 Welcome to lecture 3 of module 1. In the previous lecture we have discussed about phase relations and phase properties and we also solved some example problem 1 in module 1. Now in this lecture before addressing the particle shapes and their arrangement and soil structure, we are going to discuss about one problem which belong to the previous discussion and then we have one practice problem set in this module M1, it is named as M1A. So in this lecture we are going to discuss about particle sizes, shapes and arrangement and about the recent trends we are going to discuss further in subsequent lectures. Before going into that this particular lecture topic, let us try to address the example problem and practice problem set M1A. In this example problem 2, here a soil has an institute in place void ratio E0 which is equivalent to 1.87. Natural moisture content W suffix N is given as 60% and the specific gravity of the solids is given as 2.75. We need to find out what is the bulk unit weight and degree of saturation of the soil deposit. So as we discuss this particular problem can be solved by drawing a phase diagram. So if you draw the phase diagram, this is basically a partially saturated soil. So this is nothing but a three phase diagram. So you have air, water, solids. Now we let us adopt the specific volume approach where volume of the solids is set as 1 or unit meter cube. Now with this if you set the volume of the solids as 1, now the volume of voids will be equivalent to 1.87. Now from the definition of void ratio, volume of voids to volume of solids which is actually given as E0 is equal to 1.87, if you take this implies that the volume of the voids is equal to 1.87. So the total volume is nothing but 1 plus 1.87 that is the 2.87 meter cube is the total volume. Now here we were actually given the water content, natural water content that is 60%. Now by using this definition of the specific gravity of the solids, Gs is equal to gamma s by gamma w and by taking gamma w is equal to 9.81 kilo Newton per meter cube we can write Ws is equal to Gs vs gamma w and Ws is equal to 1 with that what will happen you have Ws is equal to 2.75 into 9.81. So this is nothing but the weight of solids. From the definition of water content, water content is defined as weight of water to weight of solids. So weight of water is nothing but 0.6 times 2.75 into 9.81 which is nothing but weight of solids. So weight of water is equal to 0.6 into 2.75 into 9.81 and weight of air being 0. So the total weight is W is equal to Ws plus Ww which is equal to 43.16 kilo Newton. By knowing the weight of water we can actually obtain by dividing by gamma w we get the volume of water. So volume of water is equal to Wgs which is nothing but 0.6 into 2.75. So by knowing volume of voids and we can actually now obtain volume of air which is there in the volume of voids which is nothing but in the present problem it is volume of air is equal to 0.22. Now we have all parameters defined. So in this case now if you wanted to obtain the bulk unit weight you need to use the definition weight of volume, weight of water plus weight of solids divided by the total volume you should get the bulk unit weight. And if you want say dry unit weight of the soil weight of the solids divided by the total volume you are able to get the weight of the dry unit weight of the soil. If you want dry unit weight of the soil solids and that is nothing but which is given by weight of solids divided by volume of the solids which is actually one in this present problem. So what we discuss here the gamma bulk or bulk unit weight is nothing but W by V. So weight which is actually given or was obtained as 43.17 divided by 2.87 you get 15.04 kilo Newton per meter cube. From the definition of degree of saturation we can actually get SR is equal to volume of water to volume of voids which is nothing but 1.65 divided by 1.87 you get 0.882 which is expressed in percentage 88.2%. By having all these we can deduce other relations also like gamma D Ws by V which is nothing but weight that is total weight minus weight of water which is nothing but the weight of solids divided by total volume you will get the dry unit weight of the soil mass. Air content in the soil mass can be obtained by volume of the air divided by volume of voids that is nothing but 0.22 divided by 1.87 and we all know that by using AC is equal to 1 minus SR you will also get 1 minus 0.882 that is nothing but 11.8%. So the air content can also be obtained from degree of saturation or air content can also be obtained from the definition of volume of air to volume of voids. The percentage air voids are air voids n suffix a which is nothing but the volume of air in the total volume so which is nothing but 0.22 divided by 2.87 that is 0.077 that is which is nothing but 0.077. So also by using the definition like NA is equal to N into AC or N into 1 minus SR with that we can actually get we can also get the similar value which is nothing but 0.076. So like this we can actually employ these phase diagrams for the respective state which is actually given in the problem we can actually solve the problems particularly when the soil is actually excavated and the place then there will be changes in the void ratios so this allows us to estimate the actual volumes which are changes which takes place. So based on the discussion I suggest you all to have a look at these problems which are actually given in the practice problem set M1A. The first problem reads like this, a fully saturated soil sample was extracted during an oil well drilling that means that there is offshore investigation. The wet mass of the soil sample was the wet mass of the sample was 31.5 N and the volume of the sampling tube was 0.001664 meter cube that is total volume of soil sample. After the analysis of the soil sample was found to contain 28.2 percent of the liquid as kerosene and the end the dry mass as 26.7 N. The specific gravity of the soil grains was 2.68, determined the bulk unit weight void ratio and the water content of the sample. So this will be an interesting problem to solve based on the discussions we had in the previous lecture. In the second problem a sample of natural glacial till was taken from below the ground water table. So the water content was found to be 55 percent and the volume of the specific gravity of the solids is 2.7. Estimate the submerged unit weight and porosity. The submerged unit weight is nothing but gamma sat minus gamma w, gamma sat is nothing but the saturated unit weight of the soil mass, gamma w is nothing but the unit weight of water. In the third problem this is a derivation for a partially saturated soil deduce the following expression where E is equal to the void ratio of the soil, gm is nothing but the mass specific gravity of the soil, gs is nothing but the specific gravity of the solids and SR is nothing but the degree of saturation. So based on the for the given phase diagram or the partially saturated state of the soil you need to express the void ratio as gs minus gm divided by gm minus SR. In the fourth problem the water table is in certain area is at a depth of 3 meter below the ground surface. To a depth of 12 meter the soil consists of very fine sand having an average void ratio of 0.8. Above the water table the sand has an average degree of saturation of 50 percent. What you need to determine here is a the average unit weight of the soil above the water table, b the saturated unit weight of the soil below the water table and c the submerged unit weight of the soil below the water table. So now let us come to the present you know topic of this lecture three where particle shapes and their arrangements. Before discussing that let us revise once again or let us review once again how the origin of the soil deposits occur. In this particular slide as it is shown here the origin of the soil occurs from rocks predominantly igneous rock, metamorphic rock and sedimentary rock. Some soils particularly the residual soils when they go with some agencies or they get transported with some agencies and then deposited they form sediments. When they undergo subjected to a process of hardening for over a period of time then they can actually get converted into a sedimentary rock. That means that the sediments because of the process of duration there is a possibility that they can get converted into rocks that is sedimentary rocks and sedimentary rocks can get transformed into metamorphic rocks or sedimentary rock can get transformed into igneous rocks or the mechanical weathering of these rocks can also lead to the particularly formation of these soils. So the geological process affecting the origin of soil deposits which was actually discussed in the previous slide reads like this. The progression of mechanical and chemical weathering that converts all types of rock to residual soils and these soils transport and deposition to form sediments and deposition to form sediments and eventually conversion of sediments to sedimentary rock through a process of injuration. That is what actually we have discussed in the previous slide about the how the origin of the soils can take place. So as we have discussed the different types of soils are possible like we have predominantly coarse grained soils and fine grained soils and the coarse grained soils basically they are large in size and in case of fine grained soils they are actually very small in size. And the residual soil profiles or the soils where they after formation they are deposited at the place of origin and they resemble the properties of the original or parent rock from where it has been deduced. So in this slide a schematic of the profile showing approximate parallelism in the weathering zones is shown and here an actual residual soil profile which is observed is actually shown here. The transported soil profile is nothing but the soil depth bears no particular relationship to the rock surface and the soil thickness varies according to the physical conditions during deposition the particular soil is transported by the different agencies like air, water and other modes of agencies. If you look into the Indian context we have different sets of soils like we have alluvial deposits and we have desert soils particularly towards this particular portion and we have a major portion is the black cotton soil deposits and along the coastal zone we have the marine deposits and in the hilly regions we have the boulder deposits. So if you look into this the particular reference to Indian map or Indian context we have the varied nature of soils. Alluvial deposits where there is a positivity of the silt clay or sand silt clay layers of status. The desert soils predominantly they are sandy soils and in some part of the portion of the western portion where you have the laterites and laterite soils and the black cotton soils which are also called as expansive soils and which are actually has large predominance in India and other countries also and then we have the marine deposits which are basically soft in nature and the foundation constructions are required to be done with utmost care. So as we discussed the soils can be divided into two major categories the cohesion less and cohesion. What is this cohesion less and cohesion? Cohesion less soils such as gravelly means that the soils which are particles are large in size sand comparatively smaller in size and the silty soils have particles that do not adhere or stick together even with the presence of water. So cohesion less soils such as gravelly, sandy and silty soils have particles that do not adhere or stick together even with the presence of water but in some silty soils presence of the carbonates make them to have a true cohesion in them. On the other hand cohesion soils predominantly called as clays are characterized by their very small flake like particles that means that they resemble the sheets of the book which can attract water and form the plastic matter by adhering or sticking to each other. That means that this clays say soils exhibit a sort of plasticity and they have a tendency of sticking in the presence of water. So this is predominantly two sets of soils one is called cohesion less soils other one is cohesion soils which will be discussing in length in the process of this advanced geotechnical engineering course modules. Now what is the grain shape? What is the what is the shape of the grain? How the shape of the grain looks like? Is it rounded or is it has got a square shape or has got any specific shape? We all know that the soils are formed by nature so they have there is no possibility of having a particular shape. So the shape of soil grains is useful is useful soil grain property in the case of coarse grain soils and is important in influencing the engineering behavior of soils. So the shape of the soil grains basically is useful particularly in case of coarse grain soils and it is important in influencing the engineering behavior of soils. The shape of grains in a coarse grain soil can be examined with naked eye whereas the fine grain soils require microscopic examination. That means that you can actually see the shape of the coarse grain soil clearly but if you wanted to see the fine grain soil shape you actually need to resort to adopting adoption of microscopic examination. So the grains basically they are based on their sizes they are divided into classified into three types one is bulky grains and flaky grains and needle shaped grains. The bulky grains are small grains or bulky grains are soil grains where all dimensions of grain are more or less the same and these are characteristic of sand and gravity soils. So basically the bulky grains are large in size and they are the soil grains where all dimensions of grain are more or less the same and these are the characteristics of the sands and gravels. Coarse fractions exemplified by sand are made up of grains usually composed of chiefly of quads. The individual grains may be angular subangular or rounded that means that these grain shapes can be angular or subangular because of the some process of weathering or if they are under riverbed they can get actually a rounded shape. The coarse fractions of these grains exemplified by sand are made up of grains usually composed chiefly of quads and the individual grains may be angular subangular or rounded. Some sands contain fairly high percentage of mica flakes that make them very elastic and springy. In the fine and very fine fractions only one grain usually consists of one mineral the other particles may be angular, flake shaped or tubular. So round particles however consistently absent so round particles are not generally present. The bulky grains the source how the what is the source of these bulky grains the mechanical breakdown of the parent rocks. So during their transportation by wind or water the sharp edges of the grains may get worn out and the grains may become rounded. So river gravels and wind blown sands basically they are rounded, alluvial sands they get actually subangular to sub rounded shape. If you have got alluvial deposit and if that the predominant soil is say sandy soil the grain shape is approximately ranges to subangular to sub rounded. River gravels and wind blown sands they have a round shape. Now in this slide here a very rounded aggregate is shown typically a very rounded aggregate is shown schematically and here a sub rounded aggregate is shown and here the rounded aggregate is shown angular and where sharp edges in the crushed stone. But here this is actually most possible where you have got sharp edges in the crushed stone and this is said to be angular and here edges are slightly rounded. So that is if the edges are in a particular crushed stone or a crushed particle if they are sub angle if they are Indian context we have different sets of soils like we have alluvial deposits and we have desert soils particularly towards this particular portion and we have a major portion is the black cotton soil deposits and along the coastal zone we have the marine deposits and the hilly regions we have the boulder deposits. So if you look into this the particular reference to Indian map or Indian context we have the varied nature of soils. Alluvial deposits where there is a possibility of the silt clay or sand silt clay layers of status the desert soils predominantly they are sandy soils and in some part of portion of the western portion where you have the laterites and laterite soils and the black cotton soils which are also called as expansive soils and which are actually has large predominance in India and other countries also and then we have the marine deposits which are basically soft in nature and the foundation constructions are required to be done with utmost care. So as we discussed the soils can be divided into two major categories the cohesion less and coissue. What is this cohesion less and coissue cohesion less soils such as gravelly means that the soils which are particles are large in size sand comparatively smaller in size and the silty soils have particles that do not adhere or stick together even with the presence of water. So cohesion less soils such as gravelly sandy and silty soils have particles that do not adhere or stick together even with the presence of water but in some silty soils presence of the carbonates make them to have a true cohesion in them. On the other hand coissue soils predominantly called as clays are characterized by their very small flake like particles that means that they resemble the sheets of the book which can attract water and form the plastic matter by adhering or sticking to each other that means that this clays say soils exhibit a sort of plasticity and they have a tendency of sticking in the presence of water. So this is predominantly two sets of soils one is called cohesion less soils other one is coissue soils which will be discussing in length in the process of this advanced geotechnical engineering course modules. Now what is the grain shape what is the what is the shape of the grain how the shape of the grain looks like is it rounded or is it has got a square shape or has got any specific shape. We all know that the soils are formed by nature so they have there is no possibility of having a particular shape. So the shape of soil grains is useful is useful soil grain property in the case of coarse grain soils and is important in influencing the engineering behavior of soils. So the shape of the soil grains basically is useful particularly in case of coarse grain soils and it is important in influencing the engineering behavior of soils. The shape of grains in a coarse grain soil can be examined with naked eye whereas the fine grain soils require microscopic examination that means that you can actually see the shape of the coarse grain soil clearly but if you wanted to see the fine grain soil shape you actually need to resort to adopting adoption of microscopic examination. So the grains basically they are based on their sizes they are divided into classified into three types one is bulky grains and flaky grains and needle shaped grains. The bulky grains are small grains or the bulky grains are soil grains where all dimensions of grain are more or less the same and these are characteristic of sand and gravelly soils. So basically the bulky grains are large in size and they are the soil grains where all dimensions of grain are more or less the same and these are the characteristics of the sands and gravels. Those fractions exemplified by sand are made up of grains usually composed of chiefly of quarts. The individual grains may be angular, subangular or rounded that means that these grain shapes can be angular or subangular because of the some process of weathering or if they are under riverbed they can get actually a rounded shape. The coarse fractions of these grains exemplified by sand are made up of grains usually composed chiefly of quarts and the individual grains may be angular, subangular or rounded. Some sands contain fairly high percentage of mica flakes that make them very elastic and springy. In the fine and very fine fractions only one grain usually consists of one mineral the other particles may be angular, flakes shaped or tubular. So round particles however consistently absent so round particles are not generally present. See bulky grains the source how they what is the source of these bulky grains the mechanical breakdown of the parent rocks. So during their transportation by wind or water the sharp edges of the grains may get worn out and the grains may become rounded. With river gravels and wind blown sands basically they are rounded, alluvial sands they get actually subangular to subrounded shape. Suppose if you have got alluvial deposit and if that the predominant soil is say sandy soil the grain shape is approximately ranges to subangular to subrounded and river gravels and wind blown sands they have a round shape. Now in this slide here a very rounded aggregate is shown, typically a very rounded aggregate is shown schematically and here a subrounded aggregate is shown and here the rounded aggregate is shown angular and where sharp edges in the crushed stone but here this is actually is most possible where you have got sharp edges in the crushed stone and this is said to be angular and here edges are slightly rounded so that is if the edges are in a particular crushed stone or crushed particle if they are rounded then that is actually called as subangular. So the difference between angular and subangular is that the edges are slightly rounded. So soils containing particles with high angularity tend to resist displacement hence possess high shearing strength compared to those with the less angular particles. So because of these sharp edges they offer very high shear resistance that is the reason why we use for construction where the load bearing is important you need to actually use the angular particles which are actually having sharp edges. So in this slide a typical photo micrographs of sand particles is shown here. So here there are three types of the sands which are actually collected by different depositions is shown one is beach sand other one is quartz sand other one is june sand. So if you see here the particles they have angular to sub rounded edges and the area of the contact between each grains is extremely small and even small forces between the grains produce very high pressure that means that the contact areas between these grains are very very small and when the contact areas are very very small and because of this application of the load they produce very high contact stresses and these contact stresses if they overcome or if they become larger than the crushing strength of the particles then the particles can lead to the crushing and that indicates that the entire soil mass also can experience settlements because of the large crushing takes place because of the increasing in contact stresses. The other type of the grain other than the bulky grain what we said is called flaky grains or plate shaped grains these are the ones which one dimension of the grain namely its thickness bears no relationship with the other lateral dimensions which are much bigger. So the lateral dimensions of these grains are much bigger so resemble a sheet of paper or a leaf or a platelet. So that is the reason why these are predominantly occur in clay type of soils or soils which are actually exhibiting cohesion. So flaky grains or plate shaped grains are those ones in which one dimension of the grain namely its thickness bears no relationship with the other two lateral dimensions which are much bigger. So as I said they resemble a sheet of the paper in a book or a leaf or a platelet. The white spread prevalence of the plate shaped particles in the very fine fractions of the natural soil is attributed to geological process of formation. So the white spread prevalence of the plate shaped particles in the very fine fractions of natural soils is attributed to the process of soil formation. Here in this slide a micro graphic photograph of crystal with a flaky grain is shown. So it can be seen that the particle is very small having but large surface area. So this is of the point of interest which actually we should know that the particles which are actually have smaller sizes they have large surface area. Another type of the shape of the grain is called needle shaped grains. One dimension of the grain is fully developed and is much larger than the other two dimensions. Needle shaped grains are characteristics of the clay mineral atopulgite. So particularly we are going to discuss of the different clay minerals. Here I named a mineral, previous class we also named some three minerals kaolinite, enlite, matamolite and another mineral which is actually called atopulgite. Particularly the specialty of this mineral is that the grains actually have got tube shaped or full shaped or half tube. The one dimension of the grain is fully developed and is much larger than the other two. So what we have seen is that we have got different shapes of the grains. One is bulky grain, other one is we have seen the flaky grain, other one is the needle shaped grains. So here a schematic of the how a micrograph which is actually showing a tube grains can be there is shown here in the soil mass. So properties of very fine soil fractions, the most important grain property of fine grained soil is the mineralogical composition. If the soil particles are less than 2 micron that is 0.002 mm the influence of the force of gravity on each particle is insignificant. So just we have discussed that if the particle is small it exhibits the large surface area and the shape of the grain is called platelet particle or flaky shape. If the soil particles are less than 2 micron the influence of the force of gravity on each of the particle is insignificant compared with that of the surface charges. That means that if you compare surface charges and gravity forces the surface forces predominant if the particles are small. The colloidal particle of soils consisting of primarily clay minerals the colloidal state is nothing but the domination of surface charges takes place. So let us come to what is a soil structure and how it is actually defined. The soil structure or soil fabric which is nothing but the structure of a soil is taken to mean both the geometric arrangement of the particles or mineral grains as well as the inter particle forces which may act between them. So soil fabric refers to only geometric arrangement of the particles but the soil structure of a soil is taken to mean both geometric arrangement of the particles or mineral grains as well as the inter particle forces which may act between them. The inter particle forces or surface forces are relatively important for fine-grained soils at low confinement or low state of stress. That means that if you have got a fine-grained soils under the low confining stresses or at the surface of the soil stator the inter particle forces are relatively important. If they are at the high confining stresses let us say at the deeper depths then the dominance of the effect of the confinement comes into the picture. Although the behavior of the coarse-grained soil can often be related to particle size distribution the behavior of the fine-grained soil usually depends much more on geological history and the structure then on the particle size. This is after Lamb and Whitman 1979. So we have now said that on a soil particle there can be a gravity force or they can be a surface force. So let us discuss about the particle forces and behavior and how they influence in forming different soil structures. The behavior of the individual soil particles and their interaction with other particles is influenced by the following forces weight of the particle which is indicated here as f suffix g particle surface forces which is indicated here as f suffix s. The particle forces and behavior weight force of the particle is a result of the gravitational forces and is a function of the volume of the particle. So larger the particle larger will be the weight force. For equidimensional particles such as piers of diameter d the weight fg is directly proportional to diameter of the particle that is fg is proportional to dq. In case of a fine-grained soil say clay particle and we said that it is a thin platelet tape particle. So if you assume that this is the typical cross section of a clay particle and these are the net negative charges which are unsatisfied net negative charges which are actually available. And if this is considered the particle surface forces are of an electrical nature. So if you take a particular clay particle we say that the surface forces are of an electrical nature and they are caused by unsatisfied electrical charges in the particle crystalline structure. So there will be always a net negative charges on the clay particle. The surface forces f s are directly proportional to the surface area. Hence for equivalent dimension equidimensional particles the surface area suppose if it is D by D then f s is proportional to d square. So surface forces f s are directly proportional to the surface area hence for equidimensional particles f s is proportional to d square. So if you take the ratio of Fg by Fs previously we said that Fg is proportional to dq and if you take Fs is proportional to d square if you see that the ratio of gravity forces and surface forces is proportional to d now. Now as the d increases Fg by Fs increases thus for larger particle sizes which includes soil particles in the coarser fraction greater than 0.075 mm Fg is predominant over Fs. If as the d decreases Fg by Fs decreases that means that the dominance of the surface forces comes into the picture. As the particle diameter decreases the ratio of Fg by Fs decreases that means that the surface forces predominate. So soil structure or soil fabric let us once again discuss where the properties of soil mass is nothing but the function of arrangement of the grains. The system of discrete particles or grains that make up soils are not strongly bonded together hence are relatively free to move with respect to each other. So if you divide or if you classify the soil structure or the particle arrangement according to Terzaghi and Kassagrandi it is said as single grain, honeycomb or flocculent and dispersed. The size and shape of the grains and minerals from which the grains are formed determine the formulation of a particular soil structure. So how are the what environment these soil masses or soil deposits are there that also governs. So size and shape of grains and minerals from which the grains are formed determine the formulation of particular soil structure. So let us discuss about the single grain structure, this particular structure arrangement is possible because of the bulky particles. Particles having sizes more than 0.02 mm that is for actually sands and sills where you can actually have large particles and then these are actually called as single grain structure. And each particle being in direct contact with adjoining particles without any bond and cohesion between them and the structure may be loose. So if you look into this there is a possibility that the single grain structure can be loose or intermediate or medium dense or very highly having high denseness that is very dense depending upon the way in which the particles are packed in a given volume of soil mass. So the structure may be loose, medium dense or dense depending on the way in which the particles are packed together. In a single grain structure the single particles may be deposited in a loose state having high void ratio in dense state in a low void ratio. So in a single grain structure if there is a loose deposit there is a possibility of high void ratio that means that the particle to particle contact is minimum and the particles are actually arranged in such a way that they exhibit high void ratio. In case of a dense state the particles are closely packed and they exhibit very low void ratio. So for granular soils particularly sand and gravel the range of void ratio generally encountered can be visualized by considering the ideal situation in which particles are spheres of equal size. If it is assumed that the particles are approximately this particle shape is approximated as a sphere of diameter D then we can actually come out something like the loosest and densest possible arrangement. So the loosest and densest possible arrangement that we can obtain from these equal spheres can be said as simple cubic where we have a loose arrangement and the pyramidal type of packing where for example if you consider billiard balls and if they are placed in a simple cubic then it actually represents the loosest configuration and if they are actually put in the pyramidal type of packing and it actually gives the densest possible. So we can actually determine theoretically what will be the void ratio and loosest configuration and densest configuration. So here in the single grain structure which is shown here the plan view and cross section of a cubic arrangement. Let us assume that you have got each particle is visualized as a billiard ball and then you have got number of particles and this is actually a loose state wherein you have got used chunk of voids which are actually between these particles and in that state you actually have this is the plan where all the voids are actually filled with the edges and particles. So in the single grain structure in the case of natural granular soil the particles are neither equal size nor perfect spears we know that though we have actually said that the particles are equidimensional but they are neither equal size nor perfect spears however the small sizes particles may occupy the void spaces between the large ones and which will tend to reduce the void ratio of the natural soils as compared to the equal spears. So on the other hand the irregularity of the shape of the particles generally tend to increase the void ratio as compared to ideal spears. So that means that this idealization which what we assumed is that with loosest and densest configuration somewhat holds good the void ratios encountered in real solid approximates the same range as those obtained in the case of equal spears because of the when you have got single grain structure when the when you have got fine particles occupying the void spaces within the large particles they actually give the densest configuration when you have got the soil particles which are actually with large void spaces that actually can so called close to the approximation what we actually said with the equal spears. So here in this particular slide what are these maximum minimum minimum void ratios suppose if you assume the soil is in dry state then we have here two phases one is the volume of voids and volume of solids. So in the loose state you have got the very high proportion of the volume of voids compared to the volume of solids in case of densest possible state what you see is that the volume of voids is very less compared to the what we observed in the loosest condition. So here the loosest condition the void ratio emacs is nothing but the volume of voids to volume of solids where the volume of solids is very high in the case of densest condition void ratio is indicated e minimum where the volume of voids is very minimum because of the densest packing. So these type of arrangements are possible sometimes the soil deposits are loose in state and if you have a structure which is required to be constructed on a loose deposit or if they are on the saturated state there is a possibility of endangering with liquefaction hence there is a need for strengthening the soil deposits. So it is always good to estimate these particular values of maximum minimum void ratios and these are actually unique for the given soil type and suppose let us assume that we are trying to compact a soil with a particular type of sandy soil then this is actually used to achieve what compaction can be done so that the soil is actually closest to the densest condition. So if you idealize a cubic arrangement if D is the diameter of the particle so if you take a cube of having 2d a phase length here and then the total volume is nothing but 8d cube. So the maximum void ratio what we said is that nothing but the volume of voids to volume of solids. So here volume of the solids is 4 by 3 pi d cube into 8 particles that means that here 4 by 3 pi d by 2 whole cube into 8 particles when it gets simplified you get as 4 by 3 pi d cube. Now in order to get the volume of voids total volume of the this cubic arrangement works out to be 8d cube minus this volume of solids is nothing but the volume of voids. So if you simplify this it is nothing but the 6 minus pi by pi which is nothing but 0.91 that means that if you the maximum possible void ratio is of this order whether it is in real soil or this with this idealization it comes out to be about 0.91. So maximum possible void ratio corresponding to the simple cubic arrangement which actually gives the loosest state is said to be 0.91. Contrary to this if you have got a densest configuration that means that you have got a soil particle which is actually resting on the 4 equal equidimensional spheres that means that in the pyramidal packing each sphere in one layer sits on the depression between and is in contact with the 4 spheres forming a square in the layer below. So it is the result of this what we get is that in the pyramidal packing there is a possibility of you get the minimum void ratio. So it results in a phase centric cubic packing each sphere lies within the space formed by the 4 resistant spheres in the layer below the same pattern is replicated at bottom and 4 vertical sides of the cube. So the idealization which is actually shown here which is nothing but the root 2d so that is nothing but the total volume that is volume of void see here is nothing but 1.414 d cube minus 4 into 4 by 3 pi d by 2 cube divided by the volume of the soils in the particular layer which is works out to be about 0.35. Now if you see here in the densest possibility you have got a void ratio which is about 0.35 in the case of loosest possibility you actually have got a void ratio of about 0.91. Now let us define one more parameter which is very useful parameter as far as the compaction of the coarse grain soils which are actually not having fines more than 10% that means that the size of the particles is not more than 10% of the 10 to 12% of the particles not more than 75 finer than 75 micron that is 0.075 mm relative density is a 10 generally used to describe the degree of compaction packing or togetherness of the coarse grain soils and which is indicated by dr is equal to e minus e max minus e divided by e max minus e minimum. E is nothing but the in situ void ratio or the void ratio which is actually achieved if the soil deposit is say done manually. So e max is nothing but the maximum void ratio or the reference void ratio of a soil at the minimum density per unit weight, e minimum is nothing but minimum void ratio or the reference void ratio of soil at the maximum density per unit weight. So here in this particular slide the relative density which is indicated as d suffix r is given as it actually has got two boundaries when suppose if the void ratio in situ void ratio say close to e minimum that means the relative density is about 100%. If it is say close to e max that means that the gamma d minimum the relative density of a soil mass is 0 but e which is actually between these two upper bound possibility and lower bound possibility of the void ratios and that is actually exhibits a certain amount of relative density. So if you want say a loose deposit then you if you encounter with a loose deposit you have the soil relative density values close to the e max and if you have got density deposits then you have got the relative density values close to this area. So by using the if you assume that e is equal to gs gamma w by gamma d minus 1 and if you substitute these with respective densities or unit weights you will get here d suffix r is equal to e max minus e by e max minus e minimum which is if you simplify this you will get gamma d max by gamma d into gamma d minus gamma d minimum divided by gamma d max minus gamma d minimum so into 100. So the relative density is actually expressed as 100 so by determining you know the by knowing for a particular type of soil what is the maximum dry unit weight of the soil and minimum dry unit weight of soil which is possible by measuring the in situ unit weight of soil we can actually assess the relative density in the field which is actually very useful parameter in densifying the soil deposits. So here in this slide typical range or classification of the relative density of the granular soils is shown here where the relative density say if it is less than 15 percent very loose 15 to 35 indicates loose deposits 35 to 65 means medium dense 65 to 85 is dense and greater than 85 indicates that very dense soil deposit. The relative density of sand has a well defined meaning because its values practically independent of the static pressure to which the sand is subjected it depends primarily nature and denseness. It is possible for two sands for example have got to identical void ratios to have identical void ratios and relative densities but significantly different soil fabric arrangement the significantly different engineering behavior. It is possible that for example to have identical void ratios and relative densities but significantly different particular arrangement the significantly different engineering behavior. So it is very typical as far as the soil behavior is concerned possible for the two sands for example to have identical void ratios and relative densities but significant different fabrics and significant different engineering behavior. Now the maximum and minimum void ratios are found to depend upon the particle size, the roundness of the particles and the presence of the non-plastic files. It has been found that with the recent research the presence of the non-plastic finds influences significantly the maximum and minimum void ratios of the particular soil deposit and the roundness of the particles whether they are angular, sub angular or sub rounded or rounded and particle sizes. So this we will be discussing at the end of the module along with the other parameters once we introduce. According to the another possible type of the particle arrangement which is actually called as honeycomb structure and these are actually the possible if you have got a silt smaller than 0.02 mm and larger than 0.02 mm and basically this occurs because of the intermolecular forces and this actually can come if you actually have you know some silt particles so grains of silt smaller than 0.02 mm and larger than 0.02 mm settle out suspension more or less in single grains but are small that molecular forces at the contact area are large enough compared to the submerged weight to prevent grains from rolling down immediately to the position of the equilibrium among the grains already deposited. So here in the honeycomb structure when you have got a particles smaller than 0.02 mm and larger than 0.02 mm, 0.002 mm there is a possibility that it actually forms the honeycomb structure and even in case of some fine sands because of the presence of some contact moisture there is a possibility that you actually come across this honeycomb or something like a matte type appearance when you have when you see you know partially or moist sands. So in this slide the typical honeycomb structure is shown here wherein you actually have got the particles which are bridged because of the interparticle forces and the grains coming in contact held by forming a mineral arches bridging or relatively large spaces. So once you know it comes in contact with water once these intermolecular forces you know vanish it actually converts into a bulky grain structure or a single grain structure. So it is possible that the honeycomb structure which is actually shown here if in contact with when these intermolecular forces vanish it actually forms something called the again gets converted into a single grain structure. So in the next lecture we discuss about the environment surrounding the clay particles particularly here what we discussed in this class is that the clay particle is a plate plate plate shape particle which is predominantly need be charged and then there you have a water particles which are actually close to the part clay particle size and then you have a free water which is actually surrounding this particle. So we will try to discuss about this particular behavior and this part this part of the water which is called free water which is actually has got low viscosity compared to this zone and this zone which is actually called adsorbable water which is actually has highly oriented and has got very high viscosity and which is actually headed very close to the surface of the particle and so in the in this particular lecture what we try to discuss is about the particle shapes and what are the different particle shapes and what are the different possible particle arrangements which are actually possible and we actually said that there is a possibility of the single grain structure and then we said that honeycomb structure then when it comes to clay particles we need to actually discuss about two types of the structures which are actually called flocculant structure and dispersed structure and that can be introduced only once we understand about environment surrounding the clay particle.