 Welcome to course on advanced geotechnical engineering. This is in module 5 on stability of slopes lecture 7. So in the previous lecture we introduced ourselves to different slope stability analysis methods and in this lecture what we do is that we try to look into these slope stability analysis methods by using some softwares which are basically based on the Geostudio 2012. And this what we are going to demonstrate in this lecture is that how the effect of anchor will be there on the slope stability and nails how the nails can increase the slope stability and then piles as vertical reinforcement that pile members the discreetly pasted piles within the you know row of within the slope area and then finally we look into the stone columns then we look the seismic displacements of the slopes without any strengthening measures. So in this particular slide the illustration of the effect of various reinforcement options in maintaining the slope stability are discussed. So the slope stability analysis is performed numerically using limit equilibrium method software and which is a product of slope W by using slope stability and is a product of Geostudio 2012. The following reinforcement options have been considered one is that anchors nails and piles and stone columns and attempts have been made to compare the analysis results with the results published in the literature. Attempts have been made to compare the results with the published literature results. Now the example problem one illustration of the reinforcing mechanism of anchors in slopes this is the theory part we actually have discussed in the previous lectures the according to CHI and UGAI 2003. In this the analysis has been performed on a 8 meter high slope having one vertical one horizontal slope inclination and the analysis was performed by using Bishop's method. The properties and configurations which were actually given by CHI and UGAI 2003 were considered the installed anchors consists of a tendon of having 6 meter length and 32 mm in diameter and a grouted body of 6 meter 6 meter long and 90 mm in diameter that means that entire length of the anchor is actually grouted with 90 mm diameter grout and that tendon diameter is about 32 mm and was connected to a rigid circular plate of 300 mm in diameter on the slope surface. So the anchor was actually placed on the slope surface and with different inclinations so different inclinations were considered the anchor orientation with reference to the horizontal from varied from 0 to 45 degrees just to see the influence of anchor inclination on the slope stability and its spacing that is the spacing along the slope surface that means that the spacings were actually considered in the range from 1 meter to 3.5 meter. So what will be the optimal spacing or what will be the spacing effect on the slope stability analysis of slope reinforced with the anchor was studied. So this is the input file for the slope W with anchor used in the slope stability analysis and the based on the calculations and details provided by CHI and UGAI 2003 the tensile capacity was given as equivalent to that of the data which was given 1500 kilonewtons and no reduction factors have been given and the bond diameter as has been told 90 mm diameter grout body so the details have been given bond length that is the entire length is grouted so 6 meters and anchor spacing for this example which is actually shown is 1.5 and factored pullout resistance and maximum pullout resistance ranges were actually given there. Now this is the FEM mesh of the slope section showing the anchor installed this is a cross section of the slope with anchor and in this particular example the 30 degrees inclination of the anchor with the horizontal was considered. So as it can be seen here this inclination with the horizontal is 30 degrees and here is the plate which is actually placed and the slope configuration which is actually shown here so this is the horizontal distance and this is the elevation and the model is more column and unit weight is 20 kilonewtons per meter cube and cohesion 12 kilopascals and friction angle about 20 degrees. So this is the analysis was done for comparison purposes with and without anchor so this is the stability analysis results of unreinforced slope and for the configuration which is considered the least factor of safety is obtained by using Bishop's method as 1.061. So the stability analysis results of the unreinforced slope are shown and this is the zone of you know the potential failure surface so this yields a factor of safety of 1.61. Now the similar configuration was analyzed with anchor wherein in this the anchor is actually inclined at 30 degrees so the factor of safety which is actually shown here is 1.2 so there is an improvement in the factor of safety for a given type of nail and for a given type of anchor and for a given anchor inclination and it can be seen here the total resisting moment is more than the total activating moment. So here the presence of anchor enhances the stability and also contributes to the change in the slip surface that means that the slip surface goes away from the face of the slope so this can be observed from the cross section which is actually shown here. Now in this particular graph which is actually shown here anchor inclination with horizontal is plotted on the X axis and factor of safety which is nothing but the resisting moment by driving moment which is obtained by Kai and Ugai 2003 and the analysis results were actually compared so in this the parametric study was carried out wherein when anchor inclination is about 0 degrees when anchor inclination is about 0 degrees you know both you know the analysis done by you know FEM analysis was done by Kai and Ugai 2003 and the present analysis found to have you know good agreement but the trend which is actually presented like with an increase in the nail inclination there is an increase in the factor of safety from 0 degrees when the anchor inclination is increased there is an increase in factor safety and further increase beyond 10 degrees there is a decrease in the factor of safety. So this indicates that there is an optimum you know inclination of the anchor which contributes to the you know the resultant the factor of safety. So here it actually yields both from the Kai and Ugai 2003 and the present analysis by using slope W program it actually says that about 10 to 12 degrees the optimum about 9 to 10 degrees there is an optimum you know factor of nail inclination of the anchor where there is an increase in the factor of safety but with an increase in the anchor inclination there is a decrease in factor of safety and the similar trend was actually also reported by Kai and Ugai you can see that with an increase in the anchor inclination there is a decrease in the factor of safety. So this lead to you know instability of a slope so one need to consider that in the slope stability analysis by using slope stabilization measures the depending upon the slope configuration with the slope inclination or back slope inclination and one need to understand that there is an importance of this anchor inclination on the slope stability. It is not that you know each and every slope has same anchor inclination that depend upon the type of geometry of the after due analysis one need to ascertain the optimum inclination for the you know given problem. Now in this slide the factor of safety variation with the anchor spacing. So it can be seen that with an increase in anchor spacing from it has been varied from 1 meter to 3.5 meter at 1 meter anchor spacing there is an increase in the factor of safety was about 1.27 but with an increase in anchor spacing that is the center center distance of the anchor spacing along the length of the slope it appears that there is a decrease in the factor of safety and these analysis results are also found to be in agreement with Cayenne-Ugae 2003. So in this particular slide the anchor inclination is considered about 15 degrees. So for 15 degrees anchor inclination what it can be seen that there is a decrease in the factor of safety with an increase in the anchor spacing. So increase in factor of safety was observed with a decrease in spacing so it appears that for a given anchor inclination the anchor spacing between 1 to 1.5 meter for the given slope inclination and is found to be you know idle and also it depends upon the one also need to consider the position of the anchor also from the distance that means that where we are actually putting the anchor that is at the you know mid distance also. In this particular case the anchor was actually located a single row of anchors were located in the mid distance of the slope. Now after having discussed the slope stability analysis problem by using anchors now we actually have discussed about influence of nail inclination and influence of you know the layout of the nails on the slope stability. This example illustrates the reinforcement mechanism of nails in slopes and this basically 10 meter x square slope reinforced with four levels of or four rows of nails was considered and the nails are spaced at 1.5 meter in this example and they are out of the plane direction and each nail is approximately about 9.8 meters in length with a bond diameter of 0.35 meter. The inclination of the nail was kept with respect to horizontal is about 12 degrees and for a difference here the stability analysis was performed by using Jan Boos method. So in this particular example the reinforcing mechanism of nails in slopes was is discussed and it is a 10 meter high you know excavated slope and with reinforced with four rows of nails and that is at four levels the nails are actually placed. Generally in the case of excavation as the excavation proceeds the top down approach is adopted the nails were installed and then next level of excavation is done. The nails are spaced 1.5 meter both in horizontal and vertical direction that is sv is equal to sh is equal to 1.5 meter and each nail length is about 9.8 meters that means that about length of the nail is equal to height of the slope was considered and bond diameter is about 0.35 meter inclination of the nail with horizontal is about 12 degrees. So this is the you know typical input parameters for the slope W analysis the details were actually given in the as an input for the analysis and this is the you know the typical cross section of an under reinforced slope section where in the properties which are actually taken are 5 kilo Pascal's and 27 degrees is the friction angle and the slope is having you know the inclination which is actually shown in the figure with this level at 10 meters and this is the particular inclination is about 79 degrees between 63 to 79 degrees with horizontal then this is the stability analysis results of the under reinforced slope it can be seen that this particular for this particular height for the type of properties which are given the slope actually has an already you know gone below the factor of marginal below the factor of safety of 1. So the stability analysis results of the under reinforced slope cross section is shown here and which actually implies that the slope has already undergone failure. Now the stability analysis results of the reinforced slope are shown where it can be seen that nails inclined at 12 degrees placed at you know distance with 1.5 meter in vertical direction and you can see that these are the length of the nails which are actually taken that is 9.7 meter length of the nails and this is having a 0.35 meter diameter grouted body and this is the you know slip surface which is actually obtained the factor of safety resulting factor of safety is obtained as about 2.158 where the total resisting force is about 1500 kilo Newton and activating force is about 700 kilo Newton's. So this is you know the about the you know the stability analysis of the slope reinforced with nails. Now this is an example this is example 3 basically this is illustration of the reinforcing mechanism of piles in slopes and SOHITS et al 1997 have given the stability analysis of the slopes reinforced with piles by using friction circle method and the similar configuration and properties which are actually given by SOHITS et al 1997 was considered and this domain comprises a slope of height of 13.7 meter height and angle of 30 degrees the slope is actually having very flat inclination one vertical close to one vertical to horizontal inclination and the piles are assumed to be of about 600 movement dia that is 0.61 meter in dia with a center to center distance of about 1.5 meter that means that the piles are actually spaced you know as discussed in the while discussing the theory that the efficacy of this you know piles stabilized slopes depends upon the spacing of the slopes and location of the piles within the slope. So here it says that the sloping the spacing of S is equal to 2.5d approximately the 2.5d was considered but the larger the spacing you know the piles will tend to behave like a individual you know individual piles so when the closer the spacing there is a possibility that arching develops into the picture. So what will actually happen is that the piles will you know attract the load in the form of you know when they undergo the soil undergoes arching along the you know the region within the piles and that prevents the movement of the piles you know the movement of the piles the movement of the slope so hence the slope stability can be enhanced. So the stiffness of the pile is taken as 16.55 mega Newton for meter square and the stability analysis was performed by using John Booth's method. So this is the cross section of an unreinforced slope wherein the slope height which is you know by having a 30 degree inclination the cohesion is about 23.94 kilo Pascal's and friction angle of 10 degrees and gamma 19.63 kilo Newton per meter square was considered and here this is cross section of unreinforced slope and the pile was assumed to be located at 5 meters from the toe of the slope there is a possibility that the pile can be located you know at a distance it from the literature review it has been found out that the location if the location of the pile is at you know at the mid distance from here there is a possibility that there is a good formation of the good you know reason for having stability of a slope but in case if the pile is actually placed at the you know crest of the slope and there is a possibility that if the slope is actually steep enough then there is a possibility that it can undergo failure in front of the pile and the portion you know beyond the pile may be protected but the pile with you know pile which is portion which is actually beyond the pile may be subjected to failure. So the research study which is actually carried out at IIT Bombay reveals that the if this is the distance Lx if this is the distance Lx and if this is the distance Ll horizontal distance when the Lx by L is equal to 0.5 approximately you know the maximum factor of safety and maximum performance can be ensured. So this is here the piles are actually placed in a single row and the space at a 1.5 meter distance in fact here also there is a possibility that if the heads of the piles are connected and then that also contributes to the you know in additional stability and sometimes for some applications like in landslides where their deep seated failures are there the piles are actually installed and at the upper portion the walls are actually connected and these are actually called as suppressor walls and is arrest the movement and you know rock fall and any other events. So this is the stability analysis results of the unreinforced slope for the given configuration and the properties the slope the unreinforced slope factor of safety obtained as around 1.107 and the factor of safety reported by Assoids et al. is about 1.08 and the stability analysis of an reinforced slope with pile placed at 5 meter distance from the toe of the slope where in it actually says that the you know the factor of safety has improved and it is about 1.295 in the present study and as reported by Assoids et al. is about 1.3. So this is actually found to be in good agreement with the results published by Assoids et al. 1997. Now after having discussed the stability analysis using piles and we also said that one of the methods for enhancing the slope stability particularly the slopes below the you know berthing structures where unstable slopes can actually lead to the you know movements of the soil and then induce lateral forces on to the piles supporting the berthing structure and this was one of the application where it was used in Kondla and other areas where this was actually used for increasing the stability of a slope. So we actually have discussed this scheme saying that if you are actually having piles if you are having granular piles and which are actually having you know the granular charge which is actually having charges you know sizes from 10 mm to 40 mm to 50 mm and well graded mix if it is there there is a possibility that the factor of safety can increase and then we also have discussed that when we use the stone columns to stabilize an unstable slope the pile the granular piles which are actually place can serve as a restraining capacity as well as the you know they actually also have a capacity of having you know adequate drainage so that the pore water pressures which are actually possible that you know they can build up during the you know the construction of slope or in the you know in the field they can actually come contribute to the dissipation of this pore water pressure and thereafter you know there can be an increase in the factor of safety also. So here the slope stabilization by using stone columns here once again you know this you know the theory is actually shown this is actually one of the patterns of the arrangement where the triangular pattern is actually arranged like this here and it can be seen that the each pile each granular pile or stone column contributes to the you know certain area so this is nothing but the diameter of the stone column to the influencing area and that is called as the area ratio. So here this is for the square layout and this is for the these two are for the triangular layout but if you look into this here when there is a certain load and when you have got stone column material with high you know stiffness and clay or ground having you know low stiffness there is a you know the stress concentration makes it to attract more force that is sigma stone and sigma stone and sigma ground try to you know apportion the load which is actually applied on to the you know the composite system. So by using you know the method we can actually find out the you know the composite shear strength parameters or average shear strength parameters and the stability calculations are carried out by using the conventional slope stability analysis methods where in we actually have assumed that piles the stone columns has individual elements and also calculated properties by using the average shear strength parameters where C average is actually obtained as cohesion into 1 minus ar into cohesion of the stone column but as stone column is free from fines and so that is equal to 0 and similarly tan phi average is obtained based on the aspect ratio and the other parameters which are actually given. So these are notations have been already discussed and these are actually shown here once again in the stability analysis of the using stone columns. So the analysis problem which was considered is a you know a slope actually having 13.7 meter height and 13 degrees slope inclination and the stone columns are assumed to be 1 meter in diameter and the center to center spacing is about 3 meters and they are assumed to be in the triangular pattern and the stability analysis was performed by using Jan Boos method. So considering the effect of inclusion of stone column separately and by taking the respective C phi and gamma and values so the both the cases were actually done so here what has been done is that we actually have got soil and at number of locations the stone columns placed in you know at within the slope were actually considered and the respective soil parameters were actually considered that is one way but the method which is actually proposed for analyzing this is actually the calculating the average shear strength parameters based on the you know the stress concentration factor and all. So for triangular installation the influencing diameter can be obtained as 1.05 into spacing so here the spacing is actually assumed as 3.15 meter hence we can actually you know calculate the influence diameter so this 1.05 into spacing is 3 meters so the influence diameter is about 3.15 meters that is the you know the each granular pile or stone column you know caters the area which is equal which caters the diameter which is equivalent to 3.15 meters and area of the column which is nothing but diameter of the stone column is about 1 meter diameter so 5.4 into 1 square which is about 0.7857 meter square and area of the soil is 7.8 meter square so area ratio which is nothing but A column divided by A column plus A soil so based on that what we have got is 0.092 and the stress concentration factor is assumed as n is equal to 6 and it actually varies from you know 4 to you know 10 but here it is assumed as 6 and the value of m which is actually computed as the area replacement ratio into n that is stress concentration divided by 1 plus A into n minus 1 which is obtained as 0.38 so C equivalent is equal to 1 minus A into C soil plus A into C column so with that what we have got is that 27.24 kilo Pascal's similarly the tan pi equivalent is obtained as 1 minus m tan pi soil plus m tan pi column so this is equivalent to pi equivalent is equal to 72.7 degrees so this is these are the you know the resultant parameters for the you know zone which is actually influenced by the you know presence of stone columns in this slope. So this is the cross section of the unreinforced slope is actually shown here wherein we have the same properties which are actually taken the properties are clay as actually having C 30 kilo Pascal's and phi is equal to 0 and the sand actually having you know properties of friction angle of 30 degrees and gamma 20 kilo Newton parameter cube was considered. Now method 1 analysis considering the stone columns to be the individual inclusion within the slope and here 4 rows of stone columns are actually shown here so this is the zone which is you know strengthened by the stone columns here and then by using method 2 the analysis considering the slopes to be homogenized with equivalent values of C and phi with the positions of the stone columns and the rest of the portions here the properties of that of soil were given but here in this zone the equivalent properties like C is equal to 30 kilo Pascal's the C is equal to 27.24 and phi equivalent is about 17.7 degrees was actually given. So you know then the results are actually compared for without any stone columns with individual stone columns and with homogenized equivalent values of C and phi. So this particular figure shows the cross section of a slope without any stone columns that is actually an unreinforced slope the factor of safety obtained about 1.024. So hence there is a need for improvement of the factor of safety in the particular example slope stabilization by using stone columns was considered. Now here this is the cross section of a slope which result of a factor of safety where the slope is considered the effect of inclusion of the 4 individual stone columns which is actually shown so where the factor of safety found to be increased but where in the factor of safety is obtained is about 1.304. Now this is you know the by taking the equivalent properties in the zone influenced by the stone columns. So the factor of safety was found to improve where in you have the factor of safety which is about 1.432 with the presence of stone columns. So with these examples what we have understood is that the in designing this slopes with stone columns first we have to decide what is the diameter of the stone column and depending upon the method of installation the type of installation need to be selected. Once it is selected then you know we have to see the based on the you know the stone charge properties and then the gradation we need to select what is the you know the possible friction angle. For the stone metal which are used in stone columns the friction angle actually varies from 38 to 42 degrees and which are assumed to be you know placed at maximum dry density and then the proper layout has to be selected. Generally the triangular layout was found to be you know give you know uniform you know improvement in the stabilizing behavior. So then after having selected then we have to see the calculate the average shear strength parameters by using the average method which is suggested to get the C equivalent and Y equivalent and this is depend upon the layout of the stone columns and if the stone columns are spaced further and the stone column diameter is smaller then there is a possibility that their factor safety may not actually have much improvement and when we actually have got this improved area the zone increases but there is a possibility that the factor safety increases for the entire slope. So this is one you know application wherein you know the slope stabilization can be enhanced by using this presence of stone columns. So in the particular analysis what has not been taken is that the presence of stone columns when there is you know the seeping water or when the slope is saturated when there is a possibility that these stone columns can also act like drains and in that case they actually have got hybrid effects one is called you know for drainage other one is for reinforcing the slope. So after having discussed some typical methods of you know the slope stability what we try to look into is that you know the how these you know earthquake loading can affect the slope stability. So in order to investigate the effect of earthquake shaking on slope stability a coupled analysis was carried out by using you know two modules of Geostudio 2012 one is quick w other one is slope w and here a typical slope configuration was selected and was subjected to earthquake loading for about 10 seconds and the stress generated during the event was investigated by quick w and was fed to slope w to study the stability of any permanent deformation of the slope. So this particular analysis was carried out by using you know the slope w and quick w and this is the typical slope configuration selected in quick w where the soil slope with the following properties is actually shown here and this is the input horizontal earthquake record which is actually given and vertical component of acceleration has been ignored. So here with the time seconds and then acceleration which is this motion is actually given as an input for estimating for seeing this effect on the you know the displacements and then subsequently the factor of safety was calculated. So this is the deformed mesh at the end of the 10 seconds of earthquake load the this is actually magnified by 150 times so it can be seen that the slope actually has undergone deformations. So the displacements observed at the crest of the slope at selected time intervals during earthquake were actually plotted. So it can be seen that the crest displacements are actually ranging from minus 0.1 meter to plus 0.1 meter because of the you know subjected to the ground motion. So the variation is actually reported like this which is computed by using quick w module and this is the displacement observed at the toe of the slope at selected time intervals during earthquake wherein it actually shows the toe movement is about minus 0.04 meters to plus 0.04 meters which is actually reported as the maximum here. So after computing the static and dynamic ground stresses developed during earthquake in quick w and by using the equivalent linear dynamic approach the stability analysis was carried out by using slope w and an initial static stability analysis was performed by using quick w generated stresses to establish the in situ factor of safety for the slope and then next what has been done is that the variation of the factor of safety with earthquake shaking was monitored in slope w by using the quick w newmark deformation analysis that means that the deformed configurations were feed it and the analysis was actually carried out by using slope w and the rate of change of velocity acceleration deformation with the time was also studied. So in this particular analysis what has been done is that you know this is actually found to you know this particular analysis is found to be very applicable when we are actually constructing say canal embankments for you know for when you are actually constructing embankments on soils which are actually prone for earthquake. So wherein you know if the embankment which is actually coming above ground level is about say more than 5 meters then there is a need for you know performing this dynamic analysis and once this dynamic analysis is actually performed then suppose if case you are actually doing you know construction by using embankment construction filling above the ground level and then we have to ensure that the crust displacements or toe displacements are within the tolerable limits even after subjecting to a certain ground motion. In such situations we have to see that if the you know the subsoil properties are inadequate then you know there is a need for improving the subsoil by using an appropriate you know improvement measures and then enhance the and maintain the you know the compute the stability analysis you know with this particular cases. So this was actually done in one of the projects wherein for the canal embankment slopes where it actually has been taken that the limits for this you know the lateral displacements obtained from the dynamic analysis were actually set like you know horizontal displacement if at all if it is there then it has been said that it should not be you know more than the thickness of the filter which is provided in the canal embankment and vertical displacement was found to be you know should not be more than the free board which is actually maintained in that particular embankment. So if the displacement which are actually resulted after subjected to dynamic loading if they are less than these you know set parameters then we can actually ensure that you know the so and so configuration is actually stable against so called the earthquake loading and if the particular slopes which are actually being constructed either the institute or the slopes which are going to be constructed then appropriate the stabilization measures like you know after construction if they are found to be you know the analysis was the proper analysis was not done during construction then if they are found that you know they are vulnerable for failure then appropriate the slope stabilization method need to be you know considered and then used in the analysis. So here the slope properties used in the slope supportive analysis the slip surface was specified by using the entry and exit method and which is actually shown here then the initial factors safety the slope in static condition is actually obtained as about 1.131 then this is the you know particular graph which actually shows the variation of the factor of safety during the earthquake event where the factor of safety with the time which is found to be like you know varies with the time. So the lowest factor of safety for the critical slip surface is below 0.8 and that is about 3 seconds that means that the slope would have already undergone the failure into the shaking and highest factor of safety is 1.7 at about 2 seconds into the shaking so that particular you know configuration might have ensured the high factor of safety but at about 3 seconds itself it is found that you know the slope is actually subjected to failure and the average acceleration during the shaking period which is obtained as you know which is plotted here so in this what has been done is that where the time in seconds is plotted on the x axis with the average acceleration. So the accelerations are in the range of minus 2 meter per second square to plus 0.2 meter per second square and this is actually shown this is during the shaking period. So variation of the factor of safety with average acceleration so you can be seen that the factor of safety was found to you know decrease with an increase in the acceleration and yield acceleration is about 0.085 where the factor of safety 1 is actually obtained the factor of safety is inversely proportional to the average acceleration so with an increase in you know the acceleration the factor of safety average acceleration the factor of safety is found to decrease and the yield acceleration for the given problem is found to be with factor of safety is equal to 1 is about 0.085. Now these are the plot this is the plot which is actually showing velocity variation with the time and velocity was time plot during the shaking period is obtained by integrating the area under the curve and when the average acceleration corresponds to yield acceleration and these are the permanent observations observed during the shaking. So in this case you know this time which is in seconds and then deformation which are actually shown so the permanent deformations were found to increase you know but at the end of say third second or so and then found to be about 0.18 meters and then which increase it to about 0.237 the maximum value of permanent deformation is recorded as about 0.237 so this was actually obtained by integrating the area under the velocity graph when there is a positive velocity so within the positive velocity zone the whatever the area which is actually there and over a period of time that has been integrated to get the different deformation plot. So the permanent deformations observed during the shaking is found to be about this value so this analysis was actually done by using undrained dynamic deformation analysis according to Kramer 1996 this type of analysis only appropriate if there is a less than about 15% degradation in the soil strength due to shaking and this type of analysis is not considering phases when there is a large build up of pore water pressure which in turn may lead to large strength losses causing soil to liquefy. So in this particular you know the lecture what we try to understand is that the slope stability analysis methods we actually have you know many slope stability analysis method like starting from you know the method of slices and then extending to the Swedish method of slices and then extending to Bishop's method of slices and then to Jan Boos method and Sarmas method and then many you know these many investigators actually have attempted to incorporate this reinforcement elements between the slopes by modifying the you know the Bishop's method of slices or Jan Boos method of slices and nowadays there is also the horizontal slide slope analysis methods actually have come that is called you know the horizontal method of slices. In some cases particularly when we are actually trying to do with slope stability analysis by using you know geosynthetic reinforced slopes and this is actually applied for by many investigators that is the method of slope stability analysis by using horizontal method of slices. The listeners can actually refer to Shagoli's method in 2000 wherein he actually has presented about you know the authors actually have presented about the method of slices by using you know the horizontal method of slices. So now after having considered these methods and then when different methods like we have discussed about you know some information like the nail slopes and you know anchored reinforced slopes and then so here also we actually have got different possibilities like when the anchors are you know active anchors or passive anchors for example active anchors are the example is nothing but the pre-stressed anchors. So in that case there is a possibility that certain type of the pre-stressed is induced on to the top surface of the slope and that actually contributes to the additional factor of safety. Then also these methods can be extended for understanding the deformation behavior particularly in selecting the proper layout of say nails where you know whether what should be the vertical spacing what should be the horizontal spacing and what is the nail inclination which is required to be adopted. So if these slopes which are actually constructed are going to be constructed in the areas which are actually prone for earthquakes then the inappropriate dynamic analysis is required to be performed then in that case the incorporation of this you know the analysis can be performed with let us say once we ensure that an optimum nail inclination and optimum layout of the nail and that particular nail reinforced slope can be subjected to the dynamic analysis where in the dynamic with the resultant method of slope stability resulting due to you know the enforcement effect of nails we can see the whether the crest settlements or deformations of the slopes are under control or not in case if they are not then you know there is a requirement for the change in the design. Then we also have discussed about the slope stability analysis by using you know the stone columns and it appears that there is a need for doing further work in refining this particular you know method particularly by using for slope stability analysis using nails using stone columns and the another important application what has been discussed is that the slope stability analysis by using lime piles or lime columns where in the limited you know data is actually available and particularly for when the slopes like expansive soil slopes when they are actually subjected to lateral movements and this is one of the viable options if the expansive soil is actually not having adequate amount of surface then there is a possibility that we can actually consider this using the lime columns for increasing the stability. So in this particular module of slope stability we try to introduce ourselves to different methods of slope stability analysis as well as the you know the different analysis methods and we actually have solved the number of examples where in particularly without any you know strengthening measure and then with strengthening measure. So this actually gives an idea about the important of this particular module and where this techniques which were actually discussed can be used for this existing slopes or also for the you know the new slopes which are under construction.