 last lecture we have finished rotational slip total stress analysis and for undrained conditions factor of safety for resisting movement as well as disturbing movement explained. Then method of slices by swedes slip circle and for cohesion as well as friction soils we have also discussed then effect of tension crack on this slope stability analysis also has been discussed then how to find it out this location of slips circle center also we have discussed now effective stress analysis also last to last class also we have discussed this effective stress analysis by method of slices also other methods of analysis available is teller stability analysis. So, this teller stability analysis it is used for frictional and cohesive soils uses a dimension less number to iterate towards a solutions then bisapps method also I have discussed also earlier. Now, how do you measure particularly this land slip monitoring how do you monitor what is the slope failure and land slip monitoring by means of virtual instrumentation if you look at here this is a slope or embankment generally what happen there are there are if you look at here this is all your bore hole incline meter this bore hole incline meter generally provided. So, to find it out how much it will settle what is that what is that settlement along this along this and how much this flow will be there then also there are measurements of crack dilations if you look at here these are all your 1 and 2 measurement of crack dilations are if you look at here then you can find it out how much crack at the top it it generated and by means of bore hole incline meter you can also measure this what is the how much settle as well as the piezometers are there with the help of piezometer you can find it out water table fluctuation of water table in whether it is a rise in water table in rainy season how much the water table falls down particularly in summer season by means of piezometer then strain gauges has been put it anchor strain gauges anchor strain gauges along this slope it has been put it. So, this anchor strain gauges it has been put it. So, with this anchor strain gauges you can find it out how much strain that means what is the displacement of this slope then geophones also sometimes we provide to measure this generally you can generate means how what is the what is the travel geophones is there how much the travel time from top to bottom you can measure it by means of geophones. So, these are all your land sleep monitoring system then flow slides soil clay rock debris may behave like liquid it may behave like liquid water content. So, means behave like liquid if water content is greater than liquid limit if you look at here if the water content of soil of consistent of clay or may be debris if this water content is greater than the liquid limit it will behave like a liquid the assumption and in that case it is called flow slide it is called flow slide these slide will flow like a liquid flow slides are extremely mobile as given by umge peru in 1970 it has been observed if you look at here peru in 1970 earth quake triggers particularly flow slides means what will happen the water because of earth quake triggered this water content increase this water content is more than water content is more than your liquid limit. So, once this water content is more than liquid limit if this by means of in peru 1970 by triggering this earth quake it hits towns of umge 18 kilometer means away at around 150 kilometer per hour if you look at here it is started from here then this flow slides it is flowing it is flowing the slope means complete mass of the soil mass along the slope it is flowing and it is coming down then next example is also in the case of a colorado it is a national natural landslide laboratory if a measure sleep is about 3500 years ago and present sleep is 1000 years ago then the landslides will sleep has been means cross section through this mahm tor landslides if you look at here mahm tor bed is here. So, original original profile original profile of this ill side then if you look at this original profile then it has been this because of this landslides this part has been gone this part has been slip and flow towards the bottom this is a clear picture means these are all your clear examples of case 1 and case 2 different case studies I am showing there is there is there is a like correlation of movement with this rainfall they have given. So, this is out of contest thus I am showing with the rainfall how much the movement can be possible it has been some correlation has been given now this is all about basically about basically your slope stability analysis and basic principles of slope stability analysis how you are going to do this slopes slope stability analysis then we will start next part of this dam next lecture we will start with this dam dam basically if I start with the dam dam has been classified based on type and material of constructions. So, classification is what type of material you are taking into for construction point of view that this dam has been classified then criteria for selection of base dam type is feasibility first one is your feasibility that means topographic geology and climate what climate you are using and its effect on materials second is your cost that means availability of construction materials near the site that is accessibility of transportation facilities. So, what are the different types of dams available if you look at here dam different types of dams are gravity dam arch dam buttress and last one is your embankment and the material construction for gravity dam generally material use concrete rubble machinery for arch type of dam we generally use this concrete then buttress concrete also timber and also steel embankment it is construction of earth or rock start with this first one is your gravity dam if you look at this gravity dam gravity dam are dams which resist this horizontal thrust of the water entirely by its own weight if you look at here gravity dam is the dam which resist horizontal thrust of the water if this is my water level lying here horizontal thrust of the water by its own weight complete by its own weight that means if this is the dam gravity dam that means by own weights whatever the horizontal load is coming it will take or it will completely it will resist this horizontal load by horizontal thrust because of your thrust because of your water table. So, by its own weight gravity dam will take the stability they use their weight to hold back the water in the reservoir as I said they use their complete weight. So, that it stand by its own complete weight. So, that backside whatever the water level is there that can be hold can be made of earth or rock fill can be made of earth or rock fill if you look at this there are two views one is your cross sectional view or there is your plan view in this cross sectional if this is a gravity dam generally we say that where this water is reservoir water has to be stored here this water has to be stored the water has to be stored here that means this is called upstream face this is called upstream face then where this water has been stored this is called reservoir this is called reservoir and this bottom part is called hill this bottom part of this where this water reservoir this is called hill and the opposite side it is called toe it is called toe why it is called toe because of the water pressure thrust there is a chance that this gravity dam may rotate along this point. So, that is why it is called toe then there is a face this is called downstream face and this is your crest crest is your top of the dam then width is starting from the base this is your total my width of the dam width of the dam then if I start with this plan view if you look at the plan view this is a span of stream face width and downstream face then abutment these are all abutments gravity dam it depends on own weight for stability means particularly this stability analysis of the gravity dam has been done by its own weight and usually straight in plan through and slightly curved slightly curved. So, what are the different forces come into the gravity dam if you look at here in gravity dam the forces coming is your by means of gravity that means its own weight own weight. So, weight can be calculated by means v into gamma. So, v is equal to volume total volume and gamma is equal to specific unit weight of material. Suppose this gravity dam has been constructed over soil then specific or unit weight of the soil or it has been constructed with this rock then it is a unit weight of the rock that means volume this unit weight is a unit is new term is force per meter q or pound per feet q if I multiply into volume. So, this is your gravity weight of the dam then second part what is the what is the forces coming into picture hydrostatic pressure hydrostatic pressure means there are two component in hydrostatic pressure hydrostatic pressure because of your water one is your horizontal component other is your vertical component. If I start this horizontal component this is gamma w unit weight of water into h square by 2 h is your h is your depth of water at that section depth of water at that section gamma w is equal to specific weight of water gamma w is equal to specific weight of water. Now h v is equal to h v is equal to means h h is your hydrostatic pressure means horizontal component h v is your vertical component gamma w into v by h v by h is your vertical h is your vertical component gamma w into v divided by h. So, v is your volume of dam at that point. So, these are the forces third forces means we are discussing what is the gravity what are the we are discussing right now what are the dams and classification of the dam then we are starting one by one first one is your gravity dam and where it has been used how the stability can be done for the gravity dam then what are the forces acted on the gravity dam in this section force forces on gravity dam third is your uplift uplift means the water pressure that comes below the dam foundation a results in upward means uplift if I come back to water pressure coming below and in the foundation it push up this is called uplift force this uplift force u generally it is written gamma w h 1 plus h 2 by 2 into t h 1 is equal to depth of water at upstream phase hill then h 2 is equal to h 1 is equal to depth of water at upstream phase h 2 is equal to depth of water at downstream phase that means lower if I say if I say that means if I take it here. So, this is my depth of water at upstream phase h 1. So, this is the depth of water at downstream phase h 2 h 1 and h 2 now gamma w is equal to specific weight of water and t is equal to base thickness of dam t is equal to base thickness of dam this is your t is equal to t is equal to base thickness of the dam then ice pressure fourth one is your ice pressure ice pressure is created by thermal expansion exert thrust against upstream phase of the dam what will happen in particularly if there is a dam over the period of cold means once the winter season starts particularly in Europe country what will happen entire liquid entire entire water will become ice. So, that means it will become a ice and solid pressure this pressure will be higher than your water pressure. So, this is one forces suppose to come ice pressure then once we are going for analysis of the gravity dam we will do it for gravity dam in adverse conditions this gravity dam particularly in adverse conditions that means what are the different forces has to come in adverse conditions this ice pressure is not necessarily it will come particularly in summer season. So, ice will be ice formation will start particularly in winter in european country then last one is your fifth one is your earthquake forces we have to check also results in inertia forces that include vertical motion or accelerated increase or decrease in hydrostatic forces because of earthquake force earthquake load earthquake what will happen to this gravity dam. So, this earthquake forces also taken into consideration. So, gravity dam what are the different causes of failure one is your sliding along the horizontal plane that is called shear force sliding along the horizontal plane that means it will slide if I take it like this it will slide along the horizontal plane. So, that means what will happen that means what will happen it will it will it will resist against the shear force that means sliding along horizontal plane that means shear failure that means net force net force would be greater than shear resistance at that level. Then second second cause of failure is equal to because of all forces ice pressure water pressure earthquake pressure earthquake forces because of all forces there might be a chance that this particularly this hot dam it may topple it may rotate at about the toe at about the toe. So, this part has to be taken into consideration that means second type of failure is your rotation about toe. Third one is that if this construction has not been done properly it may highly possible that this material failure may occur the material may fail material failure may occur. So, example these are all means there are 2 3 case examples I put it gravity dam if you look at this this is a period dam then second one is your it is in west virginia also in india also gravity dam is there in west virginia in u s this gravity dam is there if you look at here one face this is your upstream this is your upstream side this is your downstream side if I draw the cross section if I draw the cross section simple cross section of this gravity dam look at here this is the water reservoir if I am looking like this. So, this side water reservoir is there water has to be remains stored and this side is your downstream side second case is your earth dam, second case is your earth dam these are all curve dams curve dams which is dependent upon earth action for it is strength which is dependent upon earth action for it is strength. Transmits most of the horizontal water truss Transmits most of the horizontal water truss earth dames these are particularly curve dam dam which is dependent upon r traction for its strength and transmits most of horizontal water thrust behind them to the abutments by r traction means whatever the horizontal water thrust horizontal water force is coming it will transmit by means of r traction by the r traction means whatever the water pressure is coming it will transmit to the abutment by means of r traction advantage of that it is a thinner and requires less material than any type of dam means it is a very thin and requires less material than any other type of dam used only and it has also limitation used only in narrow canyons if you look at this cross sectional view this is my width and this is your off stream side and this is your height this is your total height of water and this is your complete reservoir this is your complete reservoir and this is your toe and this is heel and this is your downstream face and this has been acted by this is your r traction then this is your axis complete axis this is your r If I take the plan view, how it looks, this plan view, this is the complex plan and this is your abutment and this is your toe and this is your downstream face and these are all your radius and central angle, particularly arse dams, it includes series of horizontal arches and series of vertical cantilevers, load distribution most, load distribution near bottom of the dam, near top of the dam and most load carried by cantilever and arches known as trial load method. So constant center that means constant radius, if I look at the types of the arches one is your constant center that means this is a constant center, this radius is the radius is constant means throughout the radius is constant, this is one shape of arches type, then another one is variable center, variable center means variable radius, if you look at here, if you look at here the radius at each point, the radius at each point is varying that means r 1, r 2, r 3, r 4, r 5, r 6, but the angle is constant, angle is constant, so there are two cases, first case is your radius is constant, angle is varying, second case is your angle is constant, but radius is varying, so this first one is called constant center, second one is called variable center, so generally it is used for u shaped canyons and used for v shaped canyons, we will see this, we will see this photographic graphical pictures of this, generally arches dam design generally thickness of arches reef, it has to be calculated from this t is equal to gamma h r by sigma w, t is equal to thickness of arches reef, t is equal to thickness of arches reef, h is equal to height of reef, gamma w is equal to allowable working stress for concrete in compression and r you can we can get it b by 2 sin theta by 2 and v is equal to b by 2 sin theta by 2 into a theta, r is equal to radius of arch, r is equal to radius of arch, b is equal to canyon width, v is equal to volume of concrete required for single arch reef, then theta is equal to central angle in radian, a is equal to cross sectional area of reef, a is equal to cross sectional area of reef. Now if you look at this in u s it is boundary dam, see at in u s if you look at here arch dam, how this arch shape photography picture may not be clear, look at this arch shape and look at this thickness, the material used is a very small quantity as compared to other arch dams, again it is not visible let me see, no, if you look at this, look at this, this is arch shape, this part is your, this part is your upstream site, this part is your upstream site, this is your downstream site, just one picture may be next class I will show that clear picture, can be one picture slide, can be make it so that more clarification, more it may be clearer to all of you, then third part we are starting with this that is your buttress dam, buttress dams are dam in which the face is held up by series of supports, face is held up by series of supports, if this is my face, this is the upstream face, this is the downstream face, face is support by series of supports held by series of supports, buttress dam can take many forms, the face may be flat or curved, the face may be flat or curved, usually buttress dams are made of concrete and may be reinforced with steel bars, usually buttress dam are made of concrete, made of concrete and may be reinforced with steel bar, may be reinforced with steel bar, so if you look at this cross section, this is the width and this is the crest and this is your downstream face, downstream face this is your height and this is your toe and this is your axis and this is your foundation, this is your upstream face with this series of supports in the upstream face is there, so in case of buttress dam sloping my membrane that transmits the water load to a series of buttress at right angle to axis of dam, at right angle to the axis of the dam, if you look at here sloping member, sloping member that transmits the water load to a series of buttress, sloping member these are the sloping member that transmits the water load to a series of buttress, transmits the water load to a series of buttress, increased form work formwork and reinforced steel compared gravity dam. If you look at this increased formwork and reinforced steel, as if I compare with this gravity dam, the reinforcement, the reinforced steel provided is more less massive than gravity dam. Here what will happen? RCC generally provided, if you come back to gravity dam, it is a less massive, means the area and mass structure is coming, it is a less massive, required one third to one half as much concrete. It requires one third to one half as much concrete, then use on a weaker foundation, use on a weaker foundation, if I make it into buttress dam, where it has been used, what is the purpose and how far it is advantage to gravity dam and particularly where specifically where it has been used, use on weaker foundation. So, some same forces means particularly same forces as gravity and r's dam, the same forces has been acted like you can say ice pressure not as a prevalent, so gap of buttress relief majority of uplift forces. So, same forces the way we have discussed this in case of gravity dam what are the forces acting, it is the same forces about to acting. Then types of buttress dam, part one is your flat slab that means flat concrete reinforced slabs, flat and concrete reinforced slabs. Second is your multiple arc, multiple arc that means series of arcs are there, these are the two types of buttress dam. Now look at this example buttress dam, first one is your buttress dam, if you look at this buttress dam upstream side buttress dam, if you look at here in cubic, one case is your buttress dam, second now it is very clear. Now if you look at here in Colorado also buttress dam has been used, this side is your upstream side, this is your particularly downstream side, maybe you can stop it here, we will start with this other part of your embankment type of dam next class.