 Today, I will start my second module that is on shallow foundation. So, before I start on the shallow foundation, I will discuss about two, another geophysical exploration that is the part of or previous module that is soil exploration. So, first I will finish that part, then I will start this shallow foundation section. So, in the last lecture, I have discussed about the geophysical exploration and I have discussed about the seismic refraction survey and seismic refraction survey. So, now today I will discuss about the two, another geophysical explorations method that is that is cause hold seismic survey and then resistivity survey. Now, in the last class, I have discussed that we can discuss can use the seismic refraction survey to determine the velocity of the seismic wave that is passing through the soil different soil layers and we can determine the thickness of the soil layer, but the condition is that in the seismic refraction survey that that velocity of each layer should increase as we go in the higher depth. So, if there is any layer which is not following this pattern that means the velocity of a particular layer which is not greater than the velocity of the particular shear of seismic wave within that layer that means that that layer velocity is less than the velocity of the is above layers, then it will be very difficult to determine the properties of that soil for that particular layer, because we then we cannot determine this property if that condition that means the velocity of the layer will the velocity of the wave in the in the layer will increase if we go in the higher depth. So, for this limitation if there is any particular layer is present whose velocity is not greater than the velocity of the is previous layer then we will go for the seismic cross hole survey. So, now in this seismic cross hole survey the velocity of the shear waves created as a result of an impact to a given soil layer that can be determined by seismic cross hole survey. Now, suppose this is the in this particular seismic cross hole survey we need the bore holes at least two bore holes where this depth of the bore holes is we can determine based on the position where we want to determine the soil properties or the velocity of the shear wave. So, that means we have to go for that depth and then we can place this two bore holes here we can place this vertical transducer by which we can measure this wave and this is the another bore hole where we can create the shear wave. So, this vertical impulse is created at the bottom of the one bore hole by means of an impulse load. So, here by this impulse rod or impulse load we can create a impulse vertical impulse for a particular bore hole. So, that means this will generate a shear wave. So, once we go for this impulse the shear waves are generated and can be recorded by a vertical sensitive transducer. So, that means here two bore holes are there. So, here we can by using the impulse rod we can create one vertical impulse here and that will generate the shear wave and in the another bore hole which is at a distance say L from this point to this point this distance is L. So, where we can place a vertical velocity transducer which can measure or record this shear wave. So, here first we create one shear wave by using a vertical impulse and this transducer can record the shear wave. So, the time this is the total system. So, time required to travel this shear wave from this point to this point that we can record. So, suppose if the distance or between this point or this vertical impulse point where the shear wave is generated and this point where the wave is recorded then this distance is say L. So, if we can measure the time required to travel the wave from this source point to this receiver point then we can determine the velocity of this shear wave by using this expression. So, that means the velocity of the shear wave will be L by T. So, in this fashion we can or in this way we can determine the shear wave velocity for any layer or within the soil. So, that means so up to that required depth we have to the depth of bore hole will be that particular depth. So, and here at the bottom of this bore hole we have to place this transducer and by the use of this impulse rod we can create shear wave. So, at that any point we can determine the shear wave velocity of that particular within that particular layer. So, here there is no such condition is there. So, that means the shear wave. So, that means here directly we can measure the velocity. So, once we get this shear wave velocity then by using this expression this is the shear wave velocity expression that is G divided by gamma by G where G is the shear modulus of the soil, gamma is the soil unit weight and G is the acceleration due to gravity. So, once we know this density of the unit weight of the soil and G value and we know this velocity. So, by using this expression we can determine the shear modulus of that soil layer. So, by using this expression we know this velocity that we can calculate from this length and time if you know this length and time and this is the unit weight of the soil and G is the acceleration due to gravity. So, we can determine the shear modulus of the soil. So, in this way we can determine the shear modulus of the any soil layer at any particular depth from the ground surface by using this technique. So, next one is the resistivity serving. So, first one is this serving cross hole seismic cross hole seismic survey we can determine the shear modulus of the soil and the velocity of the shear wave within that particular layer. Now, next one that another geophysical survey where we can use the electrical resistivity this expression this electrical resistivity is a rho will be R A divided by L, where I is the electrical resistance of a particular material and then A is the cross section area of that material and L is the length of the material. So, if we know this R A L then we can determine the electrical resistivity of that particular material. Now, for this technique or this principle we can use here also to get the properties of the soil or the thickness of the soil. Now, this resistivity survey how we can conduct the survey. So, this four electrodes are driven into the ground and spaced equally along a straight line this is this arrangement is called Wiener method. So, here this is the four electrodes is 1 2 3 and 4. So, these four electrodes are driven into the soil layer in a straight line with a equal space. So, suppose this equal space I mean this D is the distance between the electrodes. So, here we can write this is the electrodes spacing or the spacing between the two electrodes. So, these are four electrodes we can driven in the soil and then the two outside electrodes are used to send the electrical current I into the ground. So, typical range of this current 50 to 100 milli amperes. So, by using this outside two electrodes the current I is passing through this ground. So, this current is passing through the grounds and the voltage drop corresponding voltage drop V is measured between the two inside electrodes. Now, this after the passing the current through this soil layer then the corresponding voltage drop V is measured by using this two inside electrodes. So, now we know what is the value of I that the current that is passing through this soil layer by using the outside two electrodes and the corresponding voltage drop is measured by two inside electrodes. Now, this is the D is the spacing between the electrodes. So, if we know these things though these properties then we can measure for a homogeneous soil this resistivity value rho will be 2 pi D V by I. So, so here we can measure the electrical resistivity of a homogeneous soil. Now, if we use this chart. So, these are the different soil materials or different soil has its own resistivity range. So, if we know the range of the resistivity of that particular soil material then we can identify which type of soil it is. So, for the sand this resistivity value or range is 500 to 1500 ohm meter and for clay or saturated seal this range is 0 to 100 for clay sand this range is 200 to 500 for gravel this range is 1500 to 4000. So, for weather rock this range is 1500 to 2500 to 2500 and for sound rock this value is greater than 500 5000. So, if we know the range and from this resistivity survey we can measure the resistivity of this for the homogeneous soil layer then we can determine or we can identify that what type of soil it is. Now, this is for homogeneous soil, but the most of the cases the soil is not homogeneous. So, in that case how we will determine the thickness of each soil layer and the resistivity of this each soil layer that we can explain in this way that for that particular case if the soil is not homogeneous then we can change this spacing between the electros. So, this is the D. So, we can change the this D value because we will still place these four electros in a straight line, but these are equal space, but we can change the spacing here. So, if we change the spacing for these different points and then we can determine the resistivity for that particular spacing. So, once we get the resistivity for that particular spacing and then we can plot this diagram where this is the distance of the electrode this x axis represents the distance of between the electrodes or spacing between the electrodes and this y axis is the summation of the resistivity. So, we can plot. So, once we get the resistivity for this particular spacing then we can sum all the resistivity that we are calculating then we plot this graph. So, once this is the value for a particular D then corresponding summation of the resistivity we can plot here. So, ultimately we will get this type of plot. So, from here we can see from this plot that there is a junction point or change of slope of this plot or this line. So, this change of slope this point particular this point indicates and corresponding distance D that indicates the thickness of the first layer. So, if this is the first layer whose resistivity is say rho 1 and this is the second layer whose resistivity is rho 2 and then this point where this slope is changing for this particular graph then corresponding D value that will give the thickness of the first layer and the slope of each state portion where slope will give the resistivity for each layer. So, for different D we can plot this graph and corresponding the slope of each layer or each state portion will give the resistivity of the each layer. This is the slope this slope will give the resistivity of the first layer then this slope will give the resistivity of the second layer and the point where this two slope or the slope is changing then corresponding D will give the thickness of the first layer. So, this is the four different seismic geophysical exploration. So, now here this is the table and now once so this is the always we have done all the possible methods by which we can determine the soil properties the thickness of the soil layer and the depth of that soil layer layer layer from the ground surface then the location of the ground water table from the soil and we have done the laboratory test also to determine the that the sample that those we have collected from the field that we can test in the laboratory to get the different properties. So, as I have already discussed that the shear strength parameters of properties and the consolidation properties those are the most important engineering properties because for any design of foundation this shear strength strength and the settlement which is related to the consolidation of the soil are the most two important governing criteria of the design. So, shear strength parameter that means CE phi and the consolidation properties which is related to the permeability of the soil. So, these properties are the most important engineering properties of the soil. So, as I have mentioned that to determine these properties these important engineering properties we have to always collect the undisturbed sample to determine these properties because these properties are very important. So, and other properties also we can determine and where some cases we can use the representative although the undisturbed representative soil sample. I have discussed where we have to use those representative soil sample under what condition what type of laboratory test to determine what type of material properties of the soil or engineering properties of the soil. So, those things we have discussed then now once we get all the properties then we have done the soil exploration and then how we will produce or we will prepare the report. What are the components of a soil exploration report that part is that this soil exploration report this the first we have to write the scope of the investigation. So, the scope of the investigation for a particular site then the description of the proposed structure. So, what will be the type of structure that will be constructed on that particular site that description should also be incorporated in the report then the description of the location of the site where the site is located. So, that description also we have to give then the geological setting of the site then the geological condition of that site then detailed of the field exploration. So, what will be the detail of the field exploration that we have to include in the report that means the number of boring or the borehole the depth of boring and the type of boring which type of boring will use in the number of borehole and the location of the boreholes where we will place our borehole then in the in the map in the we have to indicate the position of these boreholes in the depth of boreholes. Then the general description of the subsoil condition then once we get this data what is the general description of the subsoil condition then the location of the water table that we have to also include in the report. Then foundation recommendation then the type of foundation what type of foundation either will go for the shallow foundation or will go for the deep foundation if it is a shallow foundation what type of foundation either the mat foundation or isolated footing. So, those things all will go for the combined footing those things have to recommend here in the report. So, and then the allowable bearing capacity of the soil this is very important is what is the allowable bearing capacity that means the load carrying capacity of the soil what is that how much load will allow in that particular soil. So, to criteria this basic two condition that is our bearing capacity condition and the sediment condition. So, this allowable bearing capacity what is the allowable bearing capacity those things I will discuss in the next module. Then the contusion and the limitation what are the limitation of this exploration process and what is the conclusion that means those things will do. So, that this is the complete report components that we have to include in our report. Then the graphical representation these are the then with the with this report we have to produce some graphical representation also what are the different components are this is the site location map that means site map we have to include in the report. Then the plan view of the location of the boring with respect to the proposed structure and those existing nearby. So, where the proposed structure plan and then corresponding boring location we have to show and the existing structure if there is any existing structure or so then the position of this existing structure also we have to mention in that report. Then the laboratory and field test results that we have to report and then the boring log. Now this boring log is also important. Boring log means suppose this is a particular boring log where we have to indicate the depth wise from starting from the ground surface. So, what are the different types of soil what is the classification of the soil if there is a n value and SPT we are conducting then what is the n value at different depth. What is the description of the soil type suppose this is the bore log example one. So, this is the description of in of the strata then the RL the reduced level of that particular strata then the legend then the depth of this particular soil. Then the samples where it is a representative or undisturbed R means the representative and U is the undisturbed the n is the SPT value Q U is the load carrying capacity or ultimate load carrying capacity of the soil. So, remarks of the position of the water table those things we have to mention in that bore log particular this bore log this is the this is this is the loose light brown sand the classification is SP that means this sand with poorly graded and this is RL position of this particular layer is 43.7 meter then this is the legend the depth is 2.6 meter from the below the ground surface. So, here the soil sample that is collected that is representative and the n value for this this level is 18 and 16 and this is the ultimate load bearing load carrying capacity this 160 kilo Newton per meter square and then what the position of the water table then why the diffuser of this n value is observed then all those things we have to mention in that particular bore log. So, this is the different soil strata description basically we are presenting in this form. So, again U is the undisturbed and R is the representative surface. So, this is the bore log. So, these all components we have to include in a soil report. So, once this report is finalized then we have to submit this report in the design office or any design office. So, that the foundation the proper foundation can be designed. Now, the next part that we start is the shallow foundation. So, up to this we have done the soil exploration part now we know the different components of the properties in properties of the soil then the different soil strata thickness then the location of the water table what is the allowable bearing capacity or the load bearing capacity of the soil. So, roughly these things we know now based on that we will design our foundation. So, now for the design of foundation either what type of foundation will choose either go for the shallow foundation or the deep foundation and those things we will discuss here. Now, once we get this soil exploration report and based on that we will go for this design part. Now, another thing there is here in a soil exploration part this plate load test is also another field load field test that is conducted in the field to get the load carrying capacity of the soil. But this plate load test description I will cover in this shallow foundation part in this module 2. So, the shallow foundation means what is the shallow foundation. So, this is typically two different types of foundation one is this is the shallow foundation and this is the pile or the deep foundation. Now, the definition of the shallow foundation is suppose this is the width of the foundation b and d f is the depth of the foundation. So, in the shallow foundation is if d f is less than equal to b width of the foundation then this is called the shallow foundation. If d f is greater than b then it is called the deep foundation. So, in few cases if d f is also equal to 3 to 4 b then it is also called as shallow foundation. Now, this is the different components this is the width and the shallow foundation is the pile foundation is the deep foundation. Here this load is transferred to this pile for a hard strata or this can give the resistance is coming by the frictional resistance and the bearing resistance. Now, this is the type of shallow foundation. So, this is the column and this is the particular foundation where b is the length of this foundation b is the width of the foundation l is the length of the foundation and d f is the depth of the foundation. Now, so this is the applied soil pressure which is the applied soil pressure which is basically q by b into l. Now, if it is the rectangular footing then this is b l if it is a square footing then b will be equal to l then this value will be q divided by b square. So, this is the pad found footing or the spread footing that either rectangular or square. The next one is the strip footing where this length of this footing is much much greater than the width of the footing. So, this is particular wall with load is acting here q and this is the depth of the foundation and b and then applied soil pressure we can write a q by b. Here this is if the load is kilo Newton then b is meter then this q will be kilo Newton per meter. But in this previous case if load is kilo Newton and this b l is meter then this will be kilo Newton per meter square. So, this is the strip footing where l is much much greater than the b. The next one is the another type of shallow foundation which is wrapped or matte foundation where this is the isolated this is the column or this multiple column and this is the wall of the structure. So, all this combined thing is called the matte foundation or the rough draft foundation where this is the column position and this is the total foundation system this is where this multiple columns and wall system so, this is called this type of shallow foundation is called raft or matte foundation. Now, when we design particular foundation then these are the two characteristics that the main characteristics or we can say these are two design criteria that we have to always follow. Then the foundation has to be saved against overall shear failure in the soil and the foundation cannot undergo excessive settlement. So, that means this first criteria is the bearing capacity of the criteria or that means the load carrying capacity of the soil. So, this is the first criteria that this soil should not fail against shear due to the applied loading and second one this foundation cannot undergo excessive settlement. So, this is the settlement criteria so, this both the criteria we have to follow and this the minimum so, the from here this load carrying capacity criteria will get one load that is the load carrying capacity of the soil and that means the load that is that can take this if we go for the safe load then we have to apply the factor of safety. So, here we will get one load and from this settlement criteria we will get another load or limiting load. So, the minimum one we have to provide as the allowable bearing capacity of the soil. So, we will discuss this I will discuss these things what is allowable bearing capacity how to calculate the load from this settlement criteria and this bearing capacity criteria those things I will discuss in this section. So, though before we go for the design part we should know the where we will placed our foundation then the depth and the location of the foundation before we start the design process. So, now so, this IS 1904 on 1986 this code this IS code has given some recommendation. So, that when you design these things you have to follow this recommendation where we will place our foundation or the that means the location and depth of the foundation. So, first one condition is the all foundation shall extend to a depth of at least 50 centimeter or 500 millimeter below natural ground level. So, that means the minimum depth of the foundation is 500 millimeter. So, we have to provide the depth of the we have to go for the minimum 500 millimeter depth below the ground level that is the first condition all foundation should be go up to 500 millimeter. Then foundation must be placed below the zone of volume change where volume change is expected. Now, if the type of soil is such that that is the volume change can occur. So, and we know the extent of this volume change. So, that the depth of foundation should be below that zone of the volume change. So, in case of fine sand and silt foundation must be placed below the zone in which trouble may be expected from first. So, if this soil is fine and silt fine sand and silt then foundation must be placed below the zone. If it is expected that it can be which trouble may be expected from the first we have to provide the foundation below this zone. Now, the depth of foundation for structure in a river like this bridge wire must be sufficiently below the deepest cover level. So, for the river structure we have to first we have to calculate the deepest cover level and then the foundation should be placed below that deepest for scour level or sufficiently below that deepest scour level in case of river structure. Now, next one if it is an expensive clay expensive clay like the black cotton soil where this that the swelling and sinkage this both can will occur due to the rise and lowering of the ground water table. So, that means this expand ship soil then the sinkage. So, soil may sink or soil may expand or swell. So, due to the rise and lowering of the ground water table then in such case and such soil it is necessary that either we can place the foundation and such a depth that where this change or seasonal changes are not important. So, that means this changes for the expensive soil due to sinkage and swelling. This is a seasonal change when the water table will rise the soil will swell if water table due to the lowering of the water table the soil will shrink. So, this seasonal change. So, we have to place foundation in such a depth that this seasonal change are not a important factor in that case or we make the foundation capable to eliminate such effects. So, that means either we place the foundation at a particular depth where this effect are not so significant or we can design our foundation or we can make the foundation capable to eliminate such undesirable effect due to the relative movement by the we can provide the flexible type of construction or we can provide a very rigid type of foundation. So, to eliminate this type of effect either we can provide the flexible type of construction or we can provide the rigid foundation. Now, construction activities above water supply lines then sewage pipes etcetera may not be allowed. So, we cannot construct our foundation above the water supply line or any sewage pipe. So, these are not allowable. So, these are the conditions. So, based on that we can decide where we will place our foundation. So, we can locate the or you can particularly identify the depth. So, here we will locate if this type of situation is this type of this any of this condition arises then we can by this condition we can decide where we will place our foundation. Now, if this is foundation at different levels. Suppose, if the foundation is in a slopey ground then also this I S code I S 1904 to 1986 its recommends a different recommend different conditions. So, we have to also satisfy those condition if this is a slopey ground. Suppose, this is the foundation this is slopey ground where we can place this foundation. So, one condition is that from the edge of this foundation this is the edge of the foundation to the if we draw one particular line and which intersect this edge of this slope. So, this distance minimum distance you have to provide 900 millimeter for soil. So, from this edge of the foundation to this slope surface this slope surface this minimum distance that we have to provide is 900 millimeter for soil and 600 millimeter for rock. So, we have to place our foundation such that this foundation edge is located at least 900 millimeter from this slope edge. So, this is another one condition if it is a slopey ground another condition that if we draw one line which is passing through this bottom edge of the foundation and with that line is passing making a 30 degree angle with horizontal. So, that means this line if we draw this is 30 degree for the soil and 60 degree for the rock this angle. So, then the condition is this two line that means this line which is making a 30 degree angle passing through the lower edge of the foundation and the slope line these two surfaces should not intersect. So, if this surface is intersect then we cannot provide foundation in such a condition. So, we have to locate foundation somewhere else. So, that this can satisfy this recommendation. So, we have to satisfy this recommendation for soil and as well as for the rock. Now, the next one is that if this is a slopey ground and foundation is at different level. So, this is the two types of soil and two types of recommendation. So, this is the upper foundation this is the lower foundation and for the granular soil if we join one line. So, suppose this is the position of the upper and the lower foundation then if we join the line which is passing connecting the lower this edge of the upper foundation to the lower edge of the lower foundation. So, that means this line should not be stiffer than 1 is to 2. So, that means this line should not be stiffer than one vertical to two horizontal. So, this is the condition for the granular soil. Similarly, for the clay soil if I join a line which is from the lower edge of the upper foundation to the upper edge of the lower foundation and then this line for the clay soil if I join this line should not be stiffer than one vertical to two horizontal. So, for the granular soil the lower edge of the upper foundation to the lower edge of the lower foundation and for the clay soil lower edge of the upper foundation to the upper edge of the lower foundation. So, both the cases these two lines should not be stiffer than one vertical to two horizontal. So, we have to place foundation is such that it will follow this condition. Now, next is the so this above condition this above condition when foundation at different level that cannot be applied when. So, above requirement should not be applied under the following conditions. So, it is not required to apply the above conditions this two conditions for two different types of soil and this condition when where the adequate provision is made for the lateral support such as with retaining walls of the material supporting the higher footing. So, in case of for the lateral support if we provide in case of higher footing such as retaining wall then it is not required to satisfy the above mentioned condition. Another condition is when factor safety of the foundation soil against bearing is not less than four. If the factor safety that we are taking for such condition is greater than four then it is not also required to satisfy the above requirements. So, these are the two conditions. Next this is the recommendation for the location in the depth of the highest recommendation for the footing then this is the spacing between the existing the new foundation. So, highest court recommends that the minimum horizontal spacing between the existing and the new footing shall be equal to the width of the wider one. So, suppose there is one footing that is existing condition and another new footing will be constructed. So, that the minimum horizontal spacing or required spacing will be the width of the wider one. Suppose, if B 1 is the width of the existing footing and B 2 is the width of the new footing then if B 1 is greater than B 2 then the spacing minimum horizontal spacing between these two footing existing and the new footing will be B 1. If B 2 is greater than B 1 then this minimum horizontal spacing will be B 2. Now, again the analysis for the bearing capacity and settlement has to be also carried out to consider the effect of this existing footing on this new footing. So, that analysis also have to consider to include the effect of this existing footing. So, these are the recommendation for the spacing for existing and new foundation. Now, next one that we will go for this different types of failure mechanism. So, we have now we know where we have to place the foundation. Now, where if there is a sloping ground then have to satisfy the different condition. Now, if there is a level difference between two foundation then also have to satisfy different condition. Now, based on that we will locate the position where we can place the foundation and if the existing footing is there if we are constructing a new footing foundation then what will be the spacing minimum spacing between these two foundation that also we can know by this IS recommendation. Now, when we apply the load suppose we are constructing on foundation and then we are applying the load. So, ultimately when as we increase the load that means the soil will go undergo a settlement and then after a certain point this soil will fail. So, this soil failure is because due to the shear failure. So, because of the shear. So, if the soil strength the that develop shear stress is greater than the strength of the shear strength of the soil then the soil will fail. So, for this failure there is a different three modes are there for depending upon the different types of soil. So, these mode these three modes are general shear failure this is the local shear failure and punching shear failure. So, these are the three different type of failure. So, we will explain one by one. So, this is a first type of failure is the general shear failure second type of failure is local shear failure and third this type of failure is punching shear failure. Now, first we will go for the general shear failure. Now, from this general shear failure we can say this is the load typical load versus settlement plot for general shear failure. Here we can see that as load increases the settlement will also increase and then after certain point as this settlement increases but this load decreases. That means this is basically the peak and from here after that soil has been failed. So, here for the general shear failure we can identify the failure point. So, this peak this corresponding this load versus load divided by unit area this q u is the ultimate load carrying capacity of the soil for general shear type of failure. So, here we will get a particular peak. So, the if we go for this characteristics of this general shear failure this is basically observed a soil like dense soil. If the soil is very dense or very stiff then we can this type of failure is observed. So, for the dense and this is brittle type of stress strain behavior where we will get a distinct peak. So, from here we can easily identify or we can easily determine what is the failure load or load from this type of failure. So, here the brittle type of behavior sudden failure in soil takes place and failure surface in the soil will extend to the ground surface. So, here from this graph we can see that is a sudden failure is occurred and this is the failure surface. So, we can see this prominent failure surface can be observed up to the ground surface. So, failure surface is extended up to the ground surface in case of general shear failure and the bulging of ground surface adjacent to the foundation is observed. So, we can see this is the bulging of the ground surface adjacent to the foundation both side is observed. So, this and another one this is the ultimate load can be easily located. So, here from this curve this q u ultimate load that can easily be located from the peak of the graph. The next one is the local shear failure. So, in the local shear failure the characteristics of this local shear failure this type of failure is observed for the sand or clay soil with medium compaction that means sand is in medium dense or in soft soil it is moderate type of clay where this type of failure is observed. Now, here we can see the slight bulging of the ground surface adjacent to the foundation. So, here this is the bulging is more in case of general shear failure, but is the local shear failure the slight bulging has been observed adjacent to the foundation both side. So, another the significant compression of the soil directly beneath the foundation is observed. So, there is a significant amount of the settlement or compression has been observed beneath the foundation. So, a peak value of stress is not realized or located. So, from this graph here like the general shear failure here we are getting a particular peak value. So, it is observed in this general shear failure, but in the local shear failure we are not getting a particular peak. So, any peak or the failure point is not recognized, but in this local shear failure first what will happen that when we apply the load the settlement with increase. So, when this load reaches this q u 1 or this point there is a sudden jerk has been observed. So, that means at this point. So, there is a sudden jerk or when the this is a movement or the sudden jerk is observed. So, this point is recognized or this value is recognized the first failure point where the sudden jerk is in the soil movement is observed. So, if the sudden jerk in the soil movement is observed this corresponding load is recognized at first failure load. So, after that so here we can see that the failure surface is moving towards the outer over to the foundation and to reach this failure surface to the ground failure surface to the ground there is a sufficient movement in the soil is required. So, you can see this dotted line. So, as I mentioned that there is a significant compression or sufficient deformation or compression is observed directly beneath the foundation. So, to reach this failure surface to the beyond to this ground surface. So, there is a sufficient amount of movement is required movement in the soil is required. So, at that particular point where this condition is achieved corresponding load divided by unit area is called the ultimate load or the failure load. So, if the here this is basically 2 points 1 is q u 1 that is the first failure load and then the second point q u is the second or the ultimate failure load. So, this is local shear failure next one is the third one is the punching shear failure. Now, this is observed for fairly very loose soil or very soft clay. So, it is a loose sand or soft clay then poorly defined shear plane. So, here from this 2 surface we can say this is a failure surface or shear plane is observed or this mean occurred here there is a poorly defined failure surface there is no such that surface is observed or identified. Now, from this is shear plane then soil zone beyond the loaded area being little affected. So, here the soil zone beyond this foundation area or loaded area is little affected. Now, the failure surface in soil will not extend in the ground surface. Here in this case is general shear failure the failure surface is extended up to the ground surface, but here failure surface is not extended up to the ground surface. Now, the beyond the ultimate failure load q u the load settlement plot will be stiff and particularly linear. So, we can see that beyond this failure surface here also that this is the say suppose the failure surface q u this point is the failure ultimate failure load q u after that this line is basically linear and this line is very stiff. So, point after which the line is linear and very stiff corresponding this point and the load is called the ultimate failure load in case of this punching shear failure. Because here also significant penetration of wedge shape soil zone beneath the foundation. So, here also significant settlement is observed and will not get any peak like the general shear failure here also. So, here for after this point where this load settlement curve is very stiff and linear then this point is corresponding load is called the ultimate failure load. So, in this are the three different types of failure general shear, local shear and the punching shear. So, based on the laboratory test conducted by basic 1960 C on circular and rectangular plate supported by sand with different relative density. So, basic conducted laboratory test on circular and rectangular plate supported by sand with various relative density and he proposed zone of this different shear failure. So, from this is the load conducted. So, then this line is this side axis is q u by half gamma into b where gamma is the unit weight of the soil, b is the width of the circular plate or rectangular plate in case of circular plate it is diameter and in case of rectangular plate it is width and then this is q u 1 and q u. So, here we can see this is the smaller size of this it is sign indicates the first failure point which is observed in case of this punching in case of local shear and punching shear type of failure which is not observed in case of general shear type of failure and the bigger one is the ultimate failure load. So, here you can see that if the relative density is greater than 70 percent then the general shear failure is observed this is conducted on particular sand. So, general shear type of is observed is if the relative density is in between say 35 to 70 percent then the local shear failure is observed if it is less than 35 percent then the punching shear will be observed. So, this is the graph from this test we can draw the this another charts is presented this is in d f d f is the depth of the foundation and b star where b star is the 2 b l divided by b plus l where if it is the square footing or circular then b will be equal to l then b star will be equal to b. So, in that case we can see that this is the zone of the punching shear failure this is the local shear failure this is the general shear failure. Now, say suppose if this d by b star is say 2 and relative density is 60 percent then that if we place foundation depth such that it is b d f by b star is 2 and the relative density is 60 percent then this will be the local shear failure. Now, corresponding if the relative density is 20 and d f by b star is 2 then this is the punching shear failure. Similarly, for this this is from this based on this result we can draw this one plot is presented this is for relative density is a dry unit weight and this is the settlement versus by b b is the width of the foundation and this is the settlement of the foundation at failure. So, here we can say if it is the general shear failure then the settlement is observed around 4 to 10 percent if this is the settlement is observed say in between 4 to 10 percent if it is within this zone. So, for relatively small depth and in case of general shear to get the failure point the smaller settlement is observed that is 4 to 10 percent of the width of the foundation whereas, in case of local local shear and punching shear failure. So, this settlement is 15 to 25 percent of the width of the foundation. So, as we can conclude if the local shear or punching shear the more settlement is occurred to reach the failure point whereas, in general shear type of failure the less settlement is occurred to reach the failure point. So, now in this lecture we have discussed the different components of this failure and the different location where we will place the foundation. The next lecture I will describe of the different bearing capacity expression or equation and how to calculate load bearing capacity of the foundation or basically in case of shallow foundation how to calculate the load bearing capacity. Thank you.