 So welcome to lecture number 18 of the course advanced geotechnical engineering module 2 the permeability and seepage 7. So in this lecture we are going to discuss about some case study based on whatever we have discussed in the previous lectures and also I would like to present to you some assignment problems so that which can which can be used for you know addressing the topics we have discussed in this particular module. So this lecture is titled permeability and seepage 7. So in order to you know address that case study which we are going to discuss let us try to recollect what we discussed in the previous lecture in order to check against the piping failure for a single row of sheet pile wall then Terjiki actually has given a method for checking the stability of a soil prism in front of the row of a sheet pile wall. So if you consider in this diagram if you have got a row of sheet pile wall having you know head of water H1 here and H2 is the water and the downstream level so the differential water level is H1 minus H2. So this particular portion of the prism of soil will be subjected to instability. So one of the methods you know to prevent this failure is to provide an apron or nowadays in with modern applications involving the geosynthetics can also be explored. So by considering a soil prism on the downstream side of the you know of having unit thickness and having a section D is the depth of penetration and D by 2. So this particular you know deliberation of D by 2 was actually arrived based on the model test carried out and then reported in this subject area. So that is the possible failure zone and we knew that as the water flows from this side from left hand side to right hand side the water flows in the vertical direction. So the uplift force of uplift pressure uplift force exerted on the prism of this soil having D by 2 into 1 that is the perimeter length of the you know prism is being considered that is the area over which the uplift pressure is acted is D by 2 into 1 and the D is the you know the depth of penetration. So this is the self weight of the prism and this we are actually considering the self weight that is the submerged unit weight in order to do that the head which is actually you know considered is the total head not the pore water pressure at the base of the prism. So using the flow net the hydraulic uplift pressure can be obtained. So as you know the you know from the flow net the equipotential lines and then within that prism area over a distance of D by 2 the average head can be estimated. So which can be given as h m is equal to h a is the head at this point h a is the head at this point and h p is the head at this point the average of this is can be obtained. So this is the uplift force that is nothing but of gamma w into D into h m h m is the average hydraulic head at the average hydraulic head at the base of the soil prism. So the self weight the submerged unit weight of the self weight of the soil is given by W dash is equal to half gamma dash D square. So from for the factor of safety to in order to obtain the factor of safety against heave or piping is nothing but the resisting force is nothing but the self weight of the prism and disturbing force is nothing but the uplift acted by the actor on at the base of the soil prism. So this is obtained as factor of safety is equal to W dash by U where W dash is equal to half gamma dash D square divided by half gamma w D into h m by simplification of that we get D by h m into gamma dash by gamma w. But however we knew that the critical hydraulic gradient is defined as gs minus 1 by 1 plus e is equal to gamma dash by gamma w. So by substituting for gamma dash by gamma w I c and writing h m by D as I m then we can write the factor of safety against the heave or piping is nothing but I c by I m which should be generally more than 4 or so. So what is required to be noted is that from the flow net diagram to find the average mean hydraulic head find the total head within the D by 2 zone horizontally. So this is required to be noted. Then according to Hasra method Hasra has given in 1935 the safety of hydraulic structures against piping. So this I exit was defined here this is the maximum hydraulic gradient which is nothing but factor of safety is equal to I c by I exit. The I exit can be done with two methods one is that the penultimate portion of the flow net in the downstream direction that is delta h is the head drop let us say the last two equipotential lines that the potential drop between the two equipotential lines in the downstream direction over a length of that along that flow direction. So that is one is that this can be obtained from flow net according to Haar 1962 I exit can also be estimated by 1 by pi into h by d where h is the maximum hydraulic head which is nothing but whatever the difference which is actually there between upstream water level and downstream water level and d is the depth of penetration of the sheet pile wall which is actually taken as d is the depth of the penetration that is the penetration of the sheet pile wall. So for structures other than the single row of sheet pile walls that means that if you have got a concrete dam then in order to increase against the safety against the uplift and all it is practice to provide it is a practice to provide cut off walls in the particularly in the downstream direction as well as if required in the upstream direction if required if the condition persist in the middle of the concrete dam also. And one of the other measures also in order to divert the equipotential here to prevent the flow close to the dam here a provision of impervious blanket is also another alternative. But if you have got a structures other than row of sheet pile walls it has been recommended that the soil which actually occurs between d dash and d where this over a length of d by 2 that remains same but here it will not be completely d but it is actually a depth of d dash. So this particular portion is actually subjected to instability and the rest of it will remain same that is the self weight of the soil which and uplift was exerted in the horizontal direction by the water and this can be determined from the flow net from the total head. So for the structures other than single row of sheet pile walls Terzaghi 1943 recommended that the stability of several soil presence have to be taken that means that of the sizes of d by 2 and d dash into 1 and can be investigated to find out the minimum factor of safety. So the according to Terzaghi's method it is that you have to one has to take several soil presence and then determine the one which actually gives the minimum factor of safety. So for 1962 suggested that a factor of safety of 4 to 5 with d dash is equal to d should be sufficient for the safe performance of the structure again going back with d dash is equal to d that is equivalent to the depth of penetration is sufficient for the safe performance of the structure. So with that background let us look into a case study on the seepage analysis of a cofferdam. So this particular cofferdam is located on the bank of a river and the real soil conditions are that it actually has got stratified soil deposits being close to the river. And the cofferdam is generally constructed to facilitate the construction of the foundation for the a bridge which is being constructed. So in this particular case the cofferdam is intended to be constructed on the river bank where there is no flow of water but if the cofferdam is intended to be constructed within the river where the flow of river happens then the issues relevant to the velocity of the flow and then seepage analysis and the stability against the wave forces all those things need to be considered in designing a cofferdam. So this particular cofferdam section is having a typical status like this and this is the river bed which is at minus 0.81 meters and the entire stata from the river bed to the minus 8.31 meters about 7.5 meters it is with a clay stata below that there is a sand it is named as sand 1. So about 3 meters there is a sand layer and then from minus 11.31 to minus 18 meters there is a sand 2 layer that is two types of sand layers are there and the one of the you know row of a sheet pile wall of a cofferdam is shown here where in what is actually shown here is that this sheet pile wall penetration from is from plus 5.5 to minus 14.5 meters and above this there is a backfill was placed and the upstream water level that is high tide level is plus 5.25 and the soil backfill is actually up to plus 5 meters. So plus 5 meters and then plus 5.25 meters is the high tide level and the top of the sheet pile wall is plus 5.5 tip of the sheet pile wall is minus 14.5 meters it is penetrated into the sand layer then here there is so you can look into this is the you know source for the water this is the river bed and then water actually tries to enter into this thing into the cofferdam. So basically this area is being created to make to enable the installation of foundations for example for this particular bridge pier foundation is founded on piles. So you know to enable to construct the piles in the middle of the river or the close of the bank of the river what it is intended is that to create a land area that is achieved through a cofferdam with ensuring all the stability is again structural stability as well as stability from the seepage point of view and the question here is that in this particular type of sequences there is a need for providing a PCC plug that is called precast this is nothing but plain cement concrete layer is provided. The question here involved is that whether the intended thickness of 1 meter of PCC concrete plug is adequate or not this is basically done to prevent any piping and piping failure and second thing also the resistance offered by the PCC plug onto the stability is not considered. So here one interesting thing to be noted here is that there is a clay layer which is actually having very low permeability and then it is followed by two sand layers. So if the clay layer would not have been there there is a possibility that you know the situation of the likelihood failure for the against piping but let us look for the given data here what would have been the what would be the you know how the you know failure factor of safety is against Terzaghi's method and Hazra's method will arrive. So here the bottom of the you know the minus 4.50 meters is the downstream water level so this is the intended water level which is to be maintained and then minus so 1 meter is the thickness of the you know concrete plate and this is the bottom of the pile. So above this the pile cap will come and then the bridge pier foundation will come. So once this foundation is actually constructed and once the foundation is in place then what happens is that the cofferdam is removed and so that the foundation can be commissioned. So the below the sand layer that is below minus 18.1 meters again the clay layer is there so this is actually assumed to be an impervious stratum so water actually flows in this direction. So this particular problem the seepage analysis has been carried out by using the finite element based software CW 2012 version and the cross section adopted for the seepage analysis shown in this slide as I have told you that this is actually having a length of about 50 meters about 40 meters in this direction and the different soil layers have been represented here this is the clay layer this is the sand 1 and sand 2 and then this is a clay layer. So and here this is the PCC plug which is actually considered here the plain cement concrete clay. So based on this the flow vectors can be obtained but before that let us look into material properties especially the clay permeability though the permeability can be of the order of 10 to the power of minus 9 meter per second but however here it has been considered about 10 to the power of minus 7 phi into 10 to the power of minus 7 meter per second and sand is having high permeability that is 10 to the power of minus 3 meter per second and sand 2 is around 10 to the power of minus 3 meter per second and clay bottom which is at the bottom most clay layer that has been considered as 1 into 10 to the power of minus 9 meter per second which is practically an impervious layer. So these are the flow vectors which are actually obtained from CW wherein you can see that the trend of flow which is a flow line which is actually coming from this direction to this direction. So in order to do the factor of safety against the stability like piping then we require to know the consider a particularly a prism of soil having horizontal distance d by 2 and d depth of penetration and then we have to see the factor of safety against the stability without and with the PCC flag. So here the close view of cofferdam section is shown here wherein you can see the cluster of flow vectors and as the movement of the flow vectors towards the downstream side of the sheet pile wall structure can be seen. So here in this diagram a check again is the piping failure for that to enable to that a block diagram of a prism of d depth of penetration from the PCC plug to the tip of the sheet pile wall and d by 2 distance from the tip of this sheet pile wall horizontally was considered. So this is the soil prism which is actually having you know gamma 1 H1, gamma 2 H2, gamma 3 H3 and then gamma 4 H4 or this particular layer this is actually required to be considered. Then once we know the total head from the flow net diagram we can actually calculate what is the average head here and determine the factor of safety against the piping. So this is the total head variation at the bottom of the soil wedge with horizontal distance from the tip of the sheet pile wall. So total head variation at the bottom of the soil wedge with horizontal distance from the tip of the sheet pile wall I can be seen here the this is the x ordinate which starts from the tip of the sheet pile wall horizontally. So it can be seen that the total head variation in the range of 2.217 meters to 2.213 so the average will be about 2.2 meters. So the check against piping one is the check one Terzaghi's method. Let us consider a case of without a PCC slab of 1 meter thickness then factor of safety what we have defined is that d into d is the depth of penetration into gamma dash divided by HA into gamma w HA is the average hydraulic head at the base of the soil prism. So based on that the factor of safety can be obtained with the d1 into gamma 1 dash d2 into gamma 2 dash and d3 into gamma 3. So based on the unit weights respective unit weights and by taking the submerged unit weights we can actually get the factor of safety without a PCC slab here the PCC slab of 1.1 meter thickness is not provided. So the factor of safety is found to be just more than 4 that is 4.74 and hence the section is safe again is the piping as far as the Terzaghi's method is concerned. Now consider the same case with the PCC slab of 1 meter thickness once we consider the PCC slab of 1 meter thickness we can see that here the gamma of PCC is taken as 23 kilo Newton per meter cube of thickness 1 meter with that the average head 2.214 meters even in the previous case also the average head HA is equal to 2.214 meters with that the factor of safety increased to from 4.75 to 5.71 because of the thickness of the because of the provision of PCC. But in addition to the you know preventing against the instability due to piping the provision of PCC also helps in preventing giving a work fat form for placement of the rigs and enabling the construction at the site. So the factor of safety greater than 4 hence the section is found to be safe against piping. Now let us look by check by Azra's method the same problem. So here we can actually obtain from the flow net IH that is the delta H the head loss between two equipotential lines in the penultimate portion of the you know flow net in the downstream side that is can be obtained by delta H is equal to 0.5 meters and L is equal to 0.96 that is the flow element length with that I exit can be obtained as 0.52. So then we can determine I critical I critical as nothing but gamma dash by gamma w where gamma dash is nothing but the sand unit weight which is actually taken as 20 kilometer per meter cube 20 minus 9.81 divided by 9.81 the critical hydraulic gradient is 1.03. So the factor of safety is nothing but I critical by I exit it is 1.03 by 0.52. So the what we obtained is about 1.98 is actually close to 2. So the remarks on the case study what we discussed is that the presence of clay layer from about a 4.5 meters from minus 4 meters base of the PCC plug 2 minus 8.3 meter helps in preventing the pumping failure towards the downstream side and this observation is based on the coefficient of permeability of 1 into 10 to the power of minus 9 meter per second 10 to the power of minus 7 meter per second or 1 into 10 to the power of minus 9 meter per second clay and if you look into this the adoption of 1 meter thick PCC plug and the downstream side was found to be adequate and with the provision of the PCC plug the factor of safety against the piping increases and the second thing is that it also enables the construction and installation of the pines can be done with ease. So having discussed the problems you know the case study relevant to the seepage analysis of a cofferdam problem and having introduced two different problems and different concepts in module 2 pertaining to permeability and seepage. So in this particular lecture where assignment problems for the module 2 are presented and some selected problems are given so that the concepts can be revised. The problem one goes like this for the test setup shown in the figure below we need to determine the following one is that the flow rate that is per unit width through the soil seepage velocity if there is a 50% of the head causing the flow at A determine 3 is that pore water pressure at A and 4 is the seepage force per unit volume at A assume that the flow takes place in the vertical direction only and the soil is fully saturated. So the problem one the for the test setup which is shown determine the flow rate determine the seepage velocity and determine the if there is a 50% of the head causing the flow at A determine the pore water pressure at A and 4 the seepage force per unit volume at A assuming that the flow takes place in the vertical direction only and the soil is fully saturated. The setup is actually shown here where in you actually have the soil which is k having 2 into 10 to power of minus 7 meter per second the void ratio is actually given as E is equal to 0.68 and here this particular horizontal distance is 3 meters and this height is about 3 meters and this width is about 1 meters and here at the point A is that at the midpoint of this height of 3 meters and in the given problem the datum is actually shown here. So this is that this water level is actually shown as the datum. So this this site of water above this level is about 0.6 meters. So the difference in height of water is 3 meters plus 0.6 meters that 3.6 meters. So this is the you know as far as the problem 2 is problem one is concerned. In problem 2 the test setup is actually shown here which is actually having two layers of soils upper soil and lower soil and this limb is actually having a certain horizontal distance and it is actually at a height of 0.3 meter you know 0.3 meter a constant water flow is actually maintained here. Upper soil layer is having the thickness of 0.25 meter and lower soil layer having a thickness of about 0.2 meter and this is level A this is level B. The level B is interface between soil lower soil and upper soil and here there is that is the level C at the top surface of the upper soil. So the problem statement runs like this in the test setup shown in the figure below or figure which is on the right side of this slide two different granular soils are placed in perimeter and flow is allowed to take place under a constant head of 30 centimeters. Determine the total head and pressure head at point A that is A, B if 30 percent of the total head is lost as the water flows upward through the lower soil layer what is the total head and pressure head at B. So water flows vertically up in this direction because this level of this limb is actually maintained at this level. So if the permeability of the lower soil layer is 3 into 10 to the power of minus 4 meter per second calculate the quantity of water per second flowing to the unit area of the soil and what is the coefficient of the permeability of the upper soil layer. So we need to calculate what is the coefficient of the permeability of the upper soil layer. Bottom lower soil layer permeability is given and so this problem is very interesting and you can attempt based on the concepts we discussed in the this module. And the problem three statement wherein a sand aquifer is present at the depth of 5 meter below the lake in which water depth is 1 meter. Two less pervious soil overlie the sand aquifer as shown in the figure. The soil two is twice as pervious as soil one that means that soil two is more pervious having more permeability than soil one. The aquifer is under artisan pressure and it is observed that this pressure is gradually increasing. So in which soil particularly either soil one or soil two will be the effective weight stress first falls to 0 that is where the quick sand condition can come and what at what value of piezometric head measured at the point B will this occur. So the cross section of the figure is like this you have got a sand aquifer which is actually having a artisan pressure and here this is this level is 1 meter this is zero. So this soil one is having 2 meter thickness soil two is having a 3 meter thickness and this is point P is 1 meter below the soil two bottom of the soil two and here is actually having hydraulic gradient I1 I2 gamma 18 kilo Newton per meter cube gamma 20 kilo Newton per meter cube. So soil one is actually having a permeability K1 and I1 soil two is having a permeability K2 and I2. So wherein we can actually calculate what is the you know which soil will actually first undergo quick sand condition or the effective weight stress first falls to 0 and what value of the piezometric head measured at point P will this occur. So this is you know based on the concepts we discussed can be attempted. Problem 4 figure A which is actually shown in the next slide shows a reservoir and a sheet pile wall cut off where figure B shows the corresponding flow net for this problem. So in figure A and figure B a cross section as well as the flow net is also given utilizing the information given in these figures compute the following one is the rate of seepage loss for reservoir per unit width of the sheet pile wall to pore water pressure at A, B and C as shown in the figure which we are going to see and the factor of safety against boiling in the heave zone immediately to the right of the sheet pile wall. This is just what we discussed in this lecture and draw schematically the flow net and identify the lines in the given figure keeping in view of the boundary conditions. So here you are required to this is the cross section which is given impervious sand a fine sand layer having isotropic permeability Kx is equal to Kz is equal to 4 beta per day and gamma C at is equal to 20 kilo per meter cube the thickness of the stratum is 5 meters and here the tip of the sheet pile wall is at this point and this is 4 meter below this upstream soil level and this 2 meter below the downstream soil level and this is water level at the downstream side is 1.5 meter upstream side is 2 meter above the upstream soil level. So the difference is about 2.5 meters and this is the end which is P P P dash and this is the end of Q Q dash and we need to determine the points A is here point B is shown here and point C is here we need to determine from the flow net the flow the pore water pressures from the flow net diagram and so based on the datum can be selected accordingly and then pressures at A B and C can be determined. So this is the flow net which is given so this is the point A and this is the point B which is actually marked and this is the point C. So the tentative flow net which actually shown here so with that based on this the problem 4 can be attempted and by considering both Terzaghi's method and Hazara's method one can actually calculate what is the factor of safety against piping failure and with that the safety of a stability hydraulic stability of a structure can be estimated. And in the problem 5 which we have discussed in the previous lecture the similar problem and here in this section an earthen dam section is shown below we need to draw the flow net and calculate the C page. So here the 2 layers of soils are given and this earthen dam is constructed with a soil having low permeability k1 2 into 10 to the power of minus 9 meter per second and the soil on the right hand side is k2 is equal to 2 times k1 that is it is 2 times more permeable than 2 into 10 to the power of minus 9 meter per second that is k2 and the slopes are actually having one vertical to horizontal and the upstream water level is 30 meters a free board of 4 meter is actually maintained and the crest width is about 6 meters so from here to here is 3 meters from here to here is 3 meters from here to here the downstream end upstream tow to the this end is 90 meters horizontal distance. So with this the entire configuration can be constructed and this can be solved by using the concepts we discussed like flow net for the C page through a zone depth dam and we said that the soil for the upstream half of the dam has a permeability k1 and the soil for the downstream has a permeability of here it should be k2 in this example it is shown as 5k1 but here it is 2k1 so with that by using k1 by k2 is equal to k1 by k2 is equal to 1 by 2 we can actually get by putting b1 by even l1 is equal to 1 we can get k1 by k2 is equal to 1 by 2 b2 by l2 is equal to 1 by 2. So what will happen is that the breadth to the length ratios will be of ratio 1 by 2 that is on the downstream side here you will have a rectangles we are having the breadth to length ratios 1 is to 2. So this by using this concept the flow net for the C page through a zone depth dam having two different permeabilities can be constructed. So in the problem 6 a levee section is shown so here a levee section is constructed levee is generally constructed is an embankment which is constructed along the river to prevent you know the river water entering into the downstream side of the land. So for that a 12 meter about 25 meters high embankment has been constructed or a levee section has been constructed for 1 is to 2 slopes both upstream side and downstream side a free board of 2 meter was actually maintained and 23 meters is the upstream water level here it is required to indicate what is a b whether it is a equipotential line or flow line and e d whether it is a equipotential line or flow line and b d whether it is a equipotential line or flow line need to be identified and once there is identified with the permeability of k is equal to 0.3 meter per day because this can be achieved when we are actually having isotropic permeability can be achieved once we actually get a material from the single baropit area and here the drainage layer is actually placed and then this length is about 2.7 meters and then the thickness generally is provided about 0.7 meters or 0.6 meters of the order and then this will prevent the you know the prevent the periodic surface coming into the downstream side and causing the piping failure and also enhances the stability. So this length is given as 112 meters and this height is about 25 meters and the crest width of 12 meters and the downstream height is about 50 meter the downstream horizontal distance is 50 meters. So what we need to do is that what is the volume of the water lost through the levee along each kilometer in meter cube per day that means that because as we know that we do so if water loss is actually observed more than the permissible one then it can actually have an impact on the stability. So here a kilometer length of these levee sections run kilometers length so per kilometer length what is the permeability what is the seepage lost or water lost can be determined and in the problem 7 wherein we are actually having a situation that we need to draw the seepage under the structure which is the figure which is shown below. So draw the flow net for the seepage under the structure detailed in the figure below and determine the quantity of seepage. So the coefficient of permeability of the soil is 5 into 10 to the power of minus 5 meter of second that is the soil which is actually here this is the soil portion and this is an impervious zone which is not horizontal which is actually having a certain inclination and with the configuration of that is given here this is the tip of this hydraulic structure is 7.2 meters 7.25 meters here and here it is 9 meters. So what is the uplift force on the base of the structure so that is required to be determined and this horizontal distance of the hydraulic structure is given as 8 meters and this length is about 9 meters and this distance is about 2.5 meters the head of water which is nothing but it causes the flow is about 3 meters. So this is according to Craig 2004. So in the slide where a typical flow net diagram is actually given here for your convenience and the scale is also shown here and this is the impervious stratum and this being impervious stratum this becomes the flow line. So as you can see that a flow net is drawn where the head of water where here the head of the water which is available for this equipotential line is about 3 meters by the time it actually comes out it is actually 0. So equipotential line this is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 equipotential lines are there and then by considering the orthogonal principle one can actually calculate draw the curvilinear squares which involves which gives the flow net. So this is a flow channel 1 and flow channel 2 and this can be approximated as a flow channel about of a 50% of its distance. So it can be total number of flow channels can be around 2.5. So we can actually calculate the seepage and then by knowing the pore water pressure along the horizontal distance one can actually determine what is the pore water pressure distribution. So if the structure will say is empty or under construction there is a possibility of the uplift against the stability. So in during all stages of the construction on all stages of the life of the structure the safety against the uplift is required to be ensured particularly when the hydraulic structure is empty there is a susceptibility of the uplift failure that can be observed from this particular problem. So in this particular module we actually discussed about various concepts about the permeability and seepage issues and we have actually have discussed about the types of flows that is one dimensional flow and two dimensional flow and three dimensional flow. Though the three dimensional flow is not very common but the with the three dimensional flow particularly the conditions or examples are that wherein we actually have radial flow nets which can come particularly if you are having a drain which is actually having provided to drain the water. So in a given plane it can actually come the radial flow nets can come. So wherein the at the surface of the where the water source is there the highest equipotential line will be there the close to the drain surface where it is feeding water away from the particular location where that will be having the permeability equipotential line and the flow lines perpendicular to that so that causes some sort of a net of radial flow nets for the a pipeline or a drain running into the soil. And then we also have considered like the theory behind these seepage and we actually have said that for a three dimensional flow the Laplace equation for three dimensional flow having kx not equal to ky not equal to kz is not equal to 0. We said that kx dou square u by dou x square plus k y dou square u by dou y square plus kz dou square u by dou z square is equal to 0. As kx k y kz not equal to 0 in that case the three dimensional Laplace equation is that for the flow is that dou square u by dou x square plus dou square u by dou y square plus dou square u by dou z square is equal to 0. But as we have discussed with that many of our structures like we have levees, atten dams and sheet pile walls they actually can be idealized and analyzed by using two dimensional flow conditions. In that case the governing Laplace equation is dou square u by dou x square plus dou square u by dou z square is equal to 0 that is x is the horizontal distance ordinate and z is the vertical distance ordinate. And once in order to satisfy this condition the solution for this can be worked out by using the finite difference method or finite dimensional method and then we have discussed the finite element based method analysis by using construction of the flow nets manually or by using a program seepage analysis based program called Cfw 2012 and that constructs the flow nets as for the as this satisfied for different conditions. Suppose if you are having the non isotropic that is axisymmetric the permeability is asymmetric permeability that is having different permeability is an x and z direction. In that case we said that when kx is not equal to kz then need to convert that into a transformed case this condition is called transformed condition and where in kt the transformed permeability is given as root over kx kz and then once the section is transformed then the analysis is done in a similar way as was done from the isotropic case. And then further we discussed that if you are actually having a non homogeneous soils that means that soils having different permeabilities like k1, k2, k3 suppose if the flow net is intended to be constructed by using Cfw the particular software takes automatically but otherwise for different conditions like entry conditions and exit conditions need to be understood. So for that we have studied with two homogeneous soils when you are actually having two different permeabilities when k1, k1 is soil 1 and k2 is the soil to permeability when k1 is less than k2 and when what will happen when the k1 greater than k2 then subsequently we actually have done some problems and thereafter we actually have introduced like how to introduce the based on the flow net diagrams how to calculate the factor of safety against the hydraulic stability of the structures from the piping point of view. Then we have two methods one is the Terzaghi's method and we also have discussed about the Hazra's method and based on this once it is done then the stability can be against piping can be ensured and in the finally we actually have discussed about a case study which is in one of the cofferdam construction for a bridge pier foundation was discussed. And basically here the idea is that the adequacy of the intended the PCC plug which is actually planned whether that 1 meter thick is adequate or 1.5 meters in fact which I have not presented but if you have a case situation of say 1.5 meter the factor of safety against stability in wages that makes you know the more conservative but however it is found that because of the presence of the clay layer and clay layer it is adequate to actually have a thickness of about 1 meter for the downstream side and this actually has two purposes one is to prevent failure against the piping the other one is also to enable construction for the installing foundations for the pier and second further we actually have discussed about some assignment problems for you so based on this you know in this module we try to look into the all aspects which are actually framed.