 Welcome to lecture series on advanced geotechnical engineering and we are discussing module 3 compressibility and consolidation and this is lecture 9 and in this lecture we are going to discuss about methods for accelerating consolidation settlements and the radial consolidation concepts. So in the previous lecture we have solved some examples wherein it involves long time for consolidation particularly in depending upon the type of the properties of a soil it may take even even years to complete the consolidation. So in order to construct the structures or in order to eliminate the settlements before the construction of a structure there are methods which are available for accelerating these consolidation settlements. So in this lecture we will be concentrating on this aspect. So this is module 3 lecture 9 on compressibility and consolidation and we are actually addressing the methods for accelerating consolidation settlements and the radial consolidation concepts in this particular lecture. This is for accelerating consolidation settlements and we also said that the settlements which are elastic settlements, primary consolidation settlement and secondary consolidation settlement. So measured to the soils actually particularly have fine-grained soils they actually exhibit very high amount of primary consolidation settlements if they are normally consolidated or lightly over consolidated in nature. So before any discussion of a method the first and foremost method is that removal and replacement of a problematic soil. So one of the oldest and simplest method is to simply remove and replace the soil but soils that will have to be replaced include contaminated soils and organic soils if you are having or marshy soils and all. So this method is usually practicable if it is above the ground water table and also it is also practicable if the volume of the soil to be removed or replaced is have limited quantity. If it is involves the large quantities there will be difficulties or it will be highly an economical to go for removal and replacement technique. So in the instances when it appears that too much consolidation settlement is likely to occur and the volume of the soil which is actually involved also is large in nature. Then in that case in order to eliminate the appears that too much consolidation settlement if it is likely to occur due to construction of structures it may be desirable to apply some surcharge loading before the construction. So one of the earlier methods for accelerating consolidation settlements is called pre loading or pre compression. In this method a certain amount of soil fill is placed over a period of time. So we know that once the soil is loaded with a certain load intensity what will happen is that the pore water pressure initially increases and after attaining equilibrium then it undergoes dissipation. So this particular concept if you use once the dissipation is completed the soil effective stress increases then corresponding the soil shear strength increases. So in instances when it appears that too much consolidation settlement is likely to occur due to the construction of structures it may be desirable to apply surcharge loading before construction. This technique is actually called as pre loading or pre compression and has been used in many construction process with success and as reported by Johnson 1970. So this technique is called as a pre loading or pre compression and which is actually involves a loading of the entire area under consideration by a fill of desired height. So the question what we need to address is that what is the height of the fill required and how long we need to keep it and whether is there any stability issues which are actually required to be considered on when we are actually having a soft soils at the site. The pre loading of the surcharge will on top of the soil that requires consolidation this is placement what we said is that placement of a surcharge fill on top of the soil that requires consolidation and once sufficient consolidation has taken place the fill can be removed and construction can take place that means that if you are having let us say that 10 meter is the total height including the temporary fill and permanent fill then once the if the temporary fill happen to be 3 meters then the 3 meters can be removed and left with 7 meters so that after the consolidation it can be left with the permanent loading. So once sufficient consolidation has taken place the fill can be removed and construction can take place. So these surcharge fills are typically of limited height like 3 to 8 meters height and generally produces settlements in the range from 0.3 to 1 meter. So these fills when we actually load on the surface of the soil and they produce the so called the heights are 3 to 8 meters and this actually happens because the pore water pressure which is you know gets generated the excess pore water pressure gets generated because of the placement of the fill and this actually once the pore water pressure generated and it tries to you know dissipate subsequently when the process of dissipation of the pore water pressure the soil actually gains the effective stress and with that the soil actually the shear strength improves. So this is actually most effective in effective in clay soils. So in this particular slide a typical graphical form of this technique is actually shown here where we have the loading density on the y axis and time on the x axis and here this particular yellow fill area which is actually shown and that is nothing but the permanent fill and this is you know this color which is actually shown here which is the surcharge fill. So the question is that how much what will be the time for this pre loading or pre compression that is that this is the duration of the you know the pre compression and this is you know the loading density is sigma F plus sigma S once this is completed then you know this will remind the permanent fill will actually will remind and then the road embankment or highway embankment can be completed. So another question is that what should be the intensity apart from sigma F what will be the intensity of the sigma S which is required so that the desired settlements can be achieved. So in the bottom here the time versus settlement plot is shown here and this is if you are actually having permanent load only in order to get this consolidation settlement it may take long time in the sense that you know sometimes within the duration of the project it may not actually happen. So in view of that in order to accelerate the consolidation one of the viable option what we are actually thinking now is to pre load the area with a certain load intensity that is sigma S. So if that actually happens the settlement profile is actually shown here this is permanent load plus surcharge wherein you can see that moment you know the end of the pre loading comes that is the duration once it completes you can see that the settlement which is actually likely to occur after long duration after placement of the fill was found to occur and because of the additional loading there is an increase in additional generation of excess pore water pressure and then the dissipation of pore water pressure is you know faster and you can see that the settlements are also having higher magnitude. So this is the time versus settlement curve for permanent load and surcharge and this is only for permanent load only. So here in order to determine the magnitude of the surcharge pressure required to ensure that the total anticipated settlement under permanent load will be completed in a given length of time and so this is one of the objectives. One of the objectives of pre loading is that basically to determine the magnitude of surcharge pressure required to ensure that the total anticipated settlement under permanent loading will be completed in a given length of time and another objective is that to determine the length of time required to achieve a given amount of time under a given surcharge load. So to determine the length of the time required to achieve a given amount of settlement under a given surcharge load. So we will try to see the methodology which is actually involved and this is actually very simple and wherein we can actually find out generally the time which is actually defined now like let us say that we want the settlements to occur the pre loading period to be 9 months or 10 months whatever it is if you have to specify it and in that particular period to achieve the settlement what will be the intensity is required that is required to be found out based on the subsoil or the clay characteristics. So let us consider a case where given construction will require a permanent uniform loading intensity of sigma f that is what we said is that this is the sigma f then total primary consolidation settlement due to permanent loading is estimated to be equal to SCF that is the SCF that is and in order to eliminate the expected settlement due to primary consolidation a total load intensity of sigma plus sigma f plus sigma is equal to sigma f plus sigma s will have to be applied. So the additional load intensity sigma s will accelerate rate of settlement and when a total settlement of SCF has been reached the surcharge can be removed. So the additional load intensity of sigma s will accelerate the rate of settlement when a total settlement of SCF has been reached the surcharge can be removed that is the additional surcharge which is placed in the form of a temporary fill can be removed. So here one thing we need to notice here at any if you are having a double drainage that is a HD is equal to 2H and that water flows in both the directions so HD is equal to 2H and the drainage path is H here that is HD is equal to 2H by 2 that is H here and this is the at any time T so this is before applying the preload once the preload is actually applied the pore water pressure the value of the degree of consolidation is attained one here and one here at the top and bottom because of the double drainage prevalence and at this mid plane you can see that there is a major amount of pore water pressure at to be dissipated. So you can see that this much portion is at to be dissipated this much portion is already dissipated. So this is you know the UZ at Z is equal to H the pore water pressure at this particular plane and if you are actually having if you are taking average consolidation and that will actually come here. So in this case it appears here that you know though we actually take certain amount of degree of consolidation but here and here already the consolidation actually has you know achieved because of the removal of the load there can be possibility that the net consolidation settlement is because of the some settlement which continue to happen here and some swelling which actually happen here and here. So in case of one way drainage one way drainage when you are actually having then you can see that this is the isochrone at any time T after placement of the fill and this is the bottom base where the impervious layer is actually there at the if you are having another clay layer it is actually at that particular plane and this in this case the HD is equal to H because the drainage path water flows in this direction only water flows in this direction because water cannot go through the rock or impervious medium. So in this case this much portion is already dissipated and this is the mid plane consolidation here as UZ is equal to H. So the degree of consolidation UZ will vary with depth and will be minimum at mid plane that is at Z is equal to H. So if the average degree of consolidation U average is used as the criterion for surcharge load removal then after removal of the surcharge the clay close to and plane at the close to the mid plane will continue to settle and clay close to the previous layers will tend to swell that is the clay close to previous layers will tend to swell. So because of these reasons Johnson 1970 has recommended on the conservative side for assessing degree of consolidation for the removal of surcharge the consolidation degree of consolidation predicted at Z is equal to H or mid plane consolidation. So this will result in the net consolidation settlement so the entire the phenomenon what has been discussed will result in the net consolidation settlement. So now what we are doing is that according to Johnson 1970 it is preferable to use the mid plane degree of consolidation that U is equal to U at Z is equal to H. Now we can write the consolidation settlement as SC is equal to HT by 1 plus E0 CC log sigma 0 dash plus sigma F by sigma 0 dash. So here sigma F is the permanent fill and once we compute the final consolidation settlement then compute SC F plus S that is fill plus surcharge. So in this case HT by 1 plus E0 CC log sigma 0 dash initial effect to orbit and pressure plus sigma F plus sigma S divided by sigma 0 dash. So we can define the degree of consolidation as SC F that is the you know the consolidation settlement without any preload and with the preload and surcharge that is settlement without any preload and settlement with preload and permanent load that is SC F by SC F plus S. So by substituting these here 1 and 2 here in 3 we get U F plus S is equal to logarithmic of 1 plus sigma F by sigma 0 dash divided by logarithmic of 1 plus sigma F by sigma 0 dash into 1 plus sigma S by sigma F. So here if you see that this is sigma S by sigma F this is the you know the dimensionless term for sigma S is the magnitude of the fields are charged to be placed sigma F is the permanent fill and sigma F by sigma 0 dash is you know nothing but sigma F by sigma 0 dash is nothing but the ratio of permanent fill to the initial orbit and pressure. So this particular design can be done by using this or by using the charts which are actually available and further as has been told in order to get the U F plus S it is actually required to use this particular chart to determine the time factor. So by once we know the value of the suppose if you are actually let us say that we need to you know set a target for completion of the preload is say in say definite period of time say 9 months. Then for 9 months and what is the time factor we can determine. Once the time factor is actually known to us based on that you can actually determine what is U F plus S. Once the U F plus is actually obtained then by using this particular plot we can actually determine you know what is you know the ratio of sigma S by sigma F. So the values of U F plus S for several combinations of sigma F by sigma 0 dash this is the permanent fill surcharge to the initial effect to orbit and pressure the different values are actually given here and sigma S by sigma F value is actually given here and note that U F plus S is equal to U Z at the mid depth that is what actually has been considered according to Johnson 1970. Now once we know the U F plus and once we know the sigma F by sigma 0 dash we can actually calculate what is sigma S by sigma F required. So by knowing sigma F we can actually calculate what is the magnitude of the such a so once the time is actually known a period of placement then we can actually find out or vice versa we can also know go from once the fill surcharge is actually known we can actually also go from the reverse direction and calculate what is the time. So this once we know sigma F and sigma 0 dash and sigma S and sigma F they determine U F plus S and then calculate the time factor and then calculate the time which is required to be maintained in order to achieve this so called the settlement which is actually unspated because of the without any permanent load. So this is the procedure for the preload. Now let us consider an example where during the construction of highway bridge it is proposed to expected that average permanent load on the clay layer will increase by about 150 kilo Pascal's and the average sigma dash at the mid depth of the clay layer is given as 210 kilo Pascal's and given that thickness of the clay layer is 6 meters and double drainage that means that effective drainage path is 6 by 2 meters CC compression index is 0.28 and effective the initial void ratio is 0.9 coefficient of consolidation is 0.36 into meter square per month and then the clay is normally consolidated in nature. So determine the total consolidation settlement of the bridge without pre compression and determine the surcharge intensity sigma P needed to eliminate the entire pre consolidation settlement by pre compression within 9 months. So here if you notice that the time which is actually required for the placement of the field is actually defined here. So we can actually adopt like this calculate the consolidation settlement and this settlement works out to be 167.7 mm so this cannot be a tolerable settlement for a bridge. So hence by taking T v is equal to T suffix s where the time required for surcharge C v by H dr square once you get this we will get the time factor. Now once the time factor is known to us that is 0.36 and using you know this plot which we have discussed that is for sigma f by sigma 0 dash that is 0.5 over 548 and uf plus s is 47% we can determine like this for 47% and 0.548 you can see that this comes to be around sigma s by sigma f comes to be around 1.8 or so. So with this what we get is that sigma s which comes to be 1.8 into 115 that is 207 kPa so the throttle field intensity it comes to be 207 plus 115 is about 322 kPa and this looks into that you know if you are actually having an embankment which is actually constructed say equivalent to if you are having a unit weight of 20 kilo Newton per meter cube as the field material then you can see that the height which is actually required is about 16 meters. If you are actually having a soft clay and placement of 16 meter fill which requires also long time to for the placement and also it need to be done in minimum 4 to 5 stages and also have the issues of stability issues and base failure and all those things cannot be ruled out. So in such situations you know one have to think about you know other avenues for accelerating consolidations at limits and this have evolved as the you know some sort of vertical drains because in the we have also discussed one problem where if you are having a sand lens which occurs in maybe in alluvial areas and because of that what will happen is that there can be a possibility of the acceleration of the consolidation. So as the horizontal drains are difficult to install below the ground level then one of the viable options is to go for the vertical drains with the partial replacement of you know the impervious soil or soil having very low permeability with the soil actually having very high permeability or having a material which actually has got that equivalent discharge capacity as that of you know the soil which actually has got very high permeability. So before that let us look and discuss about the advantages and disadvantages of preloading and requires conventional at moving equipment any grading contractor can perform the work long track record of the success and the surcharge fill must extend horizontally at least 10 meter beyond the perimeter of the planned construction which may not be possible at confined sites. Sometimes in the confined sites you have to all and use some reinforced soil wall technique so that you will be able to have a steep slope for the particular height which is being planned and then one can actually fill within the you know area which is actually developed to be developed and transport of the large quantity of the soil required you know this is actually one thing where it will significantly affect the carbon credits of the project and surcharge must remain in place for months or years this delays the construction and more over placement of the fields beyond 10 meters can lead to you know the uneconomical issues as well as the stability issues. So in such situation you know we actually can thought of can be you know one other avenue which can be thought is that as discussed earlier the radial consolidation through radial consolidation through provision of vertical drains. In order to accelerate the process of consolidation settlement for the construction of some of structures the useful technique for building is to build vertical drains. So vertical drains influence in the form of sand it is actually started with you know the sand drains method then subsequently for a short time weak drains do exist then afterwards a prefabricated vertical drains actually have come into picture. So the sand drains basically they are of diameter ranging from 400 to 600 mm and they are actually placed by you know augurring a borehole and then removal of the soil after removal of the soil the sand is actually placed the selected sand material having certain grade characteristics and are to be replaced. And another method of this thing which actually has come because of the demerits of the sand drains is to large diameter and then also the you know the construction of these things it takes long time. So because of that you know the weak drains actually have come the weak drains also the it involves the augurring of the borehole and then replacement of the removal of the soil and afterwards a weak drain with a geotextile bag filled with sand is actually placed and but however these also have not lasted for long. But the recent past for the past two decades you know the prefabricated vertical drains which are actually having a polypropylene or suitable material as the core and the polyester or polypropylene geotextile as the jacket material and which actually is you know Tyler made product which actually has got high drainage capacity even under the hostile conditions in the field. So the clays of the clay sediments take long time for completion of consolidation. So the provision of this vertical drains what will happen is that and you know the drainage paths actually has got what we facilitated the clay you know the additional drainage paths along the radial direction. So the consolidation now in this direction it actually happens in radially as well as in the vertical direction. So because of that what will happen is that the rapid you know the mobility you know rapid settlements will occur and the project sites can be ready in a short duration of time. So by inserting vertical drains fairly at close spacing induce much shorter horizontal paths for the water pore water pressure to dissipate and in turn they enable faster dissipation of excess pore water pressure and accelerate the consolidation settlements. The vertical drains are installed under a surcharge load to accelerate the drainage of impervious soils and does speed up the construction. So generally the vertical drains when they are placed they are placed along with the preload or pre compression. So the two they go with each other where once the first of all this on the site the drainage blanket need to be placed and which also serves as a restoration layer for access layer for the site to maneuver the rigs and all. And then through that the vertical drains are installed and once above that the fill is actually placed so that the vertical drains which are actually installed in a surcharge load to accelerate the drainage of the impervious soils and does the speed of the construction. And these drains provide a shorter path for the water to flow through the and get away from the soil and time to drain clay layers can be reduced from years to couple of months. So from the drastically the time can actually be shortened and because of that which actually happens is that the time to drain clay layers can be reduced from years to couple of months. So this is a typical preloading versus sand drains cross section is actually shown here where in a typical sand drain is actually placed in a compressible soil where and this is the collected drain and this is this drainage blanket. So what is actually shown here is that you can see that the water migrates you know this is the now the drainage path for this and this is what drainage path for this. So this drain actually facilitates the water and the along with the in case of the double drainage water flows in this direction and water flows in this direction. So because of this what will happen is that there is a combination of coupled consolidation actually happens with the radial consolidation and the vertical consolidation happens simultaneously. So when you compare the components of radial consolidation and you know the vertical consolidation the vertical consolidation component will be very less the radial consolidation component will be very high. So because of that the settlements will be you know very fast settlements will be faster. So here a preloading along with the drains is actually shown here. So with the preloading along with the drains one situation what happen is that the time versus settlement diagram is shown here. So this is the pre consolidation settlement which actually is possible. So what we have discussed is that when we have got only preload and permanent load and surcharge we said that you know this much time we have to keep the permanent surcharge and then also the magnitude will be much higher. But when we have got the preloading along with the vertical drains there is a possibility that this consolidation settlement can occur in a relatively short duration of time and whereas another issue is that the settlements time versus settlement the settlement variation will be relatively faster. So because of that the clay consolidates relatively faster. So here the schematic view of preloading along with the sand drains is actually shown here. So here the vertical drains one point we need to note down is that the vertical drains accelerate the settlements but do not reduce the final settlements. It is not that you know the placement of the vertical drains will not reduce the magnitude of the settlement but they tend to accelerate the settlement. They tend to accelerate the settlement only. So here a relatively you know a typical cross section of a clay where of thickness ht and ht is equal to 2h the 2h is this side and it is a double drainage layer and where we are having a water table here and the fill which is actually placed here. So here this undergoes radial consolidation the water flows in this direction water flows in this direction and this zone what actually shown here this is actually called as this smear zone. But if you look into this each drain in the plan area it actually you know caters to a diameter which is actually called as the equivalent area for a drain and so we need to also think about what spacing we need to place them and what layout we need to place them so that the radial and vertical consolidation can occur efficiently. So the governing differential equation for both vertical and radial consolidation is shown in this here. This is after the barons and where dou u by dou t is equal to cr into dou square u by dou r square plus 1 by r dou u by dou r plus cv dou square u by dou z square. So if you look into this now we have discussed previously the one dimensional consolidation where we actually have got this particular component only. Now because of the radial component where we have got cr that is the coefficient of consolidation in the radial direction it is also referred as coefficient of consolidation in the horizontal direction as we know that coefficient of permeability is relatively more than coefficient of consolidation coefficient of permeability in the vertical direction because of sigma h less than sigma v for normally consolidated soils. In such situations what will happen is that the ch also will be more than cv. So because of the ch also ch is also more than cv so that also you know the permeability is actually more and the ch is also more because of that what will happen is that it contributes to the rapid consolidation of the clay layer under consideration. So here the u is the excess pore water pressure or is the radial distance measured from the center of the drain well. So this is the drain diameter what it is called and if you are actually having a prefabricated vertical drain it actually comes with the breadth and certain thickness then equivalent diameter or equivalent diameter of the well is actually considered and u is the r is the radial distance measured from the center of the drain well and cr is the coefficient of consolidation in the radial direction or horizontal direction. So there are the two different types of layouts of vertical drains are in vogue. One is with square layout what is called this is the square layout which is actually shown here and this is you know this is actually shown as the triangular layout. So you can see that each and every the orientation of this is a equated triangle. So this magnitude is yes is called the spacing from center to center of the drain and this height is s by root 3 and this particular you know is called as equivalent radius or this area is called equivalent diameter. So this influences that this drain caters to the this much area so the water which is actually there in this direction will actually try to come into this. So this facilitates for the drainage of the you know the water. So this drainage of the water which actually happens because of the placement of the fill above the drain this is in the case of the squares layout where you can see that the s is the center to center distance between the drain wells and this is the you know the distance s and this is the r. So the equivalent radius or equivalent diameters are obtained like s square which is nothing but s square s into s is equal to pi r square the pi r square is nothing but this influence area. So with that what we get is that r is equal to 0.564 s and r diameter is equal to 1.13 s. So this of when we have got equilateral triangles so what we do is that pi r square that is this area this area is equivalent to 6 equilateral triangles we have to take into picture. So with that what will happen is that 6 into root over 3 by 4 into s by root whole square by simplification you get equivalent radius as 0.525 s and which is nothing but d is equal to 1.05 s and similarly for the prefabricated vertical drains when you look into for prefabricated vertical drains as been told these prefabricated vertical drains or these prefabricated vertical drains are actually having certain breadth and thickness and the dimensions are relatively smaller compared to the sand rig conventional sand rigs. So this is the influence zone and this is the diameter and so here also the same you know is calculated s square is equal to pi r square r is equal to 1 by pi root 1 by root pi s and which is nothing but r is equal to 0.64 s and this is for the square pattern and in case we are having if we are having let us say is the triangular pattern and in the triangular pattern where we are actually having this x organ what you can see is that so because of this 6 equilateral triangles we are considering area of the each equilateral triangle is root over 3 by 4 into s by root 3 whole square and with this area of the 6 equilateral triangles works out to be 6 into root over 3 by 4 into s by root 3 whole square which comes out to be root 3 s square by 2 and which is equivalent to pi r square is equal to root 3 s square by 2 where r is equal to 0.525 s so this is d is equal to 1.05 s so if you look into this is the equivalent diameter so out of the two layouts which we have discussed in the square layout and the triangular layout the triangular layout was found to be efficient in inducing uniform consolidation to the soil this is actually reported based on the case studies which are actually done in the field by several investigators where by monitoring the consolidation in the field by measuring settlements or measuring pore water pressures with that it has been found out that the triangular layout of the either PVD is or the sand drains or conventional vertical drains will give the efficient way of consolidating the consolidation of a soil. So this is a typical prefabricated vertical drain which actually shown here Joe's synthetics basically here the Tyler made products which are actually used as the substitute for the sand columns and nowadays with the availability of the sand is becoming scarce and with the availability in the sense that the proper material so because of that you know the use of this type of materials is one of the viable option and also these use of this prefabricated vertical drains accelerate the consolidation settlement equally as compared to the conventional vertical drains as well as you know the installation is actually relatively simple and faster. So this actually has got a dimensions are approximately 100 mm to 4 mm there are the several designs which are actually available and the thickness is about 4 mm and which actually has got you know this is the core where it facilitates the water and this Jota style which is basically non-oven in nature and the pore size of this Jota styles to be such that the only water enters into the drainage channels or the core channel where the polypropylene core is there and the clay is actually retained at the boundary itself. So because of that what will happen is that there is a possibility that the water only enters suppose if the Jota style which is actually selected is not having adequate you know the large pore sizes there can be possible to the clay enters and then the prefabricated vertical drain channels will get blocked then the efficiency of the drains will get actually affected and the subsequent to the consolidation gets affected mostly there about 100 mm wide and 4 to 5 m thick and they come in the rolls and they are actually installed as is actually shown in the ground from the drainage blanket. So once these are actually installed then once it is subjected to loading then there is a possibility that the water actually you know uses this channel and then tries to come out, once the water is actually coming out that means that the dissipation of the pore water pressure is happening and that means the settlements are continue to happen. So with that the clay consolidation will be completed in relatively shorted duration and nowadays these prefabricated vertical drains are actually being used for number of applications in the case of like municipal salt waste landfills and in order to particularly in the bioreactile landfills and they are actually being used for you know for extracting the gas and with that what is actually happening is that the gas extraction is becoming efficient. So with the and then also the settlements are actually also relatively faster and then another thing is that if you are actually having a contaminated flume there is a possibility that these things can be installed and then can be used for you know accelerating the consolidation, the removal of the contaminated zone or contaminated liquid which is actually trapped in the certain amount, certain portion in the ground and the another application which is actually in the recent past is actually coming up is that use of these prefabricated vertical drains for mitigating liquefaction which is also in this but in this case the soils are relatively fine that is silty sand or sandy soils wherein this also facilitates for you know in the case of eventuality of the earthquake there will be excess pore water pressure generation and these are also there is a transient in nature and because of that what will happen there is a possibility of provision of these things these you know prefabricated vertical drains facilitate the drainage at the moment when it is required. So in the process what will happen is that the soil will be you know prohibited from the undergoing liquefaction so that the structure will not be subjected to the danger which is anticipated when these are not there. So these are you know the PVD roles which are actually displayed here this is which actually comes in number of the certain role length and this is the you know the core. So these are different manufacturers actually has got different core styles and this is the jacket which is the filter jacket what is called which is actually made of again nano one geotextile and these are the types of PVDs the dimensions range from 92 to 100 mm and thickness actually ranges from 3.4 to 6.1 mm. So you can see that different geotextile filters are there and in case of some limited life geosynthetics are used that is like the jute is also can be used as a filter and the core in place of the core in case of limited life geosynthetics there are also several investigators actually worked on the choir as the core within the jute jackets and these are the you know different polyethylene and polyester and polyethylene these are the different core materials and these different core configurations are shown here whatever may be the core configuration under pressure it has to be ensured that the drain will not actually you know sacrifice the discharge capacity the discharge capacity in the sense that depending upon the permeability of the soil the discharge capacity of the drain will be selected. So if we are actually having a core which actually is prone to collapse with because of the lateral stress then it is actually going to affect the performance of a performance of these PVDs. So this PVDs also they have got the certain quality control test first of all the tensile load and strain behavior need to be investigated and also we need to see under buckling or under single buckling or second to you know two buckles what will be the permeability in plane permeability and what is the discharge capacity need to be assessed beforehand and once these are ensured and appropriate material need to be selected so that the you know this can be used for put into use. So these are the different types of PVDs which is actually shown here different manufacturers vary the core which is actually shown here. So the installation in the sense that the PVDs are installed by using a mandrel mounted or an installation machine and mandrel is a metallic hollow shoe either rectangular or cylindrical and the cylindrical one which actually contains the PVD. So a disposable metallic shoe is actually connected at the end of the mandrel so that the PVD can be easily inserted within the soil. After inserting the PVD the mandrel is extracted while the PVD remains in position within the ground. So schematic way of the rig which is actually shown here and the roll is actually mounted and connected to this with that what will happen is that the roll which actually runs like this and the PVD is actually drawn into the ground. So this is the mandrel so with this you know what is actually happens is the disturbance which is actually caused because of the installation of the sand drain it can be reduced the so called the spear effect can be reduced and this is the PVD in position here. So that no time the soil is in contact only it can come in contact with the soil while extracting this mandrel once the PVD actually has been placed in the desired depth. So this is you know the one of the sites where in Mumbai where the marine clay which is actually encountered and where this is for the one of the warehousing corporation where they wanted to install prefabricated vertical drains and then place the preload of 4.5 meter height where in here because of the confined boundaries on the peripheries temporarily reinforced slopes actually have been constructed and within that fill area within the pond which is actually developed then in that the so called you know the soil actually is placed. So before that you know the PVDs of appropriate variety actually have been selected and this is the this is you know a PVD role which is actually being inserted. So we will actually look into the installation how it actually happens in the field. So here you can see the softness of the clay the this is nothing but is the drainage blanket and the mandrel is actually being driven into the, mandrel is being driven into the ground. So this is the warehouse corporation which is actually existing warehouse corporation and this is also for you know enabling you know placement of the loads over that area. So the consolidation is actually is planned to be accelerated by using the placement of the PVDs and the preloading. So afterwards it is put to use for the desired purpose. So you can see that now the mandrel is being extracted and the PVD actually has come out. Now it will be seen yeah now the PVD will be cut and the next location is actually selected and that is the placement of the sacrificing shoe and this will be penetrated into the ground and these are actually inserted at the pre-marked locations so that the desired spacing of let us say 1 meter or 1.5 meter are achieved and with that what will happen is that the grid pattern which is actually here in this case a triangular pattern has been selected as we have discussed that this will actually ensure the uniform consolidation and also the relatively uniform consolidation. So because of that this triangular pattern has been selected you can see the ground is actually planned with the number of PVDs actually have been installed and this process continues of installing the you know PVDs so in a way as we can see that the installation is very very rapid with that what will happen is that the PVD installation can happen in a relatively shorter duration. Now we have actually discussed about the placement of the fill which is normally about you know we have the issues of you know the stability as well as the placement in a procurement of these materials. So in such situations in the recent past you know the one of the techniques which is actually coming into the picture is called vacuum surcharging and this can be efficient up to equivalent to 4.5 meter fill and so this can be you know done when we are actually having a requirement of a 4.5 or 8 meters fill and then we can also when we do along with PVDs and this technique was found to be very very efficient. So if you look into this this vacuum surcharging this is the conventional preload and here what we said is that and if you are actually having you know suppose if you are having a certain hydrostatic pressure pore water pressure when you load you actually have very high initial excess pore water pressure and then subsequently what will happen is that the water transfers the pressure to the soil. So with that the pore water actually in case of preloading the only positive pore water pressure changes will be there but in case of vacuum surcharging the pore water pressure changes are under the negative side it is actually called as inducing suction to the soil. So here also what will happen is that this is the effective stress change with this what will happen as we know that once we have got the negative pore water pressure which is actually induced to the soil this also was found to be very efficient in increasing the effective stresses to the soil but the limitation is that you know the suction can be induced up to minus 80 to 100 kilo Pascal's. So it is limited to about 4.5 to 5 meter equivalent field. So when it is used in combination with you know the PVDs then there is a possibility that this efficiency will be very high and this how it looks like in the field and another thing is that you know controlling this over a long you know large sides is actually difficult. So in such situations this for the small sides where we can actually avoid the placement of the fields and another important issue actually happens here is that the vacuum generation can be generated instantaneously if you are actually having the efficient or you know pumps which are actually a vacuum pump which is actually placed. So here this time pore water pressure changes for a soil so what will happen is that initially when this is the hydrostatic pressure which is actually there in the side then once we actually have the you know suction is induced then what will happen is that the suction will actually initially will be large and then slowly that suction will get transferred into the you know increase in the effective stress. So the more on this we will actually discuss in the next lecture where in we discuss about the some design aspects of the you know the prefabricated vertical drains along with the preloading along with the drain what will happen in this particular example we discussed and we found that when you have when you do not have the drains then there is a possibility that requirement of very high you know large fill heights are required. So in such situations what will happen when we actually have combination of drain and preload and then if you are actually having the scarcity of the fill materials then one of the alternatives is to go for the vacuum surcharging so we will try to discuss about the merits and demerits of this preloading in compared with along with the vacuum surcharging. Many sites vacuum surcharging prefabricated vertical loading and also a certain amount of preloading the combination is also used.