 In the last class, I have discussed about various components of the O L foundation and how we can determine the depth, what are the forces acting on the O L foundation, what are the methodology by which we can determine the stability of the O L. So, now today I will discuss about the ISC methodology or ISC method by which we can determine the stability of the O L foundation. So, in the ISC methods, based on that the stability is given by the passive earth pressure resistance of the side soil. So, now and that resistance we are getting at the base of the O L as well as the side of the O L. Now, the ISC method first is a first method or first part that is the elastic theory method. So, that means the here assumptions which are considered that this is the soil is perfectly elastic, homogeneous and follows Hooke's law. That means soil surrounding the well is perfectly elastic, the soil edge is homogeneous and is follow the Hooke's law. So, this is first assumption the surrounding soil is perfectly elastic, homogeneous and follows Hooke's law. And then the next assumption is that the unit pressure P which is equal to K H and Z. So, that means the Z is the lateral deformation K H the horizontal coefficient of horizontal sub grade modulus and P is the unit soil reaction. So, next assumption the unit soil reaction P is equal to coefficient of horizontal sub grade modulus into the lateral deformation. So, then the third assumption is K K H varies linearly with depth. So, that means the K H value increases linearly with depth. So, that is increases linearly with depth. This is the third assumption and another well that well foundation which behave as a rigid body and acted by the horizontal force H and the moment M A at the base. So, these are the assumptions of this elastic theory method which is proposed by IRC, IRC that is IRC 45 1972. Now, next one that how we can check the stability of this well. So, that means where first we consider that W is the total force which is acting in downward direction total force or load acting downward including the self weight. Next we can we have to determine the horizontal force acting at the scour level. So, next we should know the what is the net moment on the well at scour level. So, next we should know the what is the net moment or the total applied moment about the base of the well. So, that means we should know the weight total vertical load or downward vertical load acting downward direction including the cell port that we should know the vertical load. We should know the horizontal force acting on the well at scour level what is the and we should know the moment applied the base of the well. So, once we know these three components then total load and the moment then you can check whether the well is laterally stable or not. So, first we checking have to calculate that what is the value of I B that means the moment of inertia that is acting at the base about a axis passing through the center of gravity and perpendicular the horizontal resultant force. That means the I B we can calculate pi by 64 into B to the power 4 where B is the. So, this is the moment of inertia acting as the base which is about an axis passing through the center of gravity of the well and perpendicular through the horizontal resultant force. Now, first we calculate that means we have to calculate I B. So, I B is pi by 64 B to the power 4 where B is the gravitational force diameter of well if it is a circular. If it is a rectangular then this is a width of base perpendicular cooler to the direction of horizontal force if it is a rectangular. Then next one you have to calculate the I V L d cube by 12. So, that is also a circular I V is also moment of inertia about the horizontal axis passing through the center of gravity of the projected area in elevation of the soil mass offering resistance. So, that means we have to calculate the I V which is L d cube by 12. Now, here the D is the depth of the well below scour level and L we have to calculate the projected width of the well. So, where for me this expression D is the depth of well below scour level and L is the projected width of the well into have to apply a shape factor. So, this is 0.9 the shape factor for circular and 1 for rectangular or square. So, once we calculate the I B we have to calculate the total moment of inertia I that is I B plus R into I V 1 plus 2 mu dash into alpha. So, where R is the ratio between K H by K V where K H is the coefficient of the horizontal modulus of sub gradation K V is the coefficient of vertical modulus of sub gradation. And mu dash is taken in the coefficient of friction between the side wall and the soil which is taken tan delta and alpha is taken as diameter or width of the well width of the well that means B divided by twice D. And checking that we have to once we calculate this I value then thus check checking that we have to check that whether the horizontal force that should be greater than the moment acting divided by R dash. 1 plus mu mu dash minus mu w. So, here another one that H should be greater than that value also m by m dash 1 minus mu mu dash plus mu w. So, that means first check we have to consider that that mu and mu w that we have to calculate. So, once we calculate the mu value is given mu dash is given tan delta similarly mu is given as a tan phi and here this is not this is less than that that means H 1 check is H greater than m by R dash 1 plus mu mu dash minus mu w and another H should be less than to m by R dash 1 minus mu mu dash plus mu mu w. And once we check this value then we have to calculate what is R dash. R dash is D by 2 into I by R minus mu w minus mu I by. So, this is R dash and mu dash as it is mentioned that tan delta similarly mu is taken tan phi this is between the soil and the base of the well and it is taken equal to phi because of the roughness of the concrete pile plug. So, once which this is one checking so next checking is that the check 2 is that R m by I that should not be greater than gamma k p minus k a where gamma is taken as submerged unit weight of soil if it is below the water below the water and k p and k a are the active and passive earth pressure coefficient which can be determined based on the Coulomb's theory and delta we can take two-third of phi but limited to 22.5 degree. So, this is the second check we have to perform then the third check or the check 3 that we have to calculate the soil pressure what is the stress which is acting on the soil. So, this we can calculate w minus mu dash p by area plus minus m b divided by twice I. Now, here a is the area of base of the well p is the total horizontal reaction from the side of the well and that we can determine by m divided by r dash. So, p is m divided by r dash and b is the or diameter of base of the well. So, this is the third check and then we have to consider that the maximum stress here we will get one is maximum and this is minimum stress. So, that means the next one once we calculate this q 1 and q 2 in order to check the minimum one or q minimum that should be greater than 0 and q maximum that should be less than the allowable or q allowable that should be less than the allowable or q allowable means the allowable load carrying capacity of the soil load or stress carrying capacity of soil. So, that means the minimum stress that should be greater than 0 and maximum one should be less than the allowable load carrying capacity of the soil. So, next check that we have to do for the ultimate resistance method or first one the elastic method and this is the ultimate resistance method. So, here we have to calculate that w by a that should not be greater than q u by 2 where w is the net vertical force acting or total vertical force acting when a is the area of the base and q here q is the ultimate load carrying capacity of the soil. So, next one we will calculate the resisting moment at the base. So, there are the three moment that we are getting that one is m b that is the resisting moment. So, this is the resisting moment at the base we have to calculate the m s that is the resisting moment due to passive soil resistance. Next one is m f this is also resisting moment that is due to friction. So, we have all three. So, that means the final resisting moment that is is taken at 0.7 times of m b plus m s plus m f. So, that means these all are the resisting moment. So, that is resisting moment first at the base that is given from the base reaction then the resisting moment from the due to the passive soil resistance and the resisting moment due to the friction and the total resisting moment is 0.7 times of m f and this check we have to done that m r should be greater than the moment which is applied. So, m r should be greater than the applied moment. So, next one that how to calculate this m b. So, now the m b we can calculate by q w b into tan phi where w is the total vertical weight force b is the width of the well and then q is a constant. So, here q is a constant this value you can that depend on the shape of and the depth of the well. So, d by b ratio and the q. So, if it is 0.5 then 1 1.5 2 2.5. So, q value is 0.41 is 0.45 is 0.5 0.5 0.5 6 is 0.64. So, this is recommended by I R C and it is 45 1972 and taken from the general and now 2000 and the m s value also we can calculate by 0.1 into gamma d cube k p into minus k a into l and m f is can be given by this expression 0.11 gamma k p minus k a b square d square sin delta. So, by this we can calculate the total resisting moment and then that should be equal to the that should be greater than the applied moment. Now, once we calculate this value then we can complete our check and again as I mentioned that m r should be greater than m. Once we can complete this check this checking you can say that our this well is laterally stable. Now, we will solve one problem and then we can see how we can use this expression and we can check where the well is how we can check the well against a lateral load. So, what if this is the example that here the W on net weight is taken at given was 20, 2000 or 20,000 kilo Newton or we can say this is 2000 ton. The H is given 2500 kilo Newton or 250 ton, m is given at 20,000 kilo Newton or 20,000 kilo Newton or 20,000 kilo Newton. So, these are the given vertical horizontal force and the moment that is at the scour level. Now, depth of the well below scour level that is d is taken as 18 meter. Now, gamma sat is taken 20 kilo Newton per meter cube or 2 ton per meter cube, phi value is given as 35 degree and delta value is 22 degree, K p and K a value K p value is given 8, K a value is given 0.24 and the external diameter of the well is given as 8.5 meter and internal diameter of the well b 1 is the or b or b 1 that is the external and b 2 is the internal diameter is given as 5 meter. Now, allowable soil pressure q allowable is 60 ton per meter square or 600 kilo Newton per meter square that is the allowable soil allowable load carrying capacity of the soil. Now, you have to check the lateral stability of the well. Now, first as I have mentioned that I have to check for the first to calculate the L is equal to as it is the circular well. So, that the safe factor is 0.9 into the projected base or width is 8.5 that is the external diameter. So, you can calculate L is 7.6 5 meter. Next one is that I b or b value here you have to take the 8.5 meter that is the external diameter or you can take that is external diameter. So, I b you can calculate by pi b to the power 4 divided by 64. So, pi into 8.5 meter is the external diameter 0.5 to the power 4 divided by 64 that is 256.24 meter to the power 4 and I v that is taken as L d cube divided by 12. So, L is 7.65 d cube is 18 to the power cube and 12 where d is the depth of foundation well below the scour level. So, that is d cube by 12. So, that is equal to 3717.9 meter to the power 4. So, once you calculate I v and I b then total I is I b plus R into I v 1 plus mu dash into alpha. So, once you calculate that 1 plus mu dash into alpha then the total I will be I b is 256.24 plus R we have taken R is 7.5 into I v that is taken that is k h is equal to k v that is taken equal to 1. So, I v is 1 into I v value is 3717.9 1 plus this is 1022 degree into alpha and alpha value we can take as b by 2 d. So, b is 8.5 2 into 18. So, that is 0.24. So, once you calculate we will get a value that is 4331.06 meter to the power 4. So, these are the value that we are getting from the calculation. So, in the last expression that was shown. So, there should not be a 2 that is 1 plus mu dash into alpha. So, you have to correct this equation. So, here also this is I v 1 plus mu dash into alpha. So, that we will get this moment that is this is a moment of inertia I. So, once we calculate the moment of inertia I then we have to conduct some several checks. So, first check that we will do that is the check whether h is greater than m by r dash 1 plus mu mu dash minus mu w or not. So, first we calculate the r dash that is equal to d by 2 into I divided by r I v. So, d is 18 meter divided by 2, I is 4331.07, r is taken as 1, I v is 3717.9. So, we will get a value of 10.48 meter as a r dash. So, now we calculate that m divided by 2 is by r dash 1 plus mu mu dash minus mu w. So, once we calculate this value here m is taken given a 4000 ton per meter, r dash is 10.48, 1 plus mu we have to take 1035 degree mu dash is 1022 degree minus 1035 degree into 2000 ton 2000 is the w value. So, this value is coming out to be minus 910.8. So, now the h value is 250. So, this value is 250 ton and which is greater than this minus 910.8. So, it is we can say it is safe. So, next one and next check that you have to conduct that h should be less than m by r dash 1 minus mu mu dash plus mu w. So, first we will calculate the m by r dash 1 minus mu mu dash plus mu w. So, m is 4000 r dash is given by this 10.48, 1 minus mu is 1035 mu dash is 1022 plus mu mu is 1035 into 2000. So, this value is coming out to be 1674.1. So, that is this ton. So, that is greater than 250 ton. So, it is safe. So, we can say that this two checks are been done. Now, we have to conduct the soil pressure or maximum q max and q mean we have to determine. So, we can determine q max q mean by given this expression w minus mu dash p divided by mu w. So, this divided by a plus minus m b divided by 2 i where plus we have to use for the q max and minus we have to use for q mean. So, once we so from here the a value will be the area of the base that is pi by 4 into the 5 8.5 whole square. So, that is the projected area of the base 8.45 square and p we can determine that is p equal to m by r dash m is 4000 ton meter r dash is 10.48. So, b value is 382 ton. Now, if now if we put this value in q max and q mean then we can determine that w is 2000 minus mu dash is 1022 degree. Then p is 382 divided by area pi by 4 into 8.5 whole square. So, that is the projected area of 5 square then plus minus m is 4000 b is 8.5 divided by 2 into i is calculated 4331.06. Now, if I consider the plus value then q max is so from here we can write that this is 32 0.54 plus minus 3.93. So, you can say that q max will be 32.54 plus 3.93. So, this coming out to be 36.47 ton per meter square or 364.7 kilo Newton per meter square and q is 364.7 minimum will be 32.54 minus 3.93. So, q minimum value will be 28.61 ton per meter square or 286.1 kilo Newton per meter square. So, we can determine we have determined that what is the maximum stress which is acting on the soil and which is the minimum stress which is also acting on the soil. So, that we will consider the maximum one to check whether this stress soil can able to carry or not. So, we can consider that allowable stress q allowable is given 60 ton per meter square or 600 ton per meter square. Whereas, q max is given 36.47 ton per meter square. So, that means we can say that q max is less than q allowable. So, q max is given 36.47 ton per meter square. So, that means we can say that q max is less than q allowable. So, we can say that the maximum stress which is acting which is coming on the soil is 36.47 ton per meter square. Whereas, soil can able to take allowable load carrying capacity is 60 ton per meter square. So, it is safe. Another one is q minimum which is greater than 0. So, that is also so that means that is also safe I mean no tension zone force is occurred in the soil. So, next check that we have to conduct is for the ultimate resistance check. So, for the ultimate resistance check method or check here first we have to calculate w by a that should not be greater than q ultimate by 2. Now here that q allowable is given 60 ton per meter square and generally the factor safety which is applied is 0.5 to 3. So, we have if we consider a factor of safety is 3 then q ultimate will be equal to q allowable into 3. So, it will be equal to q allowable we can consider this will be 60 into 3. So, now we can calculate that w is 2000 area of the base is pi by 4 into 8.5 square that should not be greater than 60 into 3 divided by. So, we will calculate we will get that this value is 35.3 and that is not greater than equal to 90. So, it is safe we can say. So, this is say 90 ton per meter square. So, this is also safe. Now, we have to calculate the all resisting moment and this expression have to determine that m r is 0.7 of m b plus m s plus m f and m r should be greater than m which is applied. So, first we will calculate what is the value of m b. So, m b is q w b tan pi. So, now the w value is given w is equal to 2000 ton per meter square. So, this is b is 8.5 meter and phi is 35 degree. Now, q value we have to calculate. Now, for q value d by b is 18 divided by 8.5. So, that is 2.1. So, once we get this b value d by b then from the table we can determine what would be the value of this q because q has this table is given. So, that means from here in this value d by b is 2.1. So, d by b is around this one and this is 0.56 and this is 0.64. So, in between this, so that q value is coming out to be around 0.58. So, the q value from here we can get 0.58. So, now, if you put this value m b is equal to 0.58 into 2000 into 8.5 into tan 0.58 into 0.58 into 0.58 into 0.58 into 0.58 into 0.58 35 degree. So, it is coming out to be 6904 ton meter. Similarly, the m s is given 0.1 to gamma d cube k p minus k a into l. So, this is 0.1 gamma is given as a because 1 because the gamma sat is given 2 ton per meter cube and as gamma sub much you have to consider because it is below soil. So, gamma sub is equal to gamma sat minus gamma water. Gamma sat is 2, gamma water is 1. So, this is 1 ton per meter cube. So, this is 1 into d cube is 18 cube, k p is 8, k a is 0.24, l is 0.9 is the safe factor into 8.5. So, we will get a total resistance due to the passive force. This is 3, 4, 6, 2, 1 ton meter. So, this is the moment due to the passive resistance. Next one you will calculate what is the value of m f. So, this is the resisting moment due to the friction. So, m f that is 0.11 gamma k p minus k a into l into l into l into b square d square sin delta. This is for the friction. So, we will have 0.11 into 1, k p is 8, k is 0.24, b square is 8.5 square into d square is 18 square into sin 22 degree. So, we will get a total resistive moment due to friction 7485.36 ton meter. So, we can calculate the total resist moment that is the m r 0.7 into sin 22 degree. So, we will get a total resistance of m b plus m s plus m f. So, this is 0.7, m b value is 6904, m s is 7485, m s value is 34621 plus m f is 7485.36. So, this ton meter. So, ultimately m b value is 6904, m s is 7485 sorry m s value is 34621 plus m f is 7485.36. So, this ton meter. So, ultimately m r total resistive force or moment is 34307.3 ton meter and m applied load at the scull level, which is given 4000 ton meter, where this is 34307 ton per meter. So, we can say that m r is greater than m applied. So, this is same. So, this way we can say that the dimension that we have chosen based on the loading condition that is the vertical load, horizontal load and the moment at the base. This well is checked for all the possible condition and all the checkings are ok. So, that means it is safe for lateral stability checking. So, that means we can say that under this condition this well is safe against the lateral. That means this well is lateral checking. That means this well is laterally stable. So, that means we have this one we have done the checking for the moment, resistive moment that is applied. Then we have checking for the stress, which is acting on the soil. That means the q max and q min, the q max should be less than the allowable load carrying capacity of the soil. And also we have checked the horizontal stress, horizontal force actually that is acting on the well that we have to also check whether that due to that horizontal force is the stability will be disturbed or not, whether well is also stable under that horizontal force. So, that all the checkings are done and it is passed all the checking. So, it is safe against the lateral stability. So, that means here first basic is that we should know what is the vertical load acting. So, based on that the load which is acting on the base of the soil that we can determine. So, that is the purpose to for the for that checking we should know the vertical load. We should know the lateral load or that mean that will also help you to check whether this is safe against lateral condition or not. We should know the moment which is acting on the base of the soil. So, that means that moment also disturb the lateral stability of the well. So, we should know the this all three components before we start the checking of the well against the lateral stability. And as well as we should know the what the properties of the soil and based on that we have to determine what is the scour level and what is the scour depth. And then we should know what is how much foundation how much depth of the foundation will provide below the scour level. So, that we can determine what would be the depth of the foundation beyond scour level and based on that we will determine that level the soil stress will determine and then we will check whether that soil stress is good enough soil condition is good enough to resist the stress which is coming on the soil. So, that means we should know the external load or the moments that means the vertical load horizontal load and the moment we should know the soil properties or based on that we have to decide how much diameter or the depth of the well will provide. So, what would be the diameter what would be the depth of the well below the scour level. So, those things we have to determine. So, now in this way we can check this well foundation and then we have to design this well. So, now this part in today's class I have discussed about the this IRC method and how we can check the lateral stability of a well by using the IRC method. And previous class I have discussed about how we determine the depth and that depth is also here required to check this lateral stability and what would be the diameter of the well and then how much minimum amount of the depth or the grip length because this grip length is also required to determine how much depth will provide. So, how much required grip length have to provide what would be the minimum depth of the well that things also be explained here. So, based on that we should provide the particular depth of the well below the scour level and then based on that we will decide we will check the lateral stability of the well. So, now in this class or in this course we have discussed various component of the foundation that we have discussed about the shallow foundation or discuss about the deep foundation that means of the pile under different loading condition then the well foundation we have discussed about the reinforced earth how we can design the reinforced retaining wall. Then we have discussed about the soil foundation interaction I mean how soil can be modeled to interact with the foundation and as well as the soil properties which are very important things and then how we can determine the soil property by the exploration. So, what those things also be discussed here and the we have also designed that retaining wall not only the our reinforced retaining wall also the the normal or traditional retaining wall this is cantilever retaining wall or gravity retaining wall. So, those things also be discussed in this course. So, this is the complete this is the last lecture of this course and here. So, I have tried to incorporate all the basic components of the foundation and how to analyze these things and how to design these things. Thank you.