 Welcome to module 5 on stability of slopes lecture number 4 in the course on advanced geotechnical engineering. So in the previous lecture we actually have discussed about the number of methods of stability analysis of slopes and along with some solute examples. In this lecture we will try to introduce ourselves how to introduce a critical failure surface through some conventional methods as well as some numerical methods as well as by using some renowned softwares. In addition to that we will try to look into a special condition called rapid drawdown condition. This will occur after a dam or reservoir when it is established with steady state seepage conditions when there is a change in the water levels outside the slope then these conditions can be trivial as far as the reservoir or dam slope stability is concerned. So this is the lecture number 4 in module 5 on stability of slopes and this particular topic for this lecture we will be discussing in length about the rapid drawdown condition or sudden drawdown condition. In addition we will try to see what is the effect of rainfall on a stability of a slope if there is a consistent intensity of rainfall with long duration or with increasing intensity of rainfall for a given duration and how this can vary or can affect the stability of slope if the slope inclination changes. Before discussing this rapid drawdown condition let us look into the determination of the most critical slip surface. Most critical slip surface implies that the slip surface whichever the surface which actually gives the minimum factor of safety. The criteria for selecting the most critical surface is that the surface which actually gives the minimum factor of safety and which can be the potential failure surface. So there are trail and error approaches are involving basically it involves the location of the center of the rotation and radius of the slip surface and distance of intercept of the slip surface from the toe and minimum factor of safety is achieved. Generally it is done by if a slope is there with a perpendicular bisector from that within that a grid of centers are selected and among the grid of centers when we have when we select innumerable number of circles with radius r minimum and r maximum like this when we have this grid of centers which are selected or located at the almost at the perpendicular bisector of the slope surface and each grid of center when you analyze for number of slip surfaces the one whichever is the center or grid of center which gives the least factor of safety that is actually treated as the minimum factor of safety. So if that grid selected grid is inadequate or inappropriate then one needs to reselect the grid such a way that the minimum factor of safety is achieved. The way back Phillinius 1935 proposed empirical approach for the cohesive soils particularly for unrained condition for Phi U is equal to 0 that is with soil with Cu that is with unrained condition and different slopes like one way one is to one one way one way one vertical one point horizontal or one vertical point 0.58 one is to two one is to three and one is to five with alpha that is this angle and psi this angle these are the cosines direction cosines with that for these are the beta is the slope inclination. So draw a line through the corners of the slope at angle alpha and psi as per in the table and o1 will be the center of the rotation. So this is one of the conventional method. The another conventional method which was actually given by Jumkes that is the possible location of centers for a C dash and Phi dash soil where in here when the center of the rotation of the critical circle is assumed to be lie at point P o1 P o1 and point P is at a distance h above the h below the toe that is this h below the toe and 4.5 times the height towards the from the toe of the slope. So when you draw the line wherever it actually meets along this line the one which at this an o is nothing but the different factor of safety and this is the one which actually gives the least factor of safety and that is actually selected as the possible potential failure surface. But however some LE methods which are actually done through you know softwares like Geo studio wherein slope w which actually takes like grid of centers and it also gives the possible tangent lines. So it sets the circles within this grid of the tangent lines and with the prescribed intercepts with the at the top at the top and then at the near the toe and with the grid of the centers it tries number of circles and the one which actually gives the least factor of safety is evolved as a you know the critical failure surface and this is actually called as the entry point and this is actually called as the exit point. So we know that whenever there is a soft soil and then there is a tendency that the circle actually draws down towards the base of the slope but if there is you know the hard stratum then with the if the slope is actually constructed above the ground surface or above the hard stratum then the slope fails within the toe or the slope surface. So this entry and exit option is actually used for circular critical surface slip surfaces and this is actually you know used widely for selecting the potential failure surface or potential slip surfaces or slip circles in the LE methods by using a slope stability software. So comparison to when we have let us discuss about if you are having an embankment which is a you know a dam reservoir and water reservoir with imperimble strata at the base and this is the embankment which is constructed with a material having unit weight of 19.64 kilo Newton per meter cube, cohesion is about 4 kilo Pascal's and friction angle is about 32 degrees. So this is actually subjected to you can say water head is there and the slope height is about 6 meters and the slope is one vertical is having one vertical 1.5 horizontal you can see that this horizontal distance is 8 meters vertical height is 6 meters. So the slope inclination is about one vertical 1.5 horizontal and this is an example after Lamby and Whitman and assume that there is a drainage layer at the base there is a drainage layer at the base. So this is the filter layer having very high permeability compared to the embankment soil. So let us see that when we do the seepage analysis and when we perform the seepage analysis what we get is this is called the priartic surface and this is the priartic surface as this being the flow line and you can this being the equipotential line as this being the equipotential line with head is equal to 0 here what you see is the upper most flow line and the soil below this is actually saturated and this condition is actually once this conditions are prevailing then this is actually said to be subjected to a steady state seepage conditions. So afterwards this selected the grid of centers are selected as we discussed in the previous slides and from each center the number of circles are actually have been tried and out of this the one which actually gives the least factor of safety is actually reported here that is nothing but here which is actually having a factor of safety of 1.289. So when you look into the you know this is actually analysis is done by Bishop's simplified method and we know that where tangential forces along the slices were assumed to be 0 and the forces on the normal to the slice vertical slice surface that is actually considered. So if you see the free body diagram of the slice 11 that is actually counted from here this is actually shown here and this is when it is projected here what you can see is that these are the normal forces which are actually acting on the vertical surface of the slice and this is the base of the slice and this is the self weight of the slice depending upon the so this is this portion is partially saturated and this portion is saturated. So this portion this weight of the slice is given and that is indicated here as a full force polygon here and this is the normal force this normal force is indicated here and this tangential force which is nothing but the shear stress that is indicated here the difference of this forces acting this side that is this one. So for example if you do this analysis by using the Swedish method of slices as these forces are assumed to be 0 you will see that there will be a force the triangle there will be a polygon will be in the form of a triangle but here because of this condition you will see that there is a net horizontal forces because this is our represented here. Now when you plot this distance from the toe of the slope with the normal stress at the base of the slice then you can see that the mobilized normal stress at the base of the slice is about 35 kilo Pascal's and then which actually drops down when you go away from the toe of the slope. Similarly here the shear stress mobilized is also plotted in the whatever it has been recorded in from the program. So this is the plot showing the distance from the toe of the slope to the shear stress in the shear stress mobilized along the base of the slice. So the same problem has been analyzed by using plaxies by strength reduction method and with that the factor of safety is actually obtained as 1.29. So what you can see is that the possible failure surface is actually obtained the same periodic surface what actually has been obtained from the seepage analysis has been feeded here in plaxies two-dimension analysis and the potential failure surface which is actually obtained is recorded here. So what actually has been obtained from the LE analysis and then from the you know for the example of lambain bit man problem is found to be in agreement. The factor of safety which is actually obtained by using LE analysis is found to be 1.289 and with this method it is found to be about 1.29. So the comparisons of factor of safety with the LEM and FEM is given here. If you perform the artery method of slices it is actually given as 1.161 and if you do the Bishops method it is 1.289 and Jean-Bouche method which is 1.22 and Morgan-Strand-Price method with finite equilibrium where 1.306. So what does it imply is that if you look you know the slope with the factor of safety 1.2 if you go with the artery method of slices we actually tend to over-conservative but if you adopt say Bishop's method or Morgan-Strand-Price method it indicates that the slope will be stable up to a factor of safety of 1.3. So you know this is the advantages of you know the different methods so the comparison is actually shown here in this particular slide. So here again the slide which was actually shown earlier was actually shown again and this was the REL 2003 work where in the limited group analysis was actually done by using Bishops method and Jean-Bouche method and Morgan-Strand-Price method and the results were actually found whatever the results which are actually obtained for the Lamby bitman problem were found to be consistent with the results actually presented by REL 2003. As you can see that 1.758 and then Morgan-Strand-Price method is actually coming around 1.737 and the plaques is actually giving about 1.654. Now this is a particular slope which is having an inclination of about one vertical one horizontal these lines which are actually shown here it shows that if you are inducing a seepage from the side of a slope then how the periodic surface will raise to the slope. So you can see here in the fourth day so this is the slope boundary and in the fourth day the periodic surface is only this and as the flow takes place and as the head is actually raised you can see that the periodic surface reaches up and the pore water pressure for example at this particular point continues to increase. Now what will happen is that if the given slope is actually stable and with these periodic surface conditions or the flow line top flow line condition the slope will be actually subjected to steady state CPS condition and remain safe but in the long term what will happen is that the internal erosion is the one thing which actually can occur rapidly. So for that to in order to avoid this internal erosion and piping problems at the downstream of the slope there is a need to take care adequate measures about preventing the internal erosion piping at the downstream of the slopes. So the reason why this has been actually shown is that the periodic surface which are actually obtained experimentally or actually combined were compared with the one which are actually obtained from the CPS analysis as well as from some experimental works which is carried out at IIT Bombay. So this is for the slope of this comparison is actually for a slope of 63.43 degrees what you can see is that this is the result of the CPS analysis with the water actually at this level and this is the the periodic surface which is actually measured from this height to this height and with Cpw what actually is obtained is this and from the experimental investigation the obtained is this much. So this is actually found to be consistent and wherein what you can see is that both Cpw and this actually found to be in order. So when you with increase in you know u by gamma h the u by gamma h which is nothing but pore water pressure measured at a certain horizontal distance from the crest of the slope and if you normalize that with a bulk weight of the soil into height of the slope and if you do then you can see that of once this u by gamma h reaches to attains a value of you know 0.5 for a 45 degree slope the slope is actually attaining the value of 1 that means that the slope as the u by gamma h is actually increasing as the periodic surface is traversing and then in contact with the toe of the slope then there is a possibility that the slope instability can be instigated. So before discussing the rapid drawdown conditions let us looking to the example 4 for the practice and this in this particular problem a cutting of 9 meter deep is to be excavated in a saturated clay having a unit weight of 19 kilo Newton per meter cube the design shear strength parameters are base are Cu 30 kilo Newton per meter square and 5u is equal to 0. A hot stratum underlines the clay at a depth of 11 meter below the ground level so using the Taylor stability method which we have discussed earlier determine the slope angle at which is the failure would occur and what is the allowable slope angle if a factor of safety 1.2 is specified that means that you need to determine what is the determine the slope angle at which the failure would occur and what is the allowable slope angle if a factor of safety of 1.2 is specified. So this is an example for the Taylor stability method which we have discussed and here a cutting of 9 meter high deep is to be excavated in a saturated clay of unit weight 19 kilo Newton per meter cube and shear strength parameters are undrained that is Cu is equal to 30 kilo Pascal's is given and hot stratum underlies the clay at a depth of 11 meter below the ground level. The another example for the practice example 5 is for the given failure surface which will be shown in the next slide. We need to determine the factor of safety in terms of effective stresses for the slope detailed in figure using the Phelanus method of slices. The unit weight of the soil is 21 kilo Newton per meter cube and the characteristic shear parameters are C dash that is the drain parameters effective cohesion is 80 kilo Newton per meter square and effective friction angle is 5 dash is equal to 32 degrees. So the slope is actually shown here and where in the this distance so here this particular portion is the tension crack and the depth of the tension crack actually is given as 1.37 and the horizontal distance from the crest of the slope is about 4.26 meters. So the failure surface is assumed to be fitted up to from this point to this point. So this is the entry point because this portion is already cracked. So there cannot be any generation of the you know mobilized shear resistance. So what we do is that we select from the tip of the crack to the say 2 of the slope in this case and this is the center of the rotation and this is the horizontal distance from this point to this point and this height is 19.2 meters and this is 12 meters height and this horizontal distance is given as 24.8 and these are the equipartition lines and these are the flow line which is actually given here like this. So for this condition the scale is actually given here and this is after Craig 2004 and this by using this the failure surface for the condition which is actually shown the this particular example 5 need to be solved. So now the coming to the rapid drawdown condition the topic for this particular lecture wherein we before addressing that one let us look into the steady state seepage condition. Once the reservoir or a dam which is actually has been full for some time the condition of the steady state seepage becomes established through the dam with soil below the top flow line in the fully saturated state. So the soil below the top flow line nothing but the periodic surface is completely saturated. The condition must be analyzed in terms of effective stresses with the value of pore water pressure being determined from the flow net and the values of RU that is the pore water pressure coefficient which is nothing but the ratio of U by gamma H and gamma sat H is nothing but up to 0.45 are possible in case of homogenous dams but much lower values can be achieved in dams having internal drainage that means that if you are having dams with internal drainage that is like filters or chimney drains as the periodic surface will be subjected to a dip and because of that the RU value can be much lower. The factor safety for this condition should be at least 1.5 but one thing one has to be established is that there can be eventuality of the occurrence of the internal erosion problem so this need to be addressed. So after the reservoir a dam which has been full for some time the condition of steady seepage becomes established through the dam with the soil below the top flow line is actually completely saturated and effective stresses conditions need to be considered. So this so in the rapid drawdown condition suppose any change in a once you once you know steady seepage conditions are established because of certain constant water level a drawdown of the reservoir level will result in a change in the pore water pressure distribution within the slope and this actually depends upon the rate at which this drawdown is actually taking place and also the permeability or coefficient of permeability of the soil. So after condition of steady seepage condition has become established a drawdown of the reservoir level or the water level in the dam will result in a change in the pore water pressure distribution. So if the permeability of the soil is low a drawdown period measured in weeks maybe rapid in relation to even if you are having permeability of soil is low drawdown period which is actually measured in weeks maybe rapid can be treated as a rapid in relation to dissipation time and change in pore water pressure can be assumed to take place under undrained conditions. The pore water pressure changes can actually take place in undrained conditions. So in this particular slide a slope stability analysis in drawdown condition or a response of a slope to the drawdown condition is shown. So here this particular first figure actually shows the pore water pressure under hydrostatic under high water level that means that this is the initial equilibrium condition wherein the pore water pressure is under hydrostatic conditions. Here with a drawdown which actually has taken place the water level which actually from here to here it has dropped at a certain rate but before the NE consolidation settlements or consolidation adjustments that U the pore water pressure at this point is initial U whatever is the hydrostatic water condition plus delta U from the change in the water load against the surface of the slope. So this is actually nothing but there is an increase that is nothing but initial U plus delta U. So at this particular stage with an increase in the pore water pressure within the slope there can be a danger for the slope stability that is that the factor of safety of a slope will reduce to a certain value. So after once it is subjected to consolidation adjustments and pore water pressure obtained from the transient flow net is actually shown here and once the equilibrium is existed and with low water levels the pore water pressure is actually established to these things. So when these things happen under cyclic manner with increasing water level and then decreasing water level so there can be possibility of it can get hampered with the factor of safety. So in this particular slide let us consider the analysis which is actually pertaining to rapid drawdown condition. So here consider a slope which is after the Bishop and Jerome 1960 which is a particular dam or a reservoir and this is the water level and steady state condition and this particular this is the potential failure surface and this was the initial hydrostatic this is the water level and this can be a periodic surface after a certain drawdown. So at point P the pore water pressure before drawdown at point P on a potential failure surface is given as so which is nothing but U0 which is nothing but the pore water pressure at this point gamma w h that is this water level plus h w so we are actually at this point but this h dash which is actually loss which actually has taken place because of the drawdown which actually has taken place from this level to so the h dash is nothing but the loss of the head because of the C page. So U0 is equal to gamma w into h plus h w minus h dash. Now it is actually here assumed that change in total major principle stress that is due to the resulting due to the soil slope is equal to total or partial removal of water above the slope that means that the any change the net change in the total stress that is nothing but the major principle stress nothing but the sigma 1 that delta sigma 1 is equal to gamma w h w that the gamma w h w which is nothing but minus gamma w h w. At the end of the change in water pressure what will happen is that this delta u which is actually minus b dash delta sigma dash so which is written as minus b dash gamma w h w. So this for delta sigma 1 is equal to delta u so for this once you when you substitute here and when you write u is equal to u0 plus delta u then delta u when we substitute for b dash gamma w h w which is minus and u0 is substituted which is nothing but gamma w h into plus h w minus h dash when you write here then we get u is equal to pore water pressure at point p immediately after the rapid drawdown once it is actually then gamma w into h plus h w into 1 minus b dash minus h dash. So by using the pore water pressure ratio that is gamma w is equal to u by gamma sat h now substituting for u here this particular expression which is gamma w into h plus h w into 1 minus b dash minus h dash. So this u that gamma u now r u will be gamma w by gamma sat into 1 plus h w by h into 1 minus b dash minus h dash by h. So for a decrease in total stress the value of b which is nothing but b bar is slightly greater than 1 and upper bound value of the r u can be obtained by assuming b is equal to b dash is equal to 1 and neglecting h dash so neglecting h dash it is not h not it is h dash. So with the neglecting h dash this will be 0 and with this will be 1 so the upper value is nothing but gamma u by gamma w by gamma sat the ratio of gamma w by gamma sat is approximately equal to 0.5. So the upper value will be upper bound will be basically about close to 0.5. So typical values of r u immediately after the drawdown within the range of 0.3 to 0.4 a minimum factor of safety of 1.2 may be acceptable after rapid drawdown condition. So when we are actually investigating we have to ensure that a minimum factor of safety of 1.2 is ensured. So the pore water pressure distribution after drawdown in soils of high permeability decreases as the pore water drains out of the soil above the drain drawdown level. So one inference is that the pore water pressure distribution after drawdown in soils having high permeability decreases as the pore water drains out of the soil. The saturation line moves downward at a rate depending upon the permeability of a series the rate at which the saturation line or the periodic surface or top flow line moves that depends upon the type of the soil or a soil actually having a particular permeability that means that it depends upon the type permeability of the soil. So based on this a series of flow nets can be drawn for different positions of saturation line and values of pore water pressure can be obtained. The factor of safety can thus be determined using an effective stress method for any position of saturation line. So as the slope the condition is actually coming close to the before coming close to the equilibrium condition or just after the rapid drawdown we can determine and once the slope actually reaches to some equilibrium condition we can determine. So the vulnerability is that you know once actually immediately after drawdown rendition the factor of safety reduces. So for that condition we need to ensure that it is actually having an adequate factor of safety. So in this particular slide a typical flow net with a particular saturation line for a particular drawdown. So here the drawdown actually happened from here to here and this is the core which is actually with the low permeable soil and this is a relatively permeable soil and this is the flow net in the case of a drawdown. So this is the top flow line for a particular state this is the top flow line. So you can see that this is the top flow line, this is the top flow line. So you can see that these are the flow lines which are actually these are the flow channels and these are the equipotentials this is the impervious surface. So it is assumed that the water actually will not penetrate through this and this is the impervious stratum. So the typical flow net in the case of a drawdown condition is given. So for this particular flow line and flow net condition we are able to do the stability analysis and then we have to see that for this drawdown with particular this thing what will be the factor of safety by using the effective stress analysis parameters with C dash and phi dash can be determined. And the pore water pressure ratio can be used for stability analysis as explained by Bishop and Morgan-Strain 1960 this best third is based on the effective stress analysis it involves the following parameters slope inclination depth factor that is nothing but the soil below the stratum that is D slope height and the ratio depth factor is nothing but soil below the toe that is the height is if it is if that height is a D and the slope height is h that is the ratio of this D by h and angle of hearing resistance that is the friction angle phi dash and non dimensional parameter which is nothing but C dash by gamma h and h is the ita slope and pore water pressure ratio. So factor of safety can be computed using the charts provided by this thing but these are not covered in this particular lecture. So but however what has been done is that a typical slope which is actually after Bellingen 2007 was actually considered and here the seepage and stability analysis for drawdown conditions were calculated and by using Geostudio 2012. So the schematic diagram of the slope which is actually shown here and the drawdown rate is which is two drawdown rates are considered one is actually rapid drawdown and other one is slow drawdown the rapid drawdown which is actually 1 meter per day. So the 1 meter level that is nothing but D falls down with time so in a day 1 meter in a day the other one is that slow drawdown this is submerged slope of height 7 meters. So initially the water level is up till here and the slope is actually having soil parameters which will be disclosed and one vertical 3 horizontal is the slope inclination and 7 meter is the height of the slope. So the flow chart which actually involves this thing is that first study state seepage analysis and constant hydraulic boundaries total head and transient seepage analysis and the stability analysis consideration of driving forces for failure body forces and pore water pressure. So the properties which are actually considered are unit weight for the slope is 20 kilometer cube and coefficient of permeability is 10 to the power of minus 6 and 10 to the power of minus 8 meter per second and the cohesion is about 10 kilo Pascal's and internal traction angle is 20 degrees. So this is drained parameters cohesion 10 kilo Pascal's and internal traction angle 20 degrees. So this is the study state seepage condition analysis using CpW so at the study state seepage condition this is the pore pressure conduits and the flow path during the drawdown phenomenon you can see that when the drawdown is actually occurring how the flow vectors actually eliminating here that can be seen here. Now here with a drawdown rate of 1 meter per day and with a permeability of 10 to the power of minus 6 meter per second what can be seen here the pore water pressure from here the periodic surface from here depleted to this particular level and the variation of the pore water pressure at point P1 if it is plotted you can see that the pore water pressure dissipation with time can be seen here. So the pore water pressure actually dissipates with the time so that it can be seen from this particular slide. So the stability analysis by using the slope value for the problem for that case where critical factor of safety is equal to 1.497. So you can see that as with 10 to K with 10 to the power of minus 6 meter per second with 1 meter per day is the drawdown rate that is the water depletion is nothing but a drawdown rate is nothing but a height to the height of water per unit time. So the critical factor of safety obtained is about 1.497 so you can see that the initially the factor of safety is high but as the drawdown actually taking place you can see that the factor of safety depletes and then remains constant and increases slowly. So this particular condition you know here in this case for this condition we actually have got a factor of safety of 1.497. Now when you have actually got slowed drawdown so both you know what will actually happen is that here this R1 is 1 meter per day and R2 which is 0.1 meter per day so you can see that at the end of the drawdown there is a depletion of the periodic surface takes place. So this is because you know the dissipation of the pore water pressure takes place simultaneously when that drawdown is actually happening. So if you plot the variation of the pore water pressures with time at this particular point what we selected here and these points when you compare so you can see that with slow drawdown there will be high dissipation of pore water pressure takes place with a rapid drawdown there is a very less dissipation of pore water pressure takes place. This implies that with high pore water pressures in the soil there can be you know factor of safety can be affected and low factor of safety can be obtained. So the same thing is actually presented here when we have the variation of factor of safety with the seepage time and here with a drawdown rate of 1 meter per day and 0.1 meter per day the one which actually with a rapid drawdown of 1 meter per day you know gives very low factor of safety or compared to the one with actually higher with relatively slow drawdown. So what it implies that you know when the drawdown rate is high and because of the high pore water pressure development the factor of safety of a slope can be endangered. So here higher factor of safety due to dissipation of pore water pressure can be seen with the distribution with minimum factor of safety with the time in days which is actually plotted here. So this for a for a for a for a for a for example let us say second or third day the factor of safety is 2 here but the same slope with slow drawdown the factor of safety ensured is about 3.5 or so that is what actually is actually explained here in this slide. Now what will happen when the drawdown rate is same but the permeability is actually soil is low. So if you see that if the permeability of the soil is low then there is possibility that the pore water pressure dissipation at the depletion of the periodic surface is marginal for soils with low k values. So depletion of periodic surface is marginal for soils with low k values. So here you can see that this is a soil with 10 to the power of minus 6 meter per second and this is this analysis actually carried out with soil with 10 to the power of minus 8 meter per second. So what you can see is that this and this the drawdown rate is same but permeability is actually here 1 by 100 times which is actually less. So you can see the magnified version of the insert which is actually shown here. So this is the depleted periodic surface. So the depletion of periodic surfaces is marginal for soils with low permeability. The same issue is actually shown here the pore water pressure distribution at particular point P1 and with two soils having two different permeabilities 10 to the power of minus 6 and 10 to the power of minus 8 meter per second the dissipation of pore water pressure is less for soils with low permeabilities. And similarly the factor of safeties if you look into this higher factor of having higher factor of safety for the soils having high coefficient of permeability. So that means the soil with relatively the because of the because of the you can see that because of the dissipation of the pore water pressure with this thing there is a possibility that high factor of safety is obtained but soils with low permeability the factor of safety is low that is actually shown here and you can see that this particular case reaches to the critical factor of safety which is equal to 1 here. So here this particular value where it can actually if this situation prevails at the site there is a possibility that this slope can undergo failure due to drawdown condition with a 1 meter per day condition. So that was actually the discussion about the rapid drawdown condition and so we in this particular forthcoming two slides we discuss about the total stress analysis and effective stress analysis requirements and some general comments we actually have discussed the requirement is that the total stress in the soil mass and which is actually common in both the methods but the strength of the soil when subjected to changes in total stress similar to the stress changes in the field the accuracy is doubtful since the strength depends upon the induced pore pressures. And in the effective stress analysis here also we require total stress in soil mass and common in both the methods that is both the methods in the sense that effective stress and total stress analysis. The strength parameters are in relation with the effective stress and considerable accuracy since there is a intensity of the test condition and determination of changes in external loads accuracy depends upon the measurement of the pore water pressure in this case. So after having discussed about this particular issue of rapid drawdown condition and method so what will happen when the slopes particularly the slopes can be as we discussed they can be natural slopes or can be man made slopes or they can be you know some conventional retaining walls or when they are subjected to say rainfall storms what will happen. So the rainfall intensity is actually vary from they measured in a so many millimeters per day or per hour and if the rainfall intensity with certain intensity and is actually subjected to certain duration what will happen to the stability of a slope. So this particular discussion is actually we try to present to you with the analysis by a performer through CW. So the CW is a program which actually finite element based program in the geo studio 2012 which allows the simulation of a rainfall of different intensity intensity with different durations numerically. So the slope instability is basically a common problem in many parts of the world causes you know number of casualties and several infrastructure damages each year and the rainfall basically what will happen is that at the onset of the rainfall the suction which is the need to pore water pressure increases and changes into pore water pressure and that results in you know lead to the loss of cohesion and that makes the slopes to fail. So rainfall has been identified as a major cause for the triggering landslides in slope failure. The mechanism leading to the slope failure is that pore water pressure starts increasing when water infiltrates into the unsaturated soil. In unsaturated soil where the predominantly the suction prevails and that gets nullified. The problem becomes severe if the film material has low permeability and cannot dissipate the pore water pressure generated due to rainfall. So if the pore water pressure generated cannot be dissipated and that can lead to as we have seen in previous analysis can lead to the low factor of safety. To investigate this effect of rainfall and slope stability a limited equilibrium analysis was carried out by using slope W a product of GeoStudio 2012 software. The two slope configurations were considered here one is one vertical one horizontal other one purposefully a steep slope inclination of two vertical one horizontal that is 63 degree slope inclination horizontal was selected and were subjected to rainfall of various intensities like intensity ranging from 2 mm per hour to 80 mm per hour 80 mm per hour is very high intensity and the duration of the rainfall for each intensity is about 24 hours that day one day. The periodic surface were fed into the slope W and the stability analysis were performed at the onset of rainfall during rainfall and up to 24 hours of the rainfall. Basically this intention is to bring out the effect of rainfall with rainfall intensity and its duration on the stability of a slope. So here in this particular slide a slope configuration is actually shown here wherein we have the horizontal this particular lines which are actually shown here this is nothing but applied rainfall intensity and this is the initial water table position which is actually assumed that means that initially the static water table is actually assumed there and then above that it is assumed that that means that the portion here assumed to be saturated and then here this particular portion is unsaturated and wherein after giving the adequate appropriate soil parameters to this and this analysis is carried out. And the parameters which are actually considered in the slope W are like this computed by Bishop's Modified Method of Slices and the cohesion is about 3.5 kilo Pascal's and phi is about 31.5 degrees. So here in this particular slide it can be seen here effect of rainfall intensity and slope stability. So here with factor safety is plotted on the y-axis and time in ours on x-axis and can be seen here this is the threshold factor safety or one is actually marked here but with for a slope in the slope the duration of this is actually up till here you know the rainfall is actually you know rainfall is actually allowed that means that the duration of the rainfall is from here to here. So you can see that for a rainfall intensity of 2 mm per hour on that particular slope having certain configuration you can see that the factor safety decrease from 1.2 to 1.8 to 1.6 but the same slope with increase in the rainfall intensity you can say that let us say that at 36 per mm per hour you can say that the factor safety at the beginning of the rainfall is say 1.8 and at the end of the rainfall it is actually reduced to about 1.15 or so that indicates that the criticality of the slope. And for a slope with a subjected to a rainfall intensity for 80 mm per hour for 24 hours duration as can be seen here and the factor safety touches to 1 that means that the slope actually can be subjected to failure on the wet job once it is subjected to a particular rainfall intensity for the particular duration. So this shows the slope stability reduces with increase in intensity of rainfall. So these are actually very much important particularly if you are having and but once we after the rainfall let us assume that here what you can say that once the rainfall is actually is elapsed then you know you can see that there is an increase in factor safety that because there is a dissipation of pore water pressure is taking place but what will happen with the slopes which are actually constructed with low permeable soils and the dissipation minute is actually not happening. So the decrease also will not take place rapidly but even if the decrease actually take place but the increase in factor safety will not result rapidly. So that actually determines the vulnerability of a slope to fail. So this particular analysis which is actually demonstrated for a particular slope inclination of 45 degrees with increasing rainfall intensity the factor safety decreases till the period of rainfall duration. So in this case 24 hours rainfall is actually shown. So with rainfall intensity as high as 80 mm per hour we can see that the factor safety reaches to limiting factor safety and subsequently if the slope survives the factor safety can increase but that actually proves to be vital for the slope stability and for ensuring slope stability. Similarly in this next slide what we are seeing is that the slope inclination of 60 degrees. Suppose if you are having a rainfall intensity on the slope stability for the let us say that in this case we are having say a factor safety which actually decreases below the limiting value. So if you are having a slope which is two vertical one horizontal which is steeper slope. So even with you know a rainfall intensity of about 22 mm per hour within the rainfall duration itself you can see that the slope is actually subjected to failure that means that you can see here with a low rainfall intensity there is not much variation but what you can see is that once the slope actually you know the slope inclination with the 60 degree 22 mm per hour you can see that within 10 hours the slope is actually coming to the limiting factor safety and further with 36 and 80 mm per hour the slope actually reaches in very very you know short durations of rainfall. So this actually shows that the steeper slopes having low initial factor safety and the effect of rainfall on such slope is more devastating as compared to that is actually a usual natural conclusion but basically this exercise is actually done to show that how the rainfall intensity is you know severely can affect the stability of a slope particularly when you are actually having you know we increase rainfall intensity even with a slope which is as flat as one vertical one horizontal can be subjected to a failure but if the slope is actually steeper say nowadays the steeper slopes are common in the urban areas because of you know land availability and you know the land scarcity. So in such situations one need to actually adopt appropriate strengthening measures for the slopes and under these conditions one has to ensure that the slope stability is actually ensured. So this leads to our topic where in you know the measures for the enhancing the stability of a slope and in the forthcoming lectures what we do is that we will try to understand about the seismic stability of the slopes and some introduction or a concept discussion on the reliability analysis of the slopes. So in this particular lecture we have actually discussed about the especially about the rapid drawdown condition and the second thing is that we also have try to understand the effect of rainfall intensity on the slope stability particularly with increasing rainfall intensity we have seen that the slope factor safety decreases and with increase in slope inclination is want to be much more devastating.