, then for the flexible foundation, this i f value is 1.36. So, we will consider first 1.36, then we will multiply, when we calculate the settlement, immediate settlement as well as the consolidation settlement, then we will multiply it by 0.8 to get the settlement for the rigid foundation. So, this is 1.36 we will consider. So, our i f will be 1.36. Now as e is 700 cu, so here we have two soil layers. So, now first layer we will consider the first layer value that means cu 1 is given 35 kilo Newton per meter square and cu 2 is 20 kilo Newton per meter square. Now as this influence zone is within that two layers, so we will get the e value as the weighted average. So, that means e 1, if we calculate e 1 for the first layer that is 700 into 35. So, this will be 24500 kilo Newton per meter square. Then the e 2 will be 700 into 20 that is 1414000 kilo Newton per meter square. So, this e 1 is 24500 kilo Newton per meter square and e 2 is 14000 kilo Newton per meter square. So, e average would be, so total thickness of this layer from the base of the foundation is 16.5 and first layer, so that means this is the figure. Here we can say the total thickness of this layer is 16.5 and first layer influence is 4.5 and second layer is 12 meter and total is 16.5 meter. So, we can take the weighted average in this fashion this for the first layer 2450 and that is for 4.5 meter plus for the second layer into that is 12 then divided by 16.5 meter. So, we will get this value 16864 kilo Newton per meter square. So, weighted average value is 16864 kilo Newton per meter square. So, this weighted average value we will consider when we calculate this immediate settlement. So, immediate settlement S i will be Q n is 50 B is 10 is 16864 kilo Newton per meter square. So, 1 minus 0.5 square influence factor is 1.36. So, after the calculation we will get this value is 30.24 millimeter. So, this is the immediate settlement amount is 30.24 millimeter without any correction. Next we will apply the corrections for the immediate settlement. So, that means, S i without corrections is equal to 30.24 meter. So, here immediate settlement calculation we will consider only two corrections that is only rigidity correction if it is a rigid foundation as it is a matte foundation. That means, here we have to apply the rigidity correction and then we have to apply the depth corrections. So, the rigidity correction factor is equal to 0.8. Now, what will be the depth correction factor? So, how we will calculate this depth correction factor? Now, from this figure this i s core recommends that how to calculate this depth correction factors. So, the depth factor this i by using this i s recommendation we can calculate. So, this is i s 8003 part 1 1976 here these are the different charts available for l by b value and this is the d by root over l b this part from 1 to 0 and this is l b root over d from this part. So, now if we consider this part where we need l by b value and we need d by root over l by b. So, once we get these two value so by using this charts say point this value we will get the depth factors. Now, this is called Fox depth correction factors. So, now to get the depth factors so we need this l by b that value is 15 divided by 10. So, 1.5 and another is d root over l b. So, d value is d at is 2.5 and root over l. So, this means this is 10 into 50. So, this value is coming 0.2. So, as d f equal to 2.5 meter d f equal to 2.5 meter. So, now here we will get l by b equal to 1.5 and d root over l b is equal to 0.2. So, corresponding this figure if I go that is so d by root l b is 0.2 and l by b is 0.2 and d by root l b is 1.5. So, this chart is for 1 this is for 9. So, this will be around this region. So, this is 0.2. So, corresponding this 1.5 this graph so this value is depth factor is around 0.97. So, this is the depth factor value this value is 0.97. So, we will get that depth factor is coming around 0.97. So, S i corrected that would be 30.24 then 0.97 for the depth correction and 0.8 for the rigidity correction. So, this value is coming up to be 23.47. So, this is 23.47 millimeter. So, 23.47 millimeter is the corrected immediate settlement value after we correct the depth factor and the rigidity factor. So, next we will calculate the consolidation settlement then how to calculate this consolidation settlement that part we will discuss. So, first we will go for the consolidation settlement. So, next one is the consolidation settlement. So, as the consolidation settlement expression that is summation c c 1 plus e 0 then h log 10 del p plus p 0 bar divided by p 0 bar. So, we have two points points a and point 2. So, we will calculate first the point a at point a. Now, at point a p 0 bar that is equal to so this is the figure. So, at point a p 0 bar effective over burden will be 2.5 into 18 then 2.25 into 8 because here it is below the and we consider it is the saturated density is 18 and consider this is the bulk unit weight also. So, this bulk unit weight and saturated unit weight both are same consider this is 18. So, here this will be 18 and here this will be 18 minus 10. So, 8. So, when you calculate the effective over burden pressure at point 8 which is 2.25 meter below the base of the footing. So, this will be 2.5 into 18 plus 2.25 into 8. Similarly, when you calculate the effective over burden pressure at point b. So, this will be 2.5 into 18 plus 4.5 into 8 plus 4.5 into 8 plus 4.5 into 8 plus 6 into 7. Here also we will consider 7 because 17 minus 10 7. So, this will be 6 into 7 plus 4.5 into 8 plus 2.5 into 18. So, that will give you the effective over burden pressure at point b. Similarly, we get the point a calculation. Similarly, the depth of this point a point is 2.25 meter from the base and 10.5 meter the depth of b from the base of the footing is 10.5 meter. So, this p 0 for at a point this will be this p 0 value this will be 18 into 2.5 plus 8 into 2.25. This 8 is coming this is 18 minus 8 into 2.25 10. So, this value is given 63 kilo Newton per meter square. Similarly, del p if I consider the 2 is to 1 dispersion of the load. So, del p will be 50 into 10 into 15 divided by 10 plus z is 2.25. This will be 2.25 into 15 plus 2.25. So, del p value is coming 35.5 kilo Newton per meter square. Similarly, at point b we calculate this p 0 bar this is this p 0 bar at b. This will be 18 into 2.5 plus 4.5 into 8 plus 7 into 6.5. Similarly, this p 0 bar this is 123 kilo Newton per meter square. Similarly, del p at b point is 50 into 10 into 15 divided by 10 plus this is 10.5 into 15 plus 10 point. So, that the total this stress is 14.35 kilo Newton per meter square. So, in this way we will get the p 0 at a point is 63 and del p is 35.5 kilo Newton per meter square. p 0 at b point is 123 kilo Newton per meter square and del p is 14.35 kilo Newton per meter square at b point. So, now if we put this values at this consolidation expression. So, S c that will be this is for the first layer C c by 1 plus e 0 is 0.06. Thickness will be 4.5 meter. Then, log 10 63 plus 35.5 divided by 63. Then, plus e 0 is 0.6. Then, plus e 0 is 0.6. So, this will be plus the C c by 1 plus e 0 for second layer is 0.15. Thickness is 10 point this thickness is 12 meter. The thickness of the second layer is 12 meter into log 10 base 123 plus 14.35 divided by 123. So, this value is coming out to be 52.4 millimeter plus 86.25 millimeter. So, total value is 138.7 millimeter. So, this is the consolidation settlement of the soil. This is 12.5 millimeter without any correction. Now, here what are the corrections that we apply again for this first one correction is the rigidity correction that is equal to 0.8. Then, the second correction is the depth correction factor that we have already calculated that is 0.97. Then, the next correction factor that the third one that we have to applied for this consolidation correction that is for the correction factor for the 3 D consolidation. This is for the 3 D consolidation correction factor. So, then how we will calculate this 3 D consolidation correction factor. See, here also this is code this is 803 part 1 is suggested a chart by which we can calculate the consolidation correction factor that here this is the chart for this different h by b value where h is the thickness total thickness of the soil layer, b is the width of the foundation. This is point and this dotted lines this represents the strip footing and the circular lines this represent the farm line represent this circular footing. So, that means the dotted lines represent the strip footing and the farm lines represent the circular footing and this x axis is values pore water coefficient this is a and then we calculate the h by b. So, according to difference footing condition and this different h b value if we know for the for a particular soil condition or for the soil this if we know this pore water coefficient a value then we will get this settlement corrections factors. So, these are settlement corrections factors. So, this for the dotted line this is for 0.25 this is for 0.5 this is for 1 and this is for 4. Similarly, for the farm line this is 0.25 this is 0.5 this is 1 and this is 4. Now, for this question that this is given that a value can take 0.8. So, this is given that a value will take 0.8 and h by b value that will get the total thickness if I consider 16.5 and b is 10 meter width of the footing is 10 total thickness is 16.5 meter this is 1.65. So, that means a value is 0.8 and h by b is 1.65 and this we can consider is a strip footing as because in this chart only this circle and the strip these two are given. So, here we consider as a strip one and here the a value is 0.8. So, this is the 0.8 and h by b value is 1.65. So, this is the dotted line 1.65. So, it is in between dotted line. So, this is 1 and 4. So, this will be in between 1 and 4 and 0.8. So, this value will be in between this. So, this value is point sorry this is this value a value. So, this value is taken as 0.6 not 0.8. So, this given value a is 0.6 not 0.8. So, this is the 0.6. So, that means the a value is 0.6 h by b is 1.65 and this is the strip footing. So, if it is given a is equal to 0.6. So, now from this chart this is 0.6 and this is in between 1 and 4. So, this is around here. So, this is 1.65. So, corresponding pore water correction factor value is 0.81. So, that means corresponding corresponding to a equal to 0.6 and this is 1 to 4 and this value is 0.81. So, this pore water correction factor we can say this is 0.81. So, now the SC corrected is equal to 138.7 into 0.97 for depth correction, 0.8 for rigidity correction and 0.81 for pore water pressure correction or this 3 D consolidation correction. So, this value is coming out to be 87.2 millimeter. So, total settlement that is the S immediate settlement plus consolidation settlement you are considering only the immediate settlement and the consolidation settlement here. So, this part is 23.47 plus 87.2 as I have mentioned for the clay type of soil this consolidated settlement is more compared to the immediate settlement. So, this is 87.2. So, this is coming out to be 110.7. So, 111 millimeter. So, this will be the total settlement of the foundation that is 111 millimeter. So, in this way we can calculate the immediate as well as the consolidation settlement of the foundation. So, next class we will discuss that other different techniques to calculate the settlement of the foundation and then by field test or that is a plate load test we can also calculate the settlement and the bearing capacity of the soil directly in the field that thing also I will discuss in the next class. Thank you.