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Module 1: Volume Change Behaviour of Soils

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Video 1
In our basic soil mechanics, we study the volume change behavior of soils in consolidation. So, when the load is applied on saturated soil mass either isotropically applied load or under ko condition, the isotropic load is applied in triaxial tests on saturated soils, andunder ko condition, this is conducted in odometers. When this loading is applied the excess pore water pressure that is generated in the soil mass soil pore system, we will get dissipated through the boundaries, and once this has got dissipated the volume changes.Because there are only 2 phases that are water and soil solids as water goes out the volume of the sample decreases. So, this decrease in volume is called consolidation and the volume changes are very important in the field problems. Especially, when you haveexpansive soils located and when you are constructing a building or any building or when you are constructing an embankment the consolidation settlements are very important. Often we theoretically determine the coefficient of consolidation in the laboratory bytaking collecting the sample from the field and conducting an odometer test, under field conditions and the coefficient of consolidation is obtained. And, this coefficient of consolidation is utilized in the field for obtaining the rate of consolidation settlement.Similar to estimate the consolidation settlements, we load the sample and let it consolidate, and again we increase the load and let it consolidate, similarly we obtain in e log p curve that is e versus σ ` effective stress relationship. This constituent relationship is similar to the stress-strain relationship. From this, you get bulk modulus that is mv is 1 over mv and you get hydraulic conductivities at any given point. And, similarly using the entire constituent relationship you will obtain the coefficient of compression Cc. So, from this, we can obtain the consolidation settlement or using the bulk modulus thatis one over mv you can estimate the settlements. Often this Terzaghis 1-dimensional approach is criticized and for highly expansive soils or when the soil is highly plastic, or when it is a slurry state like mine tailings etcetera. A large strain consolidation approachis used because Terzaghi’s consolidation consolidation approach uses small strain approximation. So, large strain consolidation approaches are also available. So; however, all theseconsiderations are based on the soil state to be saturated completely saturated. However, when the soil is unsaturated, then the change in the volume of how to determine the change in the volume or how to analyze the change in volume? So, we have often seen that, when initially a saturated or slurry state soil is kept in a small container, this is a slurry sample, and when this is exposed to the environment. So,slowly the evaporation takes place, due to this evaporation from the soil mass. So, the water content of the soil decreases. So, soil enters into an unsaturated state. So, this is often seen as the volume of the sample, and water content is plotted. So, initially, the sample state is somewhere here sample water content is at maybe slurry state or equilibrium state. So, this is done in the shrinkage test shrinkage limit test. So, this is the initial state, where it has a particular volume and particular water content. So, when the soil is subjected to drying, because when the soil is kept in atmospheric conditions. So, due to the Rh and temperatures, there is some suction load that is applied to the soil mass. So, because of which soil volume decreases up to certain water content andbeyond that this is non-linear and the change in the volume ceases to exist at one particular water content, which is called shrinkage limit. So, up to one particular water content, this is linear. So, the volume decreases linearly with water content. So, this also can be plotted as the degree of saturation sorry void ratio. So, because the volume of the soil is known and water content at any given point is known. So, we can obtain what is the total mass is also known mass of the soil sample is known because when the water content measurement is taken the soil is weighed right. So, therefore, the density of soil bulk density of the soil is known because total mass and total volume are known. So, knowing the bulk density the dry density of the soil can be obtained using thisparticular expression knowing the water content the dry density can be obtained. Knowing the dry density, knowing the specific gravity, we can obtain the void ratio. So, that is how the void ratio can be obtained and which is plotted on the y-axis and xaxis instead of w if we plot with w G s, w G s we see that there is one is to one line.There is a one is to one line exists up to certain water content; that means, the degree of saturation of the soil remains the same. And, beyond that degree of saturation becomes less than here degree of saturation is one and here degree of saturation is less than 1beyond this and here degree of saturation may remain the same constant. Because the decrease in water content is nearly constant and it almost ceases to sorry degree of saturation slowly becomes close to approaches to 0. So, the volume see here it approaches one is to one. So, therefore, if the what e = w G b Sr. And as Sr equals to 1 up to here this is this follows one is to one line. So, Sr = 1, w G and w G., therefore, it plots 1 is to 1 line. So, as the soil is subjected todrying. The degree of saturation remains the same up to one particular water content and beyond that the degree of saturation decreases. And, the volume of the sample continuously decreases from the beginning itself and what happens to the suction; suction of the soil increases. Here the suction maybe 0 the suction either psi or s smallest = 0, the suction is very high. Suction becomes very very high may be in terms of MPa you may be able to measure depending on the type of soil also.So, this particular thing happens in expansive soil or soils which exhibit volume change during drying and wetting. So, this is a drying process. So, soil exhibits a volumedecrease during this particular process. Similarly, when the soil is subjected to wetting the soil volume starts increasing. So, how much it increases or how the suction varies here the suction volume the degree of saturation the volume. So, which can be represented with void ratio and suction 3 different parameters are changing, when the suction is increased the volume may be decreasing and the degree of saturation will be decreasing. So, similarly, these 3 parameters are dependent on one and each other. So, to understand the soil behavior we need to conduct the tests under a controlled environment by controlling suction and how these parameters are changing this is what needs to be done? Similarly, this is these particular tests are conducted when there is no external load, butsimilar tests may also exist when we are constructing a building or any other structure on soils. So, this may be the foundation and you may have a groundwater table somewhere as here. So, this is a groundwater table and this is a ground surface. And, you may have a fully saturated region, that is capillary region may be up to here. So, this = the air entry head height or capillary height. So, beyond that this is unsaturation. So, if you see the profile. So, if you see the variation. So, the water content varies in this particular manner, watercontent nearly the same, or the degree of saturation is the same, but beyond that, it decreases a decrease in this manner. So, when the water content decreases in this particular manner. So, this is maybe adegree of saturation and this is height. So, the degree of saturation may decrease in this manner. So, essentially when you are constructing some particular building in the unsaturated region this is the unsaturated region, and this is a saturated region and this isa saturated region, but here the suction component exists suction is more than 0 here suction is 0 or suction is less than 0. So; that means, this is a there may be positive pore, water pressures exist below the groundwater table, but here you will have suction valuemore than 0 and here the suction value will be very high. So, when you are constructing such a building or when you are exerting some loading due to construction activity. How the soil volume changes is our important question thatneeds to be addressed. For that, some suction controlled consolidation tests are also conducted. 
Video 2
Suction controlled odometer tests are conducted. In the suction controlled odometer tests, we have an odometer similar to what we have seen earlier we have 2 porous plates, look at it on top and bottom of the soil sample, if this is your soil sample. And, here if this is a ring which keeps the soil sample intact, this is a ring, and this is a loading plate, and load is applied on this, and there is a pipe are connected to circulate the PEG solution. So, this is an osmotically controlled odometer. So, these are connected these are peg solution which is circulated into the around the soil sample boundaries. So, that the peg solution comes in contact with the pore water of thesoil, there is a semi-permeable membrane, which is kept here and again here. So, due to the semi permeable membrane in the peg molecules are not allowed to enter into the soil sample. So, therefore, as a peg solution concentration is high on at the boundaries. So, the water will leave from the soil, and the water content of the soil decreases. So, when the peg solution concentration which provides a suction value of say hundred kilo Pascal due to this 100 kilo Pascal suction it is exerted on the soil. So, the water content decreases due to a decrease in the water content. So, under either the applied load or even without the load the soil volume will decrease.So, similarly, this is an osmotically controlled test and similarly using the access translation technique. So, where at the top and bottom of the clay sample are soil samples, you will have a high air entry disc here H A E disc. And, you all have low airentry disk located at the top. That means, course porous stone is located at the top and high air entry disc is located at the bottom. So, this is connected to a gas pressure gas chamber. So, the air pressure can be applied and through which the water pressure can be applied and this air entry high air entry disc is always kept saturated. So, this is it maintains a very good hydraulic contact with the soil pore water. So, then the pore water pressure is maintained through this chamber and from the bottom and air pressure is maintained from the top. So, this way has given u a - u w is maintained within the soil sample. And, so, the volume of the soil sample can be obtained by connecting to a by measuring the height of the soil sample using a dial gauge. So, here also you will have a dial gauge, which is located, and which measures the change in the volume you will have a dial gauge. So, which measures the change in the volume of the soil sample. So, this way void ratio can be measured suction can be controlled and the water content of the soil can be obtained by having independently established soil-water characteristic curve. Therefore, knowing the suction of the watercontent or knowing the suction either water content or degree of saturation can be obtained. So, this way to independently or these 3 parameters can be obtained from these particular tests, and the constitutive relationships can be developed for different soils. Similarly, this is the k0 condition because when you apply a loaded soil exerts pressure on the boundaries. So, this is k0 condition, but in triaxial similar tests can be conducted where we isotropically. So, this is the soil sample where we isotropically consolidate. So, we exert an all-round pressure of σ3 on the soil sample. So, therefore, soil can beisotropically consolidated. So, this is isotropic consolidation. So, therefore, in suction control triaxial tests the isotropic consolidation test can be connected. So, therefore, here the total volume that can also be measured. So, the amount of water that is leaving can be determined. So, therefore, water content or degree of saturation and the void ratio because the change in the volume is also known,and suction which is controlled all these 3 parameters can also be obtained in suction controlled triaxial tests; if you look at different data that we get from these tests. So, these are either plotted with void ratio or often this is plotted with specific volume. The specific volume is nothing but 1 + e, 1 + void ratio because the void ratio is the volume of voids volume of solids. So, this is nothing, but total volume by volume of solids. As the volume of solids anyway is constant how the total volume changes by applying a different suction and mechanical loading can also be can be obtained.Therefore, specific volume is often used. So, the specific volume versus time for different applied loading, if you see so, when thesuction is 0. So, not much change, but as suction is increased you would see that the specific volume will decrease with time. So, this is an equilibrium time. So, with equilibration time the specific volume decrease for different suction higher than, 100 kilo Pascal. Similarly, specific volume is plotted with the mean stress under different suction conditions. Mean stress so, that is p net when it is plotted. So, when the soil is completely saturated. So, this is what we get this is typically an e log p similar to e log p this is a test equals 0.So, that is purely saturated soil and for other soils a dry condition, because if the soil is expansive, the initial volume of the soil sample may be here. Due to saturation initiallyunder this particular seating load, when you saturated the volume total specific volumebecomes this, and when you consolidate this is the curve that exhibits. So, initially for example, under 100 kilo Pascal, for the sample may be somewhere here specific volume somewhere here when you saturate it up to 100 kilo Pascal. So, the initial state of the soil may be here. So, this is at s equals to 0 this is at S equals to 100.So, then if I consolidate so, it may consolidate somewhat like this. The slope of the curve change, because there is a suction because of which the, it does not consolidate as much as it does not compress or volume does not change significantly as it happens when thesoil is completely saturated. So, as my suction is increasing I obtain different profiles. So, here the initial state of the soil sample is different because my suctions are different here this is much higher than 100 kilo Pascal right. So, initially, when the soil sample is taken at dry state probably, it has a suction of maybe 1000 kilo Pascal. So, then the specific volume may be somewhat here when I reduce the suction within the soil into a hundred kilo Pascal then; that means, some wetting takes place, because of which the specific volume becomes this much then I can consolidate. Similarly, if I want to consolidate a saturated state I allow the soil to completely saturateor wet it at seating load then it comes to say S equals 0 and then after that, they consolidate. So, I get different profiles like this for different loading conditions this may be in a completely dry state. So, such kind of profiles you can obtain. Similarly, the specific volume can be plotted with suction for drying and wetting. So, when the specific volume is when the suction is increased the specific volume will decrease because the specific the increase in the suction the water content decreases. So, due to a decrease in the water content, that specific volume will decrease. So, when you wet it, the specific volume increases, but it does not increase as much as we obtain in a drying state. Similarly, when you draw u a - u w, that is suction versus p net normal stress. So, during the drying process the net normal stress on the soil sample increases, which decreases as you wet it. So, this is drying and this is wetting. So, the hysteresis behavior can be studied very well and while studying the hysteresisbehavior the specific volume changes and the drying and wetting that hysteresis can also be studied very well in this particular suction controlled odometer test. Further, the void ratio versus log σ can be plotted when you plot this void ratio versus σ or σ ` the effective stress what we see is the suction value when it is 0. So, this is atypical consolidation, test result when S equals to 0. If you assume that the e versus log p` relationship is linear, then this is what we obtain. And, when the soil is expansive assumes that this is the consolidation curve when the soil is dry completely dry. So, the initial state of the soil may be somewhere here. The void ratio will be less than, the void ratio of the saturated soil under the same load; under this particular load, the soils void ratio will be smaller than the void ratio, that we obtain for the completely saturated soil. So, for the under the complete dry state, when you load it. So, this is compression this is not called consolidation when you compress the soil. So, the change in the volume willbe negligible. So, which changes in this particular manner right.So, because this is a dry soil when you are compressing by applying the loading so, change in the volume is the void ratio is not significant therefore, this is the curve you get or this is the relationship you get. And, this is at s equals too much greater than 0 or nearly dry state and this is completely saturated.So, now when the dry soil at any particular loading, if you subject to wetting how does it behave? For example, at this particular loading, if I wet the soil sample, for example, thesoil sample is now initially compacted to one particular density. And, I will explain thisone again initially the soil sample in a dry state which is taken in compacted and kept in the odometer. Now, this is under seating pressure, this is a seating pressure. Now, this is completely saturated. So, when this is completely saturated this is the void ratio the soil obtains at a fully saturated state. Now, when we consolidate this is the curve we get. So, this is a consolidation curve. So, at each load increment, we wait for the soil to consolidate. And after it consolidates this is the equilibrium void ratio and again we put next loading and that is how we consolidate the soil sample. So, this is what happens? Now, if you take a dry soil sample with the same density and which is at this particular state where the voidratio is e. Now, if the soil is compressed by applying to load and this is what we obtain a dry state. So, now, at any given loading if the soil is subject to wetting. So, what is expected is the soil will swell, or the volume of the soil sampling increases, which is called swelling.Similarly, another soil sample is taken which is again compacted to the same level, and again which is subjected to this particular loading, and again which is allowed to wet which is wetted, then it exhibits swelling, and then it shows this behavior. And, similarly here a small swelling is exhibited. Similarly, here when the soil is in thiscondition, which is wetted which exhibits such a decrease in the volume which is called collapse. Similarly, the soil when it is here initially when it is allowed to wet when it is wetted it exhibits a collapse. Similarly, here also it exhibits a collapse. So, even swelling soils are expansive soils, when the soils are subjected to wetting under different confining stress or applied stress it may swell or collapse, or the volume may increase or the volume may decrease depending on the stress state of the soil. So, therefore, the swelling and collapse behavior of soils can be determined or studied very well by conducting several tests swelling and collapse behavior of soils can be studied by analyzing their behavior under suction controlled environments. 
Video 3
So, previously we have discussed, how the suction controlled volume change behavior can be obtained in suction controlled consolidometers and isotropic consolidation tests in suction control tri-axial tests. So, mostly the behavior of such soils under controlled suction are analyzed for developing constitutive relationships and forunderstanding the stress state of the soil at any given condition, under loading condition and the change in the volume, how to obtain the change in the volume with a degree of saturation and change in the water content and suction can be combined into constitutive modeling. And, say continuous behavior of the soil from wetting to drying or drying to wetting can be model. Today, we will discuss a few topics related to initially, we will discuss the  onstitutivemodel, which is a given by recent researchers on how to incorporate the volume change also into suction water content relationship. And, after that, we will start discussing the Swelling of Soil. As we have seen earlier, the specific volume which is represented as v or nu with suction follows in this particular manner initial the specific volume maybe somewhere here, then the suction is 0 that is the fully saturated state. As the suction increases this, when it is dried it follows this curve and when it is wetted. So, this follows this relationship with this curve. So, this is similar to void ratio and loador effective stress has a load or effective stress increases the soil compresses as a load is released or when the unloading is taken place the soil expands, but it does not come to the original condition. So, the behavior of soil under unsaturated condition is very similar to the soil in the saturated condition qualitatively because of drying and wetting. So, this is loading drying is similar to loading and wetting is similar to unloading. So, here it is 1 + c, the specific volume is 1 + c. So, these 2 are related. So, now, there is aconstitutive relationship given by Gallipoli et al in 2003 to modify to incorporate volume changes also in the suction water content relationship. So, he has proposed this relationship the degree of saturation is this is a 1 by 1 of 1 + or relationship is the vengeance equation is modified by incorporating the changes in the volume.So, here the nu is a volume change or a specific volume and here ψ and phi are fitting parameters. So, as we represent ψ for suction let me use a different parameter here k kand ψ are the fitting parameters and s is suction. So, if you compare the original (ReferTime: 05:01) equation, which is written as 1 by 1 + α s over n whole power m. So, here αis a fitting parameter related to the air entry suction or 1 over air entry suction is the function of or related to air entry suction. So now, α is substituted with phi times specific value - 1 power k. So, as the air entry of the soil changes with change in the pore geometry, when the volume of the soil changes the air entry of the soil also changes because, if we consider initially saturated soil when it is dried the volume of the sample changes, but the degree of saturation remains same. So, as the water release from the soil system, the void ratio decreases. So, therefore, air does not enter into the system. So, it is before α is related to the α, which is the parameter, which is related to the air entry value is related to the void ratio. So, as the void ratio is decreasing the saturation can be kept constant until a certain value and beyond the rate decreases. So, therefore, if this is plotted as the degree of saturation versus suction, it is seen that for a given controlled volume-specific volume, it is seen that for a high specific volume, it exhibits this behavior, this is 1. For high specific volume, it exhibits this behavior and formoderate it exhibits this behavior as a specific volume decreases maybe, 1.8 or something this exhibits this behavior and this is at constant specific volume. So, this is at 2.3. So, under constant specific volumes the relation between degree of saturation and suctionfollows this relationships pattern, using this particular equation. So, it defines the surface so, soil water characteristic surface in degree of saturation s and nu space with three dimensional space. So, most of such relationships are very useful for understanding the continuous behavior of soils from wetting to drying or drying to wetting and how they behave cyclically, they can be modeled using such relationships. And, critical states soils mechanics theories require such kind of relationships such relationships too. And, let us understand, how the swelling of the soil takes place during wetting, we must have heard that there are swelling soils or expansive soils. So, these are the soils when there wetted or saturated the volume of the sample increases. So, the volume of the sample increases because the expansive soils contain clay minerals. which are mostly the mineral or mineral. The particles of these minerals are kaolinite, the particles of these minerals contain negative charge on the surface due to isomorphous substitution. Due to the isomorphous substitution so, the silica may be replaced by the alumina. So, the alumina is alumina replaces the silica in the tetrahedral sheet. So, this causes a net negative charge on the clay surface. So, due to this negative charge on the surface clay particles acquire positive ions these are cations on its surface, during the exposure to theenvironment after they formed. So, these are the exchangeable cations, exchangeable cations mean so, these cations can be replaced with other cations. So, they can be removable or exchangeable not removable exchangeable. So, the alumina we fine so now, so when this particular particle is hydrated. So, then or when water is absorbed, the water is absorbed from the atmosphere. So, they get hydrated. So, there is a thin film around the clay particle that is formed and the ions also get hydrated.So, these broken lines are hydrated or the broken lines show the hydration. So, generally,these layers are multiple layers like more number of multiple layers can be formed around these cations and the surface. So, the particle when this clay particle is completed wetted, there is a diffuse double layer or a water film that is formed around the clay particles. This is a clay particle and the water when it is available in the bulk solution.So, generally, the ions straight diffuse away from the clay particle. However, the clay particles try to hold ions around the surface because they have an affinity towards these cations. Therefore, water enters into the surface of the clay particle, when water entersthese ions gets distributed around the clay particle, in this particular manner. So, the concentration in the outer layers is very less. So, the concentration of these cations is very high near the surface, these are all in the hydrated stage only. So, this is an individual film thickness. So, this is another film thickness around the clay particle.So, this is particle thickness clay particle thickness. So, initially, this is in a dry state. So, this is a hydrated particle and this is completely wet are saturated particle. So, here if you see the potential, the electrostatic potential to present, maybe with phi with the distanceif you see so, it distributes in this particular manner. So, the potential is higher here at the surface, in nondimensional format can berepresented with z and which decreases, which is the function of x distance from the particle surface, this is the distance from a particle surface. So, this is a particle if this is a particle is a distance from the particle is x then the potential drops, the nondimensional potential drops in this particular manner and which goes to 0 at the bulk solution and diffuse regular interface. So, this thickness is your t f film thickness. So, now when particles are at dry state when they are compacted the particles may be interacting in this particular manner. So, this is one particle and this is another particle. So, particles are if there is small water that is available then there will be held in thisparticular manner and then were very close, very close to each other. They may have surface exchangeable cations particles that are very close to each other, but as soon as this is a dry state.. So, this is an interacting system. So, when the soil is completely wet. So, you have 1 clay particle and you have film thickness around individual clay particle and that is one particle and you have another particle. So, this is a positive ion double layer and this is also a positive ion double layer.
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