 Next part of this lecture is the new module that is earth slopes, embankments and dams. So, let us start this first basic principles and basic physics and basic analysis of earth slope stability. Overview we can see outlines one is what is earth slope stability overview and what are the different causes of mass movements and types of slope movements. Then in that types of slope movements, infinite slope stability analysis, then finite slope stability analysis, in case of finite slope stability analysis, what are the different basic methods we will discuss. Then particularly finite slopes method of slices, by means of method of slices what are the different methods available, by felinus method, bisapp methods and simplified bisapp methods and at the end we will try some few examples, solved examples, how it has been solved this slope stability analysis. Now, what is the first overview, what is the cause of mass movement, what is the reason that mass movement and slope failure generally occurs. If you look at here, if you look at here this is my original topography, this is the dotted lines are original topography of a region, then it has been proposed a slope or embankment has to be constructed. So, this embankment construction is this part of this embankment construction, if you look at here this is the embankment has to be this has to be embankment has to be constructed and this is a planned proposed construction. So, from this original topography what will happen, this part has been taken out, this part has been taken out and also this part has been taken out and this part also feeling this part is your feeling. So, by means of this if you look at here, once I have taken out once I have taken out this soil mass from here while constructing this embankment, then what will happen, there is a flow of the mass this direction has been made, also here it is a feeling of soil mass the flow of this mass movements. Now, what are the different how it is possible this mass movement, if you look at here there are different cases case one case two case three case four also ardent dam also it has been drawn, let us start with this case one. So, if you look at here this is your case one in this case what will happen, this there will be if I consider this is my slope and this is the embankment, this is your embankment in this embankment w is your gravitational force acting downward and this dashes line particularly this dashes line with this arrow it indicates tendency of soil mass moving towards moving away moving not away moving towards this embankment site. So, what are the different forces coming into picture the forces are because of your self weight that is your normal gravity forces acting vertically downward and this dotted or arrow lines is your tendency how this mass movement occur and you can consider also new forces taking into consideration of seismic seismic or earthquake forces this is a typical pseudo static cases. Then case two high ground water level if this ground water level suppose this initially the ground water level or ground water table is at this point and it has been raised to up to this embankment. So, high ground water level causes a seepage force this is your seepage force seepage force in the direction of potential slope movement how the in case one we saw that direction of potential slope movement this is my direction of potential slope movement how slope movement this is your direction of the potential slope movement. So, once there is a water table from here to here up to the ground surface or up to the embankment level what will happen this seepage force also acting in the direction of in the direction of your ground movement a direction of your earth mass movement. So, what will happen along with this earth mass movement there is also seepage force movement. So, seepage water along with this it will add seepage force will add additional movement or additional earth slope movement and along with this directions which has been marked. Now, case three if in this embankment if in this embankment may be in this slope particularly this slope if there is a layer there is a layer which is a very weaker which is very weaker in nature. That means very weak as compared to this if I consider this is layer one and this is layer two if I compare with this layer one and layer two layer two is weaker than your layer one what will happen because of layer two is weaker. So, it will settle once it will settle. So, this entire mass this entire mass soil movement will occur. So, another reason is susceptible layer or zone weakened from continuous continual exposure to ground water or chemical waste leech eggs. Then fourth case is temporary or permanent excavation for construction of a project. If you look at here if this is a existing slope this is already the slope is there existing slope or embankment. In this case it has been it has been proposed to construct here. That means some new load will come here construct a structure here at this surface of the embankment at the same time what will happen there is a temporary excavation here this is your temporary excavation has been made. Once this temporary excavation has been made what will happen the soil because here it is new load or new structure has to be constructed what will happen this entire mass will try to move up move towards your excavation this is another cause of your this is another cause of your slope failure. Then for particularly earth dam if you look at the cross section of earth dam if I make it this earth dam there are two cells one and two in between there is a core in between there is a core. So, what will happen because of water reservoir this cell it will this earth movement will be direction of towards your water reservoir. So, these are all common what is the reason that there is a mass movement or may be a slope stability or slope movement may occur these are the all few reasons which has been highlighted. Now types of slope movement first one we discussed what are the reasons what is the cause for your slope movements. Once you know that cause the second one what kind of slope movement may occur if you look at here there are one two three four different cases if you look at here case one is your rotational case. Rotational case means entire soil mass entire soil mass will rotate entire soil mass will rotate if you look at here in this diagram this entire soil mass will rotate this is called rotational slope movement. Then another case two is your translation translation if you look at here there is a weak stratum it has been marked and shown here. Then what will happen translation means one up another this will be movement from this. So, this is your translation movement then third one is your block or block and wedge. That means what will happen instead of moving in case one entire soil mass if you look at here there is a bigger weaker zone below the slope instead of moving entire soil mass like rotational what will happen it will move like a two wedge it will move like a two wedge. So, here to here this will be one wedge and here to here this will be other wedge that means two wedges are moving. So, that is why this is called block or wedge why it is called block it will act like a block and the movement will be like a separate this entire soil mass will be separated into as a two blocks or two wedges. So, the movement will be called or soil movement will be called block block and wedge movement. Then another one is your spread spread movement if you look at this this conditions also it has been mentioned this is a farm clay this side this this part is your farm clay that means this entire soil here is whatever mark in the white these are all your farm clay below this farm clay. There is another soil layer that is a soft clay with water bearing silt and sand layer that is a soft clay with water bearing silt and sand layer below this. Then below this there is a farm gravel clay farm clay gravel or farm gravel that means in between two farm soils in between two farm soils there is one soft soil or soft layer of soil is there that means this is your farm soil this is your farm soil in between two farm soils the third one is your soft soil layer is there. So, in this in this case what will happen this soil movement will be like a not rotational not block or wedge not like translational it will be like a spread. So, one by one it will be spread above the surface. So, if you look at here one will be one soil movement mass movement will be in this direction other will be in this direction other will be in this direction all of sudden one layer is moving downward. So, it will spread half hazard movement it will spread all over it will spread all over then last one is called flow type of slope movement last one is called flow if you look at here flow this is your source area this is your source of your soil mass source area and this is marked by your main track how the flow will occur then this is your deposition area that means if there is a hilly region there is a slopey ground slopey ground the source area from the top what will happen the slope will flow it will it will fail or it will the movement will be in terms of flow that means soil at this part it will flow in the main track and deposited at the bottom in this case it is called flow movement. If I classify into basically in broadly broadly what are the different types of slope movement once again number one is your rotational in rotational entire soil mass will movement movement that means entire soil mass will move that means as if this will be a one soil mass it will move then second case it is a translation the movement will be like in a translation then third is your block and wedge that means each soil mass will not move like a independent one soil mass that rather it will move like a block one block other block so one is moving like this other is moving like this so this is called block movement then fourth one is your spread movement in in this case spread movement if there are two firm layers in between one soft layer is there what will happen then the soil will spread spread means there will be a vertical movement lateral movement all over it will be a spread then last one is your flow flow means if in case of hilly region if there is a there is a slopey ground what will happen entire soil mass at the top will flow and deposited at the bottom this is called flow movement now there are different case studies if you look at there are different case studies now I come back to here ground means if you look at this there are different case studies has been taken one is your case one it is 1964 alaska earthquake if you look at this alaska earthquake how the soil movement will be there from the top and it has been deposited because of earthquake enter mass of the soil mass in the slope has been movement means if you look at here this is one block this is another block these are all separated out the soil will be separated out then second one is your if you look at here 1995 kobe earthquake this is a case of kobe earthquake this building hang over the head scrap of a landslide in decomposed bed rock that was triggered by the 1995 kobe earthquake if you look at here kobe earthquake what will happen this building just simply hang below this entire soil mass entire soil mass it has movement soil movement is there so the building is simply hang now come back to second in third example in 1970 an earthquake induced rock and snow avalanche on waskram peru it is particularly a peru earthquake if you look at here peru earthquake how this flow from here to here how it has been movement of this soil mass movement will be there from here to here how this flow occur and it has been deposited this soil mass here this is your third example in 1970 peru earthquake now typical one cross section earth dam has been shown in 1971 earthquake if you look at here before earthquake 1971 this is an earth dam look at here this is your earth dam this is your maximum water level and this is your dam top of the dam and this is your earth dam once this earthquake has happened the soil mass if you look at here it has been marked by dotted the soil mass entire soil mass has been moved the movement of the soil mass has been occurred or you can say that this embankment failure occurred because of earthquake because the soil movement from here to here it move towards your downstream side means particularly towards your water level or reservoir side I have shown earlier also if you look at here this diagram I have shown in this case this particularly if you look at here there is a flow and one case I have shown here this case typical case I have shown if this is an earth dam and there is a reservoir if there is some earthquake some forces are coming so this part of the soil will movement move towards your reservoir that means this soil will move towards your reservoir so this is a earthquake in 1971 occurred in sun Fernando and magnitude comes about 6.7 6.7 and total from 48 death occurred in injuries 2000 and damage is about US dollar 511 million dollar has been damage has been marked and crest if if this is my dam crest this is the dam crest drop from 142 feet to 112 feet this crest has been drop from 142 feet to 11 feet another one is your 1994 17 January earthquake this magnitude is 6.7 6.7 if you look at here limit of landslides triggered by the north ridge earthquake and area of greatest landslide concentration shaded particularly greatest landslide concentration if you look at here how the landslide has been occurred entire soil mass has been eroded eroded means it has been the because of your slope failure entire soil mass has been flow to your downstream side and this has been shown in graphically means particularly pictorial point of view top view so this is your entire area how this landslide has been occurred from here to here this landslide failure rated correlated with shaking severity then slope stiffness then strength and engineering properties of geologic materials then is your water saturation then existing landslides areas if you look at here first one is your number one number one is coming out to be somewhere else 1 2 3 4 5 6 this is your 5 10 somewhere else number one here this is your shaking severity two is your slope stiffness slope stiffness then third is your strength and engineering properties of geologic materials then fifth is your existing landslide area if you look at here this is your fifth is your existing landslide area this is your number fifth this part is your number fifth this is your number fifth that means in this area this is your area of landslides landslides means entire soil movement entire soil or entire soil movement or slope failure there are two kind of slopes one is your infinite slope so the slope is in infinite nature then another is your finite slope now if you come for this infinite slope analysis before I go to the infinite slope analysis let me come to the finite cases in case of finite what are the different types of slope failure occurs finite means it is a distinguish particularly it is a finite shape infinite means it is a long infinitely long slopes so in this case particularly there are three category one is your slope failure another is your toe failure other is your base failure if you look at here this is a slope toe failure typical for soil possessing internal friction now this is your slope failure now that means the failure will be generated from this side and it will be somewhere else along the slope this is my slope this is my slope say this slope may be one is two one or one is two two it depending upon this what generally one is two one two one is two two or one is two three has been the slope has been provided so why this is called slope failure the failure surface the failure surface extend here from the embankment at it generate and it ends at the point of slope that is why it is called slope failure same cases it is also extend here and ends at the point of before along the along the slope then third one is your if this is my toe second one is your this is my toe if this is my toe if you look at here both this the case one and case two these are called slope failures because the failure starts from this embankment at the top and it continue and fail along the slope first two example is your slope failure because this failure starts from the embankment top and the failure it will it will terminate somewhere else along the slope here it is if I if I draw a draw embankment like this if this is my slope one is two two or one is two one so these failures these failures I can say failure surface one two three as slope failure because the failure surface ends at the point of anywhere else along the slope that is why it is called slope failure the moment I say that this is a toe failure that means particularly in case of finite slope that means the failure surface starts from some from at the top at and it propagate at and it ends just at the point of toe if this is my point of toe and this is my the top of the top of the embankment top of the embankment so here it starts the failure from the top at it ends at the point of toe this is called toe failure that means there are two one is your slope failure other is your toe failure third one is your base failure base failure generally occurs if there is a kind of if you look at here this is a clay layer this this this is your embankment constructed and this is your particularly clay soil it is written here then layer or zone of hard earth it is a harder stratum is there then what will happen then the base failure means the entire failure means this failure surface will start from the embankment it will progress progress and it will pass through below the toe it will pass through below the toe if this is my toe if this is the toe so it will pass through below the toe so that is why this is called this is called base failure now shape of this rotational slides shape of the rotational slides so if you look at this rotational as I said earlier now come back to this kind of second slides as I have explained earlier rotational slides rotational failure means types of slope movement rotational movement translational movement block and wedge movement then your spread movement then third is your flow if you come back to your rotational movement in this rotational movement what is what should be a shape how this rotational movement how it looks like one is your spoon shaped one is your spoon shaped as the spoon is a kind of this so this is a kind of a spoon shape so the failure is kind of a spoon shape failure so that is why it is called spoon shaped rotational slides other is cylindrical shape that means it will go in this so that it will take a cylindrical shape that is why it is called a cylindrical shaped rotational slides now if you look at this finite and infinite slopes I am discussing about right now this what are the equations what are the driving forces what are the different forces and how this finite and infinite slope particularly analysis has been done now go back to classifications so there are two types of slope failure one is your infinite in nature second is your finite slope in case of finite slope as we have discussed in case of finite slopes there are three kinds of slope failure one is your slope failure other is your toe failure third is your base failure now if you come back infinite and finite now in this case we have to identify what are the different forces acting what is your resisting forces what is your driving forces then we can find it out this factor of safety now if you look at this a typical figure shallow disrupted slide in very weakly cemented sediment in the Santa mountains slide is about one kilometer wide at the head the slide is if you look at this it is a mound and this slide has been shown this is this slide is about one kilometer wide can you imagine this slope this mass movement one kilometer wide this entire soil mass slides this width is about one kilometer one kilometer long stretch so this width is about one kilometer now if I look at this a typical this is a photographic view now if I analyze this if you look at here this is my original ground surface this is the original ground surface this is the original ground surface and this is your crown this part is called crown now now if you look at here this is the original ground surface and this is your crown now in this case if you look at here displacement material it starts from here to here now this is a main scrap main how it is scrapped so this part is generally main scrap then head then there are also at the same time what will happen at the same time what will happen there are cracks developed there are cracks developed over the period over the side by side so here if you look at here this cracks may be vertical or may be transverse so this crack is here it is shown this is a transverse crack this is a transverse crack transverse crack then there are two scrap scrap means how it move one is your main scrap main scrap will be at the top main scrap then another one is your minor scrap once it movement what will happen this slope is very stiff at the top then it becomes slightly stabilized so there will be a kind of there will be a kind of minor scrap now this is a main body if you look at here how the slope failure if I take it how the slope failure this is your main body this part is your main body it has been shown here main body now in this main point body this is has been marked tow tow means if I say this is heel this is your tow of the slope so this has been scrapped about one kilometer what has been said wide and this how the surface of rapture occur this is a surface of rapture occur this is a kind of rotational rotational shape then this part is your surface of separation this once there are again cracks develops so this shows how this oil movement starts particularly in case of slopes slopes and what are the major parts how how this rapture surface develops now next step we are going to go we are going to derive this basic equations for infinite as well as finite slopes now if you come back to infinite slope now I take a take a slope of infinite length and take a very small elementary part small elementary part of the soil in case of infinite slope now what are the component will have to see what is your driving forces what is your resisting forces now one is your one is your self weight of this self weight if I take a very small element of the soil in the infinite slope the slope angle is beta now this is your self weight w is equal to gamma into b into z b is equal to width z is equal to depth this depth is your z but and this is your weight self weight and what are the forces acting both the sides if you look at here one is your one is your infinite extend these are lateral forces e l e r if I take is your left hand side and right hand side this is your left hand side force this is your right hand side force as well as t is your particularly t is your frictional force t is your frictional force so it will be one is your vertical down other is your vertical up now sear force on the plane so because this is a infinite slope sear force on the plane s is equal to this and this is your normal force now if I take as a this length is called as a delta l delta l width is b this length is delta l so this delta l is your b by cos beta beta so this is your b sec beta we will discuss all these things next class complete derivation of your infinite as well as finite slope I can stop it here.