 Welcome to lecture number 6 of module 1 of advanced geotechnical engineering. So in this lecture we are going to discuss about index properties. In the previous lectures we have understood about clay particle water interaction and different methods to determine clay minerals and sedimentation analysis. Before introducing sedimentation analysis we also discussed the method for determining gradation of coarse grain particles. When you have got a soil which is having fines more than 12% then we need to do sedimentation analysis or it is also referred as hydrometer analysis. So hydrometer analysis is basically used to determine the gradation of fine particles. Hydrometer is a device which is used to measure the specific gravity of liquids. As you see in this slide you have a hydrometer with dimensions in millimeters and it has got a stem and a bulb at the bottom. This is used basically to measure the specific gravity of the soil suspension. So with this it is possible to measure the specific gravity from time to time as the soil settles the specific gravity can be SS. For a soil suspension the particle starts settling right from the start and the unit weight of the soil suspension changes from time to time. So here in this slide as it can be seen that this is at the commencement of the test and once the hydrometer is placed then the specific gravity of the suspension is measured after elapsing a time t2 and again the reading is taken and here you can see that the particles which are actually settled at the base and after certain time t2, t3 and t4 and this situation of the settlement of the particles is shown. The measurement of the specific gravity of the soil suspension at a known depth at a particular time provides a point on the grain size distribution curve. So here the process of the sedimentation of the dispersed specimen is shown here. When you have got a time t is equal to 0 you have got a suspension and if you have a sampling depth at a depth z from the top surface of the suspension it can be written in the form of a phase diagram as shown here with total volume 1 and volume of the solids and volume of water and with the weight of water on the right hand side and weight of solids on the right hand side. So with these volume of solids is nothing but W s divided by G s gamma w and the volume of water which is nothing but 1 minus you know this total volume that is this volume of water is nothing but 1 minus V s and substituting here you will get volume of water is equal to 1 minus W s by G s gamma w. So the gamma i is nothing but the suspension at any time nothing but weight of W water plus weight of the solids divided by total volume 1. So that is written here as weight of solids plus gamma w V w whole divided by 1. So by substituting for V w you will get the initial unit weight of the unit weight of a unit volume of the suspension gamma i as gamma w plus W s into G s minus 1 divided by G s. So this here the G s is nothing but the specific gravity of the soil solids. In the process of the sedimentation of dispersed specimen here at level xx if you assume here the size of the particles which have settled from the surface to the depth z in time td this is from the Stokes law when you use we can actually obtain d is equal to square root of 18 mu divided by G s minus 1 into gamma w root over z by td. So z is the reference depth where the measurement is being taken. So above this level x no particle of size greater than d will be present and in element depth of d z you can see here this is small element depth above this level xx at a depth z from the surface of the suspension may is assumed that the uniform and the particles of the same diameter exist. So the particles are smaller than d and they actually have a uniform specific gravity it is assuming in that particular elemental distance. If the percentage of the weight of the particles finer than d already sedimented to the original weight of the soil solids in the suspension is say N dash. That is if the percentage of the weight of the particles finer than d which are already sedimented to the original weight of the soil solids in the suspension is say n dash then we can actually get the weight of the solids per unit volume of suspension at depth z as n dash into W by v where Ws is nothing but W by v. Unit weight of the suspension after elapsing a time td at a depth z is given by from the previous discussion gamma z is equal to gamma w into n dash into W by v into gs minus 1 by gs. So with these we can actually obtain n dash as gs by gs minus 1 into gamma z minus gamma w into v by w where n dash is in present days. So the process of sedimentation with dispersal specimen but here gamma z is nothing but gs gamma w where gs is nothing but 1 plus rh by 1000 into gamma w where gs is the specific gravity of the soil suspension which is nothing but the graduations on the hydrometer. The graduations on the hydrometer generally varies from 0.995 to 1.030 over a length of the stem. So rh is the reading on the hydrometer what it is noted during the process of experiment. So n dash is obtained here as gs by gs minus 1 into rh by 1000 into v by w which is simplified further for volume of say 1000 cc of the soil suspension placed initially we can actually get n dash as gs by gs minus 1 into rh by w. W is nothing but the weight of the solids taken for the dry solids taken for the dispersion analysis or sedimentation analysis and as we actually keep the hydrometer from time to time it is subjected to it is required to perform immersion corrections. So in order to calibrate or calibration of the hydrometer for the immersion here in this slide the two figures which are actually shown one is before the immersion of the hydrometer another one is the after immersion of the hydrometer. Before immersion of the hydrometer at level yy is the point at which the measurement is being made that is where the centre of the bulb is assumed to be occur or assumed to be there. So he is the height from the surface from that the distance from the centre of the bulb to the top surface of the soil specimen and when the surface the top surface be xx and the surface at which the centre of the bulb meets is say yy. So when the bulb is placed there is a raise in the water the raise in the water suspension is given by vh by aj because vh is nothing but the volume of the hydrometer aj is nothing but the area of the jar in which the experiment is being performed. So here it is assumed that the yy dash which is actually rises above the it is approximated that 50% of the vh by aj it will be subjected to the raise is about vh by 2ag which is about the 50% of the raise of that x dash and x dash. So with that the immersion correction can be obtained like this he is equal to here h plus h by 2 plus vh by 2ag the distance minus vh by aj. So after simplification it is obtained as h plus h by 2 minus vh by 2ag. So if this immersion correction need to be applied approximately after say 2 to 4 minutes of the you know readings whatever we take. So here we discussed about the calibration of the hydrometer for you know basically for immersion correction. Then the graduations which are actually there as I said here from it starts from 0.995 to 1.030 or in the numbers it is rh is equal to 0 or minus 5 to 30 these are actually graduated indicated on the stem of the hydrometer and he is the difference where the measurement which has been taken and these readings which are he1 and he2 are unique for the hydrometer. So need to be calibrated and then they vary over linear distance with these readings. So the rh conversion of rh into he is done like this where rh is equal to gss minus 9000. So the plot of rh with he is valid for a particular hydrometer that means that each hydrometer will have a you know plot for rh and he. So with the linear interpolation if you see up to 2 minutes or 4 minutes where we do not have any immersion correction with that he is equal to he1 this distance and minus he1 minus he2 divided by 30 into rh this is up to 4 minutes or here he that is beyond 4 minutes he1 minus he1 minus he2 by 30 into rh minus vh by 2 ag. So this is after 4 minutes. So here it is summarized along with other corrections which are actually required for the hydrometer reading where n dash is equal to gs by gs minus 1 into r by w, w is nothing but the weight of the solids and r is the corrected hydrometer reading which is used in this expression for calculating the percentage and w is the weight of the solids taken for preparing the soil suspension where r is nothing but rh plus cm that is meniscus correction plus or minus ct the temperature correction minus cd. So n combined that is if you have got a performed a sieve analysis and if the percentage of the fines is say more than 12 percent then the total soil taken for you know gradation that is wt and total soil passing 75 micron in a given soil mass which is taken for sieve analysis and n combined can be obtained by getting n dash by using gs by gs minus 1 into r by w and then putting substituting in n combined is equal to n dash by into w75 divided by wt you will be able to get the n combined. So with that percentage the finer and the particle size variation can be plotted and where w75 is nothing but the weight of the soil fraction passing 75 micron wt is nothing but the total weight of the soil skeleton for combined sieve and hydrometer analysis. So in the hydrometer corrections apart from meniscus correction cm which is meniscus correction which is applied always positive because the density readings increase downwards that is that the suspension or the hydrometer readings increase downwards. So because of that the meniscus correction is always positive ct it is positive for temperature greater than 27 degrees so rh will be less than what it should be so the reading will be less than what it should be. So because of that the temperature correction is positive if the room temperature is more than 27 degrees negative for t less than 27 degrees rh will be more than what it should be. So because of this it is higher so what it is done is that the temperature correction is done negative and cd is always negative because in order to prevent flocking of the soil particles while preparing the suspension the dispersion agent is used like sodium carbonate or sodium oxalate are used to deflock the soil. So dispersion agent concentration you know to account for that the dispersion correction is always negative. So let us see after having discussed the procedure let us see an example of for the hydrometer analysis with a particular soil kaolin passing a very fine kaolin soil. So here the volume of the suspension is 1000 ml and the volume of the hydrometer is which is taken for the test is about 90 cc and weight of the dry soil taken is about 50 grams and the specific gravity of the soil is about 2.62 the cross section area of the jar is Aja about 31 centimeter square and room temperature is 27 degrees. Dispersing agent correction about cm is equal to 0.0004 miniscule correction cd is equal to 0.0034 temperature correction ct is equal to 0.9965 and viscous to the water taken as 8.545 8.545 into 10 to raise to minus 7 kilo Newton second per meter square. With this data for the given hydrometer that is he1 which is nothing here it is indicated as h dash e1 maximum depth to maximum depth to center of the bulb from RH 0.995 that is the top most reading in the stem of the hydrometer is 21 centimeter he2 that is closer to the center of the bulb maximum depth to the center of the bulb from from for RH reading 1.030 is 9 centimeter. Let us say at time t is equal to 2 minutes after placing the suspension and the reading which is actually taken in the hydrometer is say 28.5 which is indicates that RH is equal to 1.0285 since h dash e varies linearly with RH by using this presumption and the diameter of the soil particle is actually calculated by using 1000 into 1.8 mu divided by g or gs minus 1 into square root over he 98 into 60 into t that is the time at which the you know the reading is being taken and present is finer n is equal to g by g minus 1 gamma that is RH plus or minus c that is the summation of all the corrections into 1000 divided by this mass of the solids which is actually taken for suspension. So here in this slide calculations are given where h e h dash e was obtained based on the hydrometer details where it is obtained as 9.14 and with immersion correction that is V h by 2 ag it is obtained as 8.063. Now substituting in the expression which was shown in the previous slide d is equal to 1000 into 1.8 into 8.545 into 10 to power of minus 7 divided by the specific gravity minus 1 that is 2.62 minus 1 into square root of this 8.063 divided by 98 into 60 into 2 which gives a particle size of 0.0255 mm. So with this you can actually calculate that n dash that is nothing but obtained as about 93 percent. So based on this for the different timings when the calculations are done for time 0.5 minute, 1 minute immersion correction was not taken and 25, 15, 30, 60 and then 120, 140, 140 these are the readings which are actually taken and these are the corrected h dash e and then d in particle size in millimeter. So once you plot this the particle size on the semi logarithmic scale and the percentage finer on the y axis will get this gradation plot. So here this is the percentage finer on the y axis and particle size on the x axis with this is possible that you will be able to see the percentage points. Here in this particular kaolin soil what has been taken the silt particles are about 44 percent and clay particles are about 56 percent that means that is basically a silty clay having clay fraction about 56 percent and silt fraction about 44 percent and the 100 percent fine fractions. So limitations we have used the Stokes law for calculating arriving at the particles as distribution of fine grained soils. However we knew that the clay particles are hardly spherical but they are platelet particles. So the soil particles are not truly spherical and the sedimentation is done in a jar which is actually also induces some sort of limiting boundaries type. So for d greater than 0.2 mm causes turbulence in water and for d less than 0.0002 mm the Brownian movement occurs. So this is actually too small for the velocities of settlement so can be eliminated with less concentration. So if you are having a finest fine fractions then it is suggested that very little amount of the soil solids need to be taken particularly for example when we are determining the gradation of a bentonite it should not take about not more than about 5 grams of soil solids also. So one limitation is that the soil particles are not truly spherical. Other formulation is that the flock formation due to inadequate dispersion. Sometimes what will happen is that what we measure is not the two particle size. This is because of the flock formation or inadequate dispersion and unequal specific gravity of all particles insignificant for soil particles with fine traction. So this is unequal specific gravity of all particles that is also one it is assumed that all particles are actually having the same specific gravity but there is a possibility that unequal specific gravity can exist. So basically though it is insignificant this is actually listed as one of the limitations of Stokes law. So here in this plot a total particle size distribution curve is actually shown where you have got percentage finer on the y axis on the x axis we have got particle sizes. So here it is important to know that some particle sizes are actually characterized they are called D10 as the effective particle size and D50 as the average particle size. So here in the D50 means here the 50% of the particles are coarser and 50% of the particles are finer and D10 is the effective particle size which is called. In this 10% of the particle sizes are finer and 90% of the particles are actually particles are coarser than that D10 size. So we use D10 D15 D10 D60 D30 and for some filter design requirements D15 D85 are also used. So here in this graph where a well graded portion of the well graded you know distribution is actually shown and diameter of the soil particles for which 60% of the particles are finer that is 60% of the particles are finer and 40% are coarser than D60 that is what actually the physical meaning of D suffix 60. So here we use as I said that D30 can be determined from the graph like this and Cu which is called D60 by D10 so in this case for the type of the soil it is obtained as 5.8 and D60 D10 which is used to determine the coefficient of curvature that is D30 square divided by D60 into D10. So if the value of the Cu is equal to 1 that indicates that all particles are actually having almost identical sizes. So if the slope of the gradation curve is say very very steep then there is a tendency that all uniform graded particles exist in that particular type of distribution. So some commonly used measures are the uniformity coefficient which is nothing but the Cu is equal to D60 by D10 and soils with Cu less than 4 are considered to be poorly graded or uniform that is what a steeper curve indicates that you know uniform grade distribution that means that all particles are actually having same size or it is also called as poorly graded and Cu greater than 4 to 6 is called well graded soil and coefficient of the gradation or curvature is called as Cc is equal to D30 square divided by D60 into D10. The Cc is equal to 1 to 3 so if the Cu value is say greater than 4 to 6 and Cc value is 1 to 3 then the soil is said to be well graded. So higher the value of Cu the larger the range of the particle sizes in the soil. So higher the value of the Cu the larger the range of the particle sizes in the soil. So typical characteristics of the grain stress distribution curves if you look into it as we discuss steep curves are possible with low Cu values and they are poorly graded in nature and uniformly graded is also referred. The Cu less than 5 indicates that for uniformly graded soils and a flat curves with mild slopes the high Cu values indicates that well graded soil. So most gap graded soils have a Cc outside the range that is a gap graded soil means that some range of the particle size of the particles will remain absent from the soil matrix. So the intermediate particle sizes will be absent in gap graded soils. So most gap graded soils have a Cc outside the range. We can also see that the grain stress distribution curves can also give the soils history. In this slide 3 different particle size distribution curves are shown. One is for a the one which is on this side is for a n residual soil deposit and here for the intermediate maturing soil deposit and here is fully maturing soil deposit. As can be seen here a residual soil deposit has its particle sizes constantly changing with time as the particles continue to break down. So in the process of weathering the particles subjected to the gradation is subjected to change. We can say that the grain size distribution can provide an indication of soils history and typically we also discussed that the soils get transported from one place to other place and then they are called as transported soils with different agencies and here we have got a typical grain size distribution for glacial and glacial and alluvial soil deposits. Here this particular figure which is actually shown for the percentage finer on the y axis and particle size on the x axis is for a glacial soil deposit and this one is the glacial and alluvial soil deposit. So river deposits basically have well graded and uniform or gap graded depending upon the water velocity and the volume of the suspended solids and the river area where the deposition is occurring. So here in this slide number of different types of grain size distribution curves are shown and as can be seen here on this particular portion where a gravelly sand particle size distribution is shown and here a silty and with a fine sand mixture is shown here and here there is a clay and fine sand clay clay and sandy silty soil is shown here. Then here two types of you know one is flocculated kaolinite other one is the dispersed kaolinite and these sodium bentonite which is finest of the finest of all where you can see the finer fraction the particles are very very small. So as we go from this side to this side the particle size diminishes and you have got different you know for example you have got flocculated and dispersed have got here where the dispersions are the between repulsions are very predominant and here there is a possibility of flocculation. So the flocculated kaolinite actually has got this type of distribution and dispersed kaolinite has actually got this type of distribution and here the sodium bentonite base soil actually has got a distribution which is actually shown here and particles distribution of bentonite and illite and kaolinite if you consider as we discussed in the previous slide the sodium bentonite or sodium base and matrimonite has got the finer very very small fraction of size and when you compare these three minerals the kaolinite soil is relatively coarser and comes in between is illite and then followed just finer is the bentonite. So if you have the typical gradation then it is possible for us to estimate what is the percentage gravel and what is the percentage sand and what is the percentage silt and percentage clay. So sometimes if you have got say percentage clay it is possible for us to once we know the index properties of the soil it is possible whether the soil is active or not can be estimated. So in this curve for the given example here you have the typical grain size distribution and the coarser particles is on this side that is gravel, sand, silt and clay and here the percentage gravel which is more than 4.75 is found to be 0 and the sand size is from this side to the size of the silt that is 0.075 mm where 100 minus 60 that is 40% is actually sand and silt is from this percentage that is 60% minus up to this 12% that is clay fraction where it is coming that is 48% and the clay fraction is about 12%. So that means that this particular soil actually has got about 60% as percentage finds that is passing 200 mm c. So in this example problem which is actually shown in this slide we need to determine percentage of the gravel and sand silt. So gravel is indicated as g sand is indicated as s and silt is indicated as m and clay as c for soils a, b and c. So the 3 typical grain size distribution which is actually shown here one is that the poorly graded sand and here this is well graded silt sand and here well graded sand is silt. So if you look into this here the soil a which is actually has got 2% gravel the gravel is very less the 2% fraction is here and then followed by 98% sand and the curve is actually asymptotic here and the 0% silt and 0% clay. Hence here this is nothing but a poorly graded sand in this case it is a well graded silt sand where it has actually got 61% of silt particles sand particles and 31% silt and 7% clay. So this is actually referred as well graded silt sand and if you look into this this actually has got contrast it actually has got silt particles higher. So we call it well graded sandy silt where 57% silt particles and 31% sand exist there. So some applications of the having determined the particles as distribution we can actually discuss where the grain size distribution or analysis can be used particularly in geotechnology and in construction. Basically very much useful in the selection of the film material particularly has arting material or casing material it is required for embankment and ethylam construction and as a road sub base material basically the well graded soils are preferred and for the drainage filters in order to allow and retain the final fraction the filters are required and the ground water drainage and grouting and chemical injection where the fraction of the soil which is actually required to be mentioned and concreting materials and in the dynamic compaction is the process where the soil can be densified by dropping weights from the known heights. The practical significance of the grain size distribution can be you know discussed like this grain size distribution of soil smaller than 75 micron or 0.075 mm is of little importance in the solution of engineering problems but GSTs larger than 75 micron have several important uses particularly if you look into this GSD affects the void ratio of the soils and provides useful information for use in cement and asphalt concrete particularly during the pavement constructions well graded aggregates require less cement because they have got less void spaces and if you have got uniformly graded aggregates then it requires more cement and tends to become uneconomical and then less load bearing. So well graded aggregates require less cement per unit volume of concrete to produce denser concrete and it is less permeable and more resistant to weathering. Secondly in knowledge of the amount of the percentage of the fines and gradation of the coarse particles is useful in making a choice of material in base courses under highways, runways and rail tracks etc. And as I said before if you know the percentage clay fraction whether the clay is active from the expansiveness point of view whether the soil is expensive or not can be established by with a term called activity. So activity of the clay is based on the percentage of the clay fraction and another significance of grain size distribution is that to design filters basically filters are used to control the seepage and the pores must be small enough to prevent particles from being carried from the adjacent soil or the base soil which is called. So after having discussed you know grain size distribution and in order to complete or in order to arrive at the knowledge for classifying the soils or grouping the soil we need to understand particularly as far as the fine-grained soils is concerned the different possible physical states of the fine-grained soils. As the soil water content changes soil changes from different states from liquid state to plastic state to semi-solid state to solid state that is as the soil is subjected to drying soil changes from liquid state to plastic state to semi-solid to solid states. For the most of the soil deposits which are reasonably compressed can occur at this particular water content that is at this point where they are actually close to plastic state or this particular limiting water content. So we actually need to have understand about the you know these transitions between liquid limit and liquid state and plastic state and plastic state and semi-solid state and semi-solid state and solid state. So before discussing about that we need to understand about the what is the term called consistency consistency of the fine-grained soils. So basically it is a property of a material which is manifested by its resistance to flow it represents the relative ease with which the soil may be deformed. So if the soil is very stiff then it is difficult to get it deformed. So degree of the firmness of the soil and is often directly related to its strength. It is conveniently described as soft medium stiff medium firm stiff or firm or very stiff and these terms are unfortunately are relative and have different meaning to different observers. So the consistency is defined as the property of a material which is manifested by its resistance to flow and it represents the relative ease with which the soil may be deformed. In soil mechanics basically it is required to determine the range of the potential behavior of a given soil type based on only few simple tests. Soils might shrink or expand excessively in an uncontrolled manner after they have been placed in geotechnical structures. That means that once the soils actually have been used for constructing structures like roadway embankments or roadways upgrades, dams, levees, foundation materials they can be subjected to depending upon the type of the mineral, they can be subjected to shrinking or expanding. So soils may lose their strength and ability to carry loads safely. So the consistency basically here when we are discussing about the fine grained soils the test used to detect potential problems for coarse grained soils are different from the use to detect from the potential problems for the fine grained soils that is silt and clay. It has to be noted the test which are actually used to detect potential problems for coarse grained soils are different from fine grained soils. In coarse grained soils water content generally is not a major factor and major factor leading to shrinkage is structure of the soil skeleton. And in case of fine grained soils water content is a major factor and soil expand and lose strength and soil shrink and gain strength. So if the water content of a clayser is gradually reduced by a desiccation natural process the clay passes from a liquid state to plastic state as I discussed earlier and finally into a solid state. So the water content at which the different clays passes from one state to other state is very important and this is unique to a particular type of a soil. So water content at these transitions can be used for identification and composition of different clays. So it has been thought that in order to you know classify or determine the index properties it is required to determine water content at these transitions can be determined for identification and comparison of the different clays at different fine grained soils. So here these limits are called atterberg limits or the water contents where the soil behavior changes from when they change from one state to other state. So here in this slide the soil moisture scale is shown where this is the physical state liquid and here is the consistency and this liquid state and so at this point the transition between this liquid state to plastic state is determined or called as liquid limit and above this the soil is like a liquid it is called very soft and plastic that is between liquid limit and plastic limit. So the plastic limit is the another type of atterberg limit which is a transition between plastic state and semi solid state and in this nature in this the natural soil deposits that do occur at this particular water content and shrinkage limit which is a transition between semi solid state to solid state the extremely state. So up to if you see that the degree of saturation which is nothing but the volume of water in the volume of voids so here up till here the 100% saturation is ensured and beyond this state the soil is no longer fully saturated and it tends to become air starts entering here. So liquid limit, plastic limit and shrinkage limit are the three atterberg limits what we are going to discuss. So here when the soil changes from one when transits from these physical states the finally it can actually changes into this type of solid state. So if you look into if you connect to the you know specific surface areas and electrical charges. So it was discussed that for fine grained soils we have discussed that they have high specific surface areas and electrical charges are very predominant on their particles. So because of this the fine grained soils and clays in particular can change their consistency quite dramatically with changes in water content. So why the particularly clays change you know the consistency from one water content one state to other state is the reason is that because of the high specific surface area and prevalent electrical charges and each soil will generally have different water contents at which it behaves like a solid semi-solid plastic liquid for a given soil the water content that mark the boundaries between the soil are called defined as atterberg limits. So it is pictorially it is indicated here and this particular state is liquid limit and this is plastic limit and this particular state this water content at this transition between semi-solid and solid state is atterberg limits. So atterberg limits are nothing but the water contents where the soil behavior changes. So here in this particular slide where the volume of the volume is plotted on the y axis and water content is plotted on the volume of the sample on the y axis and volume of water content on the x axis. So this particular line which is inclined at 45 degrees it can be seen here that at point A that is a point where the initial water content but when it transits from liquid state to plastic state that is the point B that is referenced here as the liquid limit W suffix L and point C is the plastic limit that is transition between plastic state to semi-solid state and but when it transits from semi-solid state to solid state up till this point the water content is 100 percent the degree of saturation is 100 percent and this water content at this particular state of transition between semi-solid state to solid state is called as shrinkage limit. But beyond this point if you look into this if you magnify here that there is a possibility that the air entry this curvilinear nature of this curve which indicates that here the air which is actually enters into the voids and the soils will no longer get compressed and the no volume change will happen. So this is nothing but the volume of air plus volume of the solids. So this is the volume remains the solid volume remains constant upon further drying. So this Vd is nothing but the volume of air plus volume of solids and V0 is nothing but the original volume at point A. So one if you define you know these at room bug limits the first limit which is called liquid limit is the water content at which a soil is practically in a liquid state but has infinitesimal resistance against the flow and which actually possesses a strength and it is said that the soils possess about strength from 1.7 to 2.7 kilo Newton per meter square or kilo Pascal's. The plastic limit is the water content at which the soil would just begin to crumble when rolled into threads of approximately 3 mm diameter. So this is a limit at which the soil will start crumbling into crumbling when rolled into the threads of approximately 3 mm diameter. Because if the soil is having sandy particles and with little amount of fine fraction it is very difficult to make threads. So that indicates that the soil is non-plastic. Shrinkage limit is the water content at which a decrease in water content does not cause any decrease in the volume of the soil mass. So at shrinkage limit the degree of saturation is 1. In this particular slide an attempt is being made to explain about the shrinkage phenomenon. So here this is the solid particle which is indicated with the edges here and this is in a water surface when it actually transiting from semi-solid state to solid state. Assume that R1, R2, R3, R4, R5 are the radii of this miniske, water miniske between the particles. And if you look into this the radius of R1 is actually very high R2, R3, R4, R5. So as it proceeds the miniske radii is decreasing and then here also same situation is shown. So this is the idealization section at the process at which where the curvilinear portion where air starts entering. So here imagine a compressible soil containing tinny grains with couplery pore spaces between the grains. So the mechanism is actually explained like this. When the pore spaces are completely filled with water there is a free water on the surface of the soil. The miniske is a plain surface that is with R1 radii and the tension in the water is zero. That means that the water is not exerting any tension on the soil particles. But as the evaporation removes the water from the surface a miniske begins to form and each of the pores at the surface with a resulting tension in water. So at some time after evaporation has started the miniske would have reduced it to some position say 2 that is from position 1 to position 2. At this stage the tension in the water is 2ts by R2. So if you look into this R2 is smaller than R1 so the tension in the water increases. The soil is compressed by the stress equivalent to 2ts by R2. So as this process continues what happens is that it is something like the particles are pushed or pulled towards closer and the tension in the water TW can be estimated by equating the tensile forces in the water to the vertical components of the surface tension force. With that we can actually calculate TW is equal to 2ts by R2. So as the further evaporation continues the fully developed miniscule in the largest pore space recedes to a smallest diameter. So this makes the particles to come closer and then to such a state that the particles will no longer get compressed into the further. So this produces an increased sigma dash and causes further shrinkage. So as the evaporation process actually goes on the miniske keeps on tending to become sharp with that the tension in the water continues to increase and because of this the fully developed miniscule in the largest pore space recedes to a smaller diameter which brings or pulls the particles to the closer distance. So this explains the typical shrinkage phenomenon we actually experience in typical fine-grained soils. As the evaporation continues the miniske continue to recede and the tension in the water continue to increase and the compression between the soil grains and the resultant shrinkage continues to increase. So eventually what will happen is that the miniske will reach the smallest radius that is what we have discussed previously. By the time miniske reduce to the least possible radius the pores in soil will not be there to compress. That means that most of the compression which is possible is might have already happened. So hence this explains the shrinkage phenomenon. So the Atterberg limits basically provide a good deal of information on the range of the potential behavior of the given soil which might show in the field and variations in the water content. So if you look into this the soils actually have got in a solid state and semi-solid state and plastic state and liquid state. In the semi-solid state or in case of in the solid state the soil is very stiff in nature and has got a so called brittle behavior and in case of a semi-solid state the soil has combined brittle and ductile behavior like a stiff cheese. In case between in the plastic state soil is very ductile is something like a malleable type behavior and here in the liquid state that is actually beyond this or at this particular point soil behaves like a thick or a thin viscous fluid. So soil is something like a viscous fluid here. So here the stress strain variation that is sigma is in this direction and epsilon is the strain in the axial direction is actually shown here. So here the plasticity index which is defined as nothing but the difference of the liquid limit minus plastic limit. It is the range of the moisture content or which the soil exhibits plasticity it is the range of the moisture content or water content of a soil which exhibits plasticity. So plasticity is defined as the property of a material which allows it to deform rapidly without rupture. So greater the difference between the liquid limit and plastic limit the more is the plasticity of the soil. This particular clay particles which are actually shown there where you have got the water droplets attached to the clay negative particle sizes and we have discussed that this forms like a adsorbed layer and the cations which are actually present in the particles are also attracted towards the negative charges here. So this means that the range of water contents or which a given soil can pull water its macro structure assimilate it and still acts like a solid. So clay soils generally with high specific surface areas and the charged particles will be able to hold large amount of water between the particles due to their charge field and the poor nature of polar nature of the water molecules. Why soils actually have higher PAs and smaller PAs if you look into this clay soils with high specific surface area and charged surfaces are able to bind assimilate water molecules and then overall soil will still behave as a plastic solid and such soils will have higher PAs and soils compared to the lower specific surface areas will not be able to bind or assimilate water molecules and thus will have smaller plasticity index values. So for embankment dam construction if we required to have say a hearting zone where you wanted to prevent the water seepage entering into the to retain the water in the reservoir or the dam then we need a hearting which actually has got higher plasticity for certain type of constructions where the low plastic soils are required. So soils with comparatively lower specific surface area will not be able to bind or assimilate water molecules and thus they have actually low plasticity indexes. So in this particular lecture number 6 we actually have understood about the particular in the form of index properties how to perform a gradation for the fine sand particles and then we discussed about the different possible water the soil states when it is actually changing from liquid state to the solid state and introduced at rubber limits like liquid limit, plastic limit and shrinkage limit and the difference of liquid limit and plastic limit is said as a plasticity index and by knowing these things and then if you can extend further then we will be able to classify the soil. So in the next lecture we will look into the soil classification and the remaining discussion about the you know about plasticity index and determination of the liquid limit and other shrinkage limit with some modern methods etc.