 The last class I have discussed about the various soil exposition techniques like indirect methods and semi-direct methods, indirect methods test or taltates, then semi-direct methods it is boring. Now, today I will discuss about the indirect method to determine the soil properties to determine the soil properties or in situ soil properties. Now, first that penetration test that I will discuss in this section is standard penetration test. Now, this standard penetration test is widely used to determine the parameters of soil in situ. The test consist of driving a split prune sampler into the soil through a borehole at the desired depth. So, up to required depth where to drill the borehole and then you have to conduct the test at that level in order to drive the split prune sampler into that level. The split prune sampler is driven into the soil a distance of 450 millimeter at the bottom of the borehole. Now, hammer of 63.5 kg was used and with a free fall 76 millimeter to drive the soils to drive the sampler. The number of blows for penetration at least 300 millimeter is designated at standard penetration value. That means, this test is conducted in three stages. In each stages you have to penetrate the sample by 150 millimeter. So, first stage you have to penetrate the sample by 150 millimeter, then you have to count the number of blows required to penetrate that soil sampler into the soil by 150 millimeter. Then next stage you have to penetrate that sampler into the soil again by 150 millimeter and in the third stage you have to again penetrate the soil sampler into the soil by 150 millimeter. So, in three stage total 450 millimeter penetration is required and each stages you have to count the number of blows required to penetrate that 150 millimeter. Now, first 150 millimeter penetration number is generally ignored and the summation of last 300 millimeter penetration number is designated at as standard penetration number and this first 150 millimeter is ignored as these required for the sitting drive or it is ignored and the next two stages penetration value that is 150, 150 each or 300 millimeter penetration is called as penetration. Now, this is the test setup that this is the hammer which is used the weight of hammer is 63.5 kg and free fall is 760 millimeter and it is used to drive the soil sample into the soil within that pore hole up to the desired depth for three different stages. So, now if I go for this penetration value, so we can see that this hammer is driven and the soil sampler is penetrated for 150 millimeter, 150 millimeter, 150 millimeter in three stages and this free fall is 76 millimeter and each time this blows number is counted that is N 1, N 2 and N 3 and then the standard penetration resistance or SPT value N is the summation of this last two blows number that is N 2 plus N 3. Now, these number of blows for the first 150 penetration is neglected due to the disturbance like they exist at the bottom of the drill hole. So, because of this reason first 150 penetration number is neglected. The next is this test can be conducted at every one meter interval sometimes it is conducted for 0.75 meter interval or later on that interval can be increased for up to 1.5 meter interval. Now, this when this test is called as a refusal then there is three conditions one is that 50 blows are required for any 150 millimeter increment. If there is 50 blows are required for any 150 meter increment then it is called a refusal. Next condition if 100 blows are required for required obtained for required 300 millimeter penetration and the last one the 10 successive blows produce no advances and if there is any three conditions are observed in the field then we can say this is the refusal of test. Now, when we are driving this split wound sampler into the soil there is a difference some corrections are required those corrections are basically in three types one is for hammer efficiency correction another is overburden correction and next one is for the drill rod bore hole diameter and then the length of bore hole all these things some corrections are required. So, first this hammer efficiency correction now this SPT is standardized to some energy ratio. What is the energy ratio? This energy ratio is the ratio between the actual hammer energy to sampler that E a and input energy that means the input energy which is E i and the actual hammer energy required to penetrate that sampler into that soil which is expressed in percentage. Now, we can calculate this input energy is half into m v square where m is the mass of the hammer and v is the velocity of the hammer. Now, we can write this half into W by G into v square where W is the weight of the hammer and G is the acceleration due to gravity. Now, we can say this velocity we can calculate by using this expression to half root over 2 g h where h is the height of the free fall. Now, ultimately the input energy will be weight of the hammer into height of free fall. So, if we know the weight of the hammer if we know the height of free fall then we can determine what will be the input energy of that particular hammer of that particular condition. Now, actually in the field that this input energy may not require to is not applied to driven that soil sample into that test condition. So, we have to apply some correction. Now, here this is the correction say suppose N dash 70 it means that that say corrected N using the subscript for the E R B and the dash to indicate that it has been corrected. That means, this dash indicate that this N value or the field this is the measured N value and this dash indicated that that this N value has been corrected. So, it indicates that it has been corrected and with this 70 indicates that with a standard energy ratio value because as we have defined what is the energy ratio and then this 70 means this is the standard energy ratio. Now, in the field it is observed that this standard energy ratio is 70. So, here the standard general express this N value as in 70 standard energy ratio. So, now, we have to apply the other correction the C N is the correction due to effective overburden pressure and we can use this expression where P 0 bar is the effective overburden pressure and then we will get the C N value by using this expression. Now, this is very important for correction for the granular type of soil where this effective overburden pressure will play a very important role when you determine this SPT value because the near the ground surface this effective overburden pressure is less and when you go into the deeper strata then this effective overburden pressure is very high. So, that is why this that is some correction is required due to this less and more effective overburden pressure in different soil strata. So, now that in this correction factor we can correct that effective overburden pressure correction due to effective overburden pressure. Now, this N 1 this other correction factors are due to several factors that I will explain that that is this first one is the hammer efficiency correction and then the correction due to overburden pressure and then the other corrections are the correction due to drilled odd sampler and bore hole. Now, here how we will get this correction due to hammer efficiency? Now, one is this first correction factor is represented as the ratio of E R and E R B where E R is the energy ratio and E R B is the any standard energy ratio. Now, depending upon the type of hammer this E R value varies now generally these two types of hammers are used one is this first one is safety hammer and this is the doughnut hammers. Now, for this first type of hammers this doughnut hammers this E R value varies from 45 to 67 and for safety hammer this E R value if it is the rope pulley or cat head system then it is 70 to 80 and if it is a trip or automatic then this E R value is 80 to 100. So, how we will calculate this first correction factor or correction due to the hammer efficiency. Suppose, suppose if at the energy ratio at any condition is 80 and the standard energy ratio value is 70 then the efficiency correction due to hammer efficiency will be 80 divided by 70 that will be 1.15. If this E R value is say 70 and this standard one is 70 then this correction factor value will be simply 1. So, in this fashion we can correct this N value at any energy ratio condition depending upon the type of hammer we are using. Now, the second correction factor or this correction factor due to rod length if this rod length is greater than 10 meter then this correction factor is 1. If it is in between 6 to 10 meter this correction factor is 0.95. If it is within 4 to 6 meter this correction factor is 0.85. If it is 0 to 4 meter then correction factor is 0.75. Now, if N is too high for length less than 10 meter. So, if we use this length of this rod is less than 10 meter then this N value is too high. Now, correction factor for this sampler is if it is without liner this sampler tube then this correction factor is 1. If with liner and we are measuring this N value for dense sand and clay this value is 0.8 for the loose sand this value is 0.9. Now, similarly for the correction for the borehole diameter. So, we are we can use a different borehole diameter then we have to apply some correction for different borehole diameters. Now, if this diameter varies from 60 to 120 millimeter then this correction factor is 1 and if this diameter is 150 millimeter then this correction factor is 1.05 for 300 millimeter this is 1.15. Now, N 4 is equal to 1 for all diameter hollow steam auger where the spt is taken to the steam. So, this is another note. So, now, if we want to solve one example then we will we can understand how to apply this correction and how to calculate the corrected N value from the measured N value. Now, suppose this measured N value the field N value is 21 and the rod length is 13 meter and this borehole diameter is 100 millimeter and the effective overburden pressure is 200 kPa and the energy ratio is 80 and the sand is loose sand and without liner. So, the sampler type is without liner then what will be the standard N value or the corrected N value under the standard energy ratio 70 and standard energy ratio value 60. First we will calculate this standard or corrected N value under the standard energy ratio 70. Now for the under this energy ratio standard energy ratio 70 now this is the expression for standard N value or the corrected N value under standard energy ratio value 70. Now, as this P 0 dash is 200. So, by using this expression 95 point root over 95.7 is divided by P 0 bar in place of P 0 bar you can put 200. So, this value is coming 0.69. Now, as this first energy the first correction due to the hammer efficiency that the energy ratio actual energy ratio in the field is 80 and the standard energy ratio is value is 70. So, the correction factor will be 1.14 and the rod length is used 13 meter. Now, from this chart we can see if this rod length is greater than 10 then this correction value factor value will be 1. So, our this correction factor value due to the rod length is 1. Now, again this sampler correction factor it is without liner. So, we can see this this correction factor without liner is 1. So, we can write this correction factor for the sampler is 1. Again this diameter of the borehole is used as 100 millimeter. So, from this chart we can say if it is 60 to 120 millimeter then this correction factor is also 1. So, we will use this value is 1. So, ultimately the corrected n value under this standard energy ratio is 17 whether this measure 1 in the field is 21. So, after applying the all the corrections and we are expressed we are expressing this n value under a standard energy ratio that is 70. So, corrected n value will be 17. Now, it is observed that if this energy ratio is increased then this n value decreases linearly. So, by using this concept we can use that any energy ratio 1 and n 1 is will be equal to energy ratio 2 energy into n 2. So, this if we use this expression then the corrected n value for 60 standard energy ratio value will be 70 divided by 60 into 17. This 70 is this energy ratio value for the standard energy ratio value 70 and we are converting this standard energy ratio value 70 to a n value for standard energy ratio value 60. So, this will be 70 by 60 into 17. So, this value is 20 we are expressing this n value in a integer form. So, we can see that as the energy ratio value decreases then this n value increases or vice versa. So, in this way we can correct any measured n value under any standard energy ratio value. So, this fashion we can corrected it can be corrected for any standard energy ratio value any standard energy ratio value here it is corrected for standard ratio value 70 and 60. Next one is our IS code this recommends that we have to apply two corrections that one is over due to overburden pressure that is granular soil and another correction that IS code recommends that is the correction due to dilatancy that for it is applicable for saturated fine sand and silt. So, this first this n is the measured n value in the field and this n dash is the corrected n value after applying the overburden correction. So, C n is the overburden correction factor. So, we will get by using this chart this is given in this IS code that we can determine this n value C n value or correction factor due to overburden pressure the any effective overburden corresponding to any effective overburden pressure. Suppose this effective overburden pressure is 20 then this correction factor due to overburden pressure will be around 0.78 or 0.79. So, now if we can see think this if this effective overburden pressure is 10 ton per meter square then this correction factor due to effective overburden pressure is 1. So, we can say this 10 ton per meter square effective overburden pressure value is the standard value where this correction factor is 1. If this effective overburden pressure value increases from 10 to say 20 or 30 then this required correction factor that will decrease and if this value increases then this correction factor will increase. So, that means we can say that this because of this overburden effect this after the correction the in shallow depth if this effective overburden pressure is less than 10 ton per meter square or the corrected n value value will increase as compared to the measure 1 and as in the corrected n value if it is in this value is greater than 10 ton per meter square that will increase a decrease compared to the measure value. So, in the shallow depth this corrected value that will increase as compared to the measure value and in the larger depth or this corrected n value that will decrease compared to the measured n value in the field. So, this is happening because of the effect of effective vertical overburden pressure. Now, the next correction is the dilatancy correction. Now, once we get the corrected n value after applying the effective overburden pressure correction then that n value will use for the dilatancy correction. Now, if this n dash value is greater than 50 then we will apply this dilatancy correction. If this n value is less than 15 then we will not apply this dilatancy correction and we can apply this dilatancy correction by using this expression. Now, this dilatancy correction is applying because that if the n value is greater than 15 then soil is basically in dense condition. Now, if the soil is saturated fine sand all the silt in the dense condition then if we apply this hammer load or the to drive the split point sampler then there is negative due to this dilatancy effect this negative pore water pressure that will induce and because of the negative pore water pressure now our effective stress is the total stress minus this pore water pressure. Now, if this pore water pressure is negative then or total effective stress will be total stress plus pore water pressure. So, because of this dilatancy effect and as this negative pore water pressure is generated so this effective pore water pressure that will increase. So, we will get a higher value of n. So, because of this reason we have to apply this dilatancy correction to decrease or the reduce this value n value although there is no such this recommendation is in the IS code and on all other code this recommendation this value this correction is not generally applied, but in the IS code this it recommends that we have to apply this dilatancy corrections also. Now, this in this standard penetration test we are basically getting the standard penetration number n value. Now, by using this n value we have based on different correlations or charts we can determine the soil properties whether it is a this granular type of soil or in case of clay soil also. Now, if this n value it is in 60 standard energy ratio value then it is not this over burden pressure is not applied only this other corrections due to hammer efficiency and this bore hole diameter rod lens sampler type. So, all the corrections are applied we are not applying any over burden corrections. So, in this value if it is 0 to 2 then this undrained cohesion value is 0 to 12 k p a. And this soil we can say it is a soft soil. So, the how will identify visual identification or how will identify this soil the thumb can penetrate greater than 25 millimeter. Now, if this value is 2 to 4 then this C value is 12 to 25 and it is a soft soil. So, your thumb can penetrate up to 25 millimeter. Now, if it is 4 to 8 then this soil is medium soil and if it is 8 to 15 then soil is stiff. If it is 15 to 30 then soil is very stiff if this n value is greater than 30 then C value is greater than 200 then soil is hard. So, and these are the condition by which we can identify this soil. Now, these correlations or these value we have to use with very caution because this is not sometimes too. So, we have to do other perform other test also to verify these correlations or these values. Similarly, the granular soil also if this n value is 0 to 4 then this soil is very loose soil and relative density or dr is 0 to 15 percent. Now, if this n value 4 to 10 then it is a loose soil relative density 15 to 35 percent. If this n value is 10 to 30 then relative density is 35 to 65 percent and it is the medium dense. If it is 30 to 50 it is very it is dense soil and if this value is greater than 50 then relative density 85 to 100 then it is a very dense soil. So, we can also use this table to based on the n value we can identify or we can find the relative density of the soil and we can identify which type of soil it is. Now, there is so many charts or correlations are available by which if we know this n value either it is a field n value or corrected n value then by using those charts or correlation we can determine the soil properties, undrained cohesion or the friction angle file or any other properties of the soil. Now, here I am just explaining one chart that this chart by using this chart how we can determine the phi value of the soil. So, this n f is the field value without any correction and if we know this n f value and if you know the any at any depth what is the effective over burden pressure in k p a then by using suppose this n f value is 30 and effective over burden pressure is 150. So, this phi value will be in between 40 degree to 45 degree. So, by interpolating also we can determine what will be the fiber. So, from here this phi value is coming around 42 to 43 degree. So, in this way we can if we know the n value and effective over burden pressure we can determine the friction angle of the granular soil. So, by using this chart. So, there are other charts also and other correlations are also available. Now, next penetration test is the cone penetration test. Now, this cone penetration test is two types one is dynamic cone penetration test that is DCPT or static cone penetration test that is SCPT. Now, this dynamic cone penetration test it is similar to SPT test that is hammer driven, but this static cone penetration test is not hammer driven it is pushed into the soil in the ground at a rate of 2 centimeter per second. That means one cone is penetrated into the soil at a rate of 2 centimeter per second where here this cone is hammer driven. Now, using cone instead of split prune in the difference of SPT and this dynamic cone penetration test is that in SPT we are giving split prune sample here instead of split prune we are using cone and we are driving the cone into the soil and another difference is that in this SPT we are as we are using the split prune sampler. So, we can collect the soil sample from the desired depth, but using the dynamic cone penetration test this is the close end this cone. So, we cannot collect soil sample from this test. So, this is the basic difference that although this both are hammer driven, but here in the SPT we can collect the soil sample from the in a desired depth and by this dynamic cone penetration test we cannot collect the soil sample. And here SPT is SCPT it gives the continuous measurement of the soil resistance. So, now this gives blow count at the rate of 1.5 meter intervals. Now, first we will go for this static cone penetration test or SCPT. Now, static cone penetration test this IS code is 4968 part 3 1976 where this penetration test this instrument it has several components. So, this is the instruments. So, one components is cone assembly this is this portion is called cone assembly. Then this portion is called friction jacket. Then this portion this one is called the bottom mental tube and this is the sounding rod. So, these are the different components of this equipment that cone have a apex angle 60 degree that means this angle apex angle is 60 degree plus minus 15 meter 15 minutes. So, this is 60 degree plus minus 15 minutes and the cross section area or the base cross section area is 10 centimeter square. So, that means this base cross section area of this cone is 10 centimeter square. Now, next is how we will collect the soil use this instrument and how will get the soil resistance from by using this instrument. So, what are the steps how will operate this things. So, these are the four stages if by which we can operate this penetrometer. So, first position is this is the first position where the cone and friction jacket assembly this is the cone assembly and this is the friction jacket assembly this is in the stationary position. Now, this is the position to where this cone assembly is only pushed by the inner sounding rod at a rate of 20 millimeter per second. Now, this pressure gauge records the force Q c. Now, here only cone assembly is pushed into the soil by using this inner sounding rod and the pressure gauge records the force Q c. Now, this Q c is the resistance coming only due to this cone assembly. Now, if we know the base area of this cone that is AC then we can determine what is the cone or point resistance by divide by dividing this AC by dividing AC with this Q c. So, this small Q c is the cone or the point resistance that is equal to capital Q c or the force divided by the base area. Now, this cone assembly in the position 2 is pushed into the soil normally up to a depth of 40 millimeter. Now, in the second stage third stage of such position the sounding rod is pushed further up to a depth of b. Now, here the sounding rod is further pushed into the soil up to a depth of b that means the total a plus b. Now, here it pushes the friction jacket and cone assembly together. So, here by using the sounding rod the first second stage only cone assembly is pushed into the soil. Here in the third position cone assembly after in this condition from second stage then in the third stage this cone assembly and friction jacket both are pushed into the soil by using this inner sounding rod up to a depth of 40 millimeter. And this total force that is measured this is the force which is coming due to this cone assembly and this friction assembly. So, that means here we are getting the cone resistance or the team resistance and the frictional resistance. So, from the second position we are getting only the cone or team resistance, but that is the total depth that force is q c and if and in third position as this total system that the cone resistance and this friction assembly and the cone assembly both are pushed into the soil. So, we are getting the total force that is coming due to this cone or team resistance and the frictional resistance that is q 2. Now, here we know this q c capital q c here we know the q t. So, if we want to find the frictional resistance or the or the force that is coming due to only friction then we can use this expression we just just subtract this q c from q t we will get the q f that is the force due to this frictional resistance. Now, if we know thus this surface area of the friction jacket then we can determine the side friction f s. So, this is similar like a pile foundation where we are getting this tip resistance as well as the friction resistance. Now, just in the fourth position so now this outside mental tube is pushed up to a depth of a plus b that is 80 millimeter to bring the cone assembly and the friction jacket in the to the position 1. So, now from the fourth position in the fourth position we have to by using this outside bottom mental tube we have to bring this total cone and friction assembly in its original position that is in position 1. And in this process we can determine the cone resistance as well as the friction resistance that is coming from the soil. Now, so this is if we further explain this process. So, this is the total system which is in the stationary condition in the first stage. So, this is sounding rod this yellow one is the mental tube and this white one is the friction jacket and this portion is the cone assembly. So, in the first in the second stage this with the help of sounding rod only this cone assembly is pushed up to a depth of 40 millimeter and we can calculate or we can determine this force coming through this cone resistance and now if we know the base area then we can determine the cone resistance on this stage. Now, in the second stage so this is the similar stages. In the second stage by with the help of this sounding rod now the total system this cone assembly and the friction assembly both are pushed further 40 millimeter depth. And here we will get the total force and here we will get the force from the cone assembly. So, if we subtract this q c from this q t we will get the forces coming due to this friction resistance and with the outer if you know the outer here we will get the friction resistance in this stage. Now, in the third stage here it is the same stage in the third stage with the help of this mental tube which is further pushed into soil 40 millimeter. And this is the force stage where this mental tube is further pushed into the soil with the friction jacket and bring this assembly in the initial condition or the first condition. So, this is the total operation of this static cone penetration test or static cone penetrometer. Now, here we can say so this is the cone here we will get this cone resistance which is coming from here and this portion we are getting the frictional resistance F s and this is q c and this is the cross section area of the base is 10 centimeter square. Now, from here we can calculate this friction ratio F r which is F c by q c or sorry F s by q c. So, this is the friction resistance and divided by the cone resistance. Now, here by if we know the cone resistance then by using this expression we can determine the undrained cohesion of the clay soil by using this expression. Now, here this sigma v is the total vertical stress and N k is the cone factor depending upon the type of cone we are using. So, if it is the electric friction cone then these cones are basically two side types one is electric friction cone another is mechanical friction cone. If we use the electric friction cone then this N k value is 15. Now, if we use mechanical friction cone then this N k value is 20. So, if we know the total vertical stress and depending upon the type of cone we are using we can use the N k value. So, and if we know the q c from the field measurement then we will get the undrained cohesion of the clay soil. Similarly, in the sand soil we can find the E value elastic modulus of the soil for young normally consolidated sand by using this expression 2.5 to 3.5 q c where q c is the cone resistance. Now, again the similar to this S P T value also here if by from this S P T test also there are various charts are available where if we know this cone resistance or cone point resistance q c then by using this charts we can determine what is the relative density of the soil and which is the frequency friction angle of the soil. So, this is for normally consolidated quartz type of sand. So, for the granular soil we can determine the friction angle by using this charts. So, here if we know the vertical effective stresses then cone point resistance q c then for using this particular chart suppose this vertical stress is 200 and cone resistance is say 30 mega Newton per meter square. So, this will be this value will be in between 80 to 90 percent. So, relative density will be 80 to 90 percent around 85 percent. Similarly, if the cone resistance value is 30 and this is 200. So, you will get the corresponding phi value is within between 44 degree and 41 degree. So, it is around 43 degree. So, this is the value why this using this chart if we know this cone resistance then we can determine the phi value and the relative density of the granular type of soil. The next one is dynamic cone penetration test this IS code is standardized by this IS code 4968 part 1 1976. Now, this equipment consist of a cone driving rod, driving head, lifting equipments and a hammer because here is a hammer driven like SPT. So, hammer used for driven the cone shall be in mild steel or cast iron with a base of mild steel and the weight of the hammer is 65 kg. Now, cone is driven by a hammer of free fall is 750 millimeter is 750 millimeter each time. Now, this number of blows for every 100 millimeter penetration of the cone is recorded. Now, blows required for 300 millimeter penetration is noted as the dynamic cone resistance. Here also this 100 millimeter penetration each 100 millimeter penetration these blows required blow is recorded and blows required for 300 millimeter penetration is noted as the dynamic cone resistance. Now, this process shall be repeated till the cone is driven up to the required depth. So, again this dynamic cone penetration test is better than the this is better than SPT or static cone penetration if the soil is very hard such as the dense gravel. Then as could the SPT because we have to realize on the we have to rely on this correlations based on the blow counts. So, again this is the split point sampler which we used in case of SPT and this is the cone which is cone assembly which is or this which is used for the dynamic cone penetration test. So, here we can say this is a split point sampler this is hollow we can collect the soil sample by through this tube, but here it is solid. So, no sample is collected. So, this after this two types of penetration test now we will explain another field test by measuring the property of the soil that is pressure meter test. Now, this pressure meter test these are the different components of this pressure meter this is the pressure meter. So, this is the cylindrical probe. So, which expand inside the borehole. So, inside a borehole we have to insert these instrument and then these two things these are the guard cell and the middle one is the cylindrical probe or the measuring cell. So, this measuring cell is expandable. So, this expand inside the borehole and by using this expansion we can determine the properties of the soil. Now, this most rational in all in situ test gives strength modulus k 0 C b 0 C v values and we can use this for all type of soils. Now, how will expand? So, here this is the borehole and here this is the measuring cell and this is the guard cell. So, this is the expandable measuring cell and this when this measuring cell is expanded this guard cell is also expand to reduce the end effect of the measuring cell. So, now, after this measurement. So, initially we measure the measuring cell volume this is 535 centimeter cube. So, this is the initial volume or the measuring cell volume capital V 0 and we insert these measuring cell with guard cell into the borehole and then we allow this measuring cell to expand. Now, this process goes until the soil fails or this volume expansion reaches the limit of this measuring cell expands. So, now, it is assumed that if the expansion. So, this and then you have to draw a card. So, this graph by this applying pressure. So, corresponding pressure when you this volume is expand this volume during the volume expansion you are also measuring this pressure. So, this we have to draw the pressure versus volume graph. So, this is total cavity volume and this is the pressure p. So, this is the initial volume of the measuring cell then there is C 3 stages this is zone 1, zone 2 and zone 3. Now, this zone 1 is called as reloading zone. So, this zone 1 is called as reloading zone because due to drilling the soil volume in this hole that is not in its in situ condition. So, this volume will change. So, when in this zone after when it is reaches p 0 condition that means this form capital V 0 to V 0 plus small v 0 portion here it is reached in its initial condition and this in its initial pressure p 0 is the in situ soil pressure. So, this is reloading zone then this portion it is pseudo elastic zone. So, here we can see this volume expansion and the pressure this curve is linear. So, this is pseudo elastic zone and this third zone it is called plastic zone. So, here we can see from this first zone to second zone this del p is the pressure increment and del v is the volume increment. So, here V f is the final volume and P f is the creep stress or the yield stress and P l is the limit pressure. So, P f is the creep pressure or the yield pressure and P l is the limiting pressure. Now, here it is assume the soil is failed when the total expansion of this measuring cell is 2 times the in situ expansion upon if it is 2 times the capital V 0 plus V 0 under this condition we can say that soil fails. So, that pressure corresponding this pressure is called the limiting pressure. Now, by using this values we can determine the pressure meter modulus E p by using this expression. Now, where this V m we can find this is the mean value of V 0 plus V m and del p is the pressure difference between the yield pressure and the in situ pressure and del v is the volume difference between the V f and V 0. Now, mu is the position ratio now it is assumed to be 0.33. So, this is position ratio it is assumed to be 0.33. So, now once we calculate this E p now by using this correlations we can determine the soil properties also. So, for the clay soil undrained cohesion that we can determine by using this expression that is P l minus P 0 by N P where P l is the limit pressure and P 0 is the in situ pressure and N P we can calculate by using this expression. So, here also this is the undrained cohesion. Now, N P value is taken between 5 to 12 and average value is 8.5. So, now in this using this expression we can determine the undrained cohesion of the clay. Now, by using the different correlations this is the N value this N is the field standard penetration value. So, this is the correlation between the field N value and the E p value. So, if for clay this is 908 into the 0.66 and for the sand this E p value 1930 into the 0.66 for the sand. So, these are the two types of expression we are generally used. So, next test is the dilatometer test which is a similar type of test where this is advanced at a rate of 20 millimeter per second and test every 200 to 300 millimeter. So, a nitrogen tank is used to inflighting the membrane. So, this is the membrane 60 millimeter diameter flexible street membrane. So, we can use the nitrogen tank for inflighting this membrane and corresponding resistance we can measure and by using the chart like the cone penetration test we can identify different types of soil. And here it will give the undrained cohesion K 0 over consolidation ratio C v K and soil stiffness. So, piezo cone is the another type of this is the modern static cone penetrometer which. So, in the normal SCPT test we can measure the cone resistance and the friction resistance where this with is the piezo cone this is the modern static cone where we can measure the pore water pressure also this is the different components. So, this is the porous stone for pore water pressure measurements. This is the cone where we can measure the cone resistance, friction resistance as well as the pore water pressure. So, once we get this static cone penetration test. So, these are the different readings this is the tip resistance this is the friction resistance or the slip resistance and this is the pore water pressure. So, these are the different graphs. Now, another test which is also important in case of clay or very mainly for soft clay to determine the in situ properties of the soil that is the vane shear test. Here in the bore hole where this vane is inserted and we can apply a torque as a desired depth and this measure torque required to quickly shear the vane pushed into the soft soil. It is quickly so that we can simulate the undrained condition into the soil. So, by applying this torque and the corresponding resistance by the using corresponding resistance. So, if we can measure the torque the torque that we are applying. So, by using these things we can determine the undrained shear strength of the soil. Now, typical d value is using for 200 to 100 millimeter. So, this is the vane said is inserting the soil then we apply the torque and from that torque we can measure the undrained shear strength of the soil which is suitable for mainly very soft clay. So, this is the vane shear said which is in progress apply the torque in the soil. So, these are different types of soil. So, these are the soil this is the SPT test where bore hole is required. So, first we drilling the bore hole then we apply the SPT test. Then this vane shear test we apply the torque in the bore hole as desired depth. Then pressure meter test also in the bore hole is required and this is the CPT test where we pushed this into the soil and this is the this test also DMT also we pushed in the soil in the soil and then we expand this membrane. So, these are the different types of soil. So, in the next class I will discuss about the soil exploration by geophysical exploration. So, next class I will discuss this geophysical exploration and that will be the last topic for this soil exploration part and how we will use the geophysical exploration to determine the soil thickness and the properties that I will explain in the next class. Thank you.