Video 1
Hello all, we have been discussing the concept of vapor pressure lowering which can be well understood using Kelvin’s equation. So, Kelvin’s equation a which states that the vapor pressure on a curved surface equals to the saturated vapor pressure times exponential of partial molar volume of water times change in the pressure across the interface divide by RT. So, the implication of Kelvin’s equations is that above a curved surface the vapor pressure is larger than in the fluid. So if you consider a capillary tube immersed in a beaker of water, the water rises in order to balance the chemical potential and it assumes a meniscus or curved surface like this depending on the interaction between the capillary tube and the fluid. So, this is a typical example of water in a glass beaker or glass capillary so you have a meniscus like this. So, the vapor pressure above a curved surface is u v which will be less than the saturated vapor pressure which will be above the flat surface, so this is the implication of Kelvin’s equation. More than that the vapor pressure even though this is less than the saturated vapor pressure water vapor condenses into water and it accumulates in a capillary tube which we will understand. As there is a pressure drop across the interface, so this is ua atmospheric pressure and this is water pressure. So, there is a pressure drop across the interface because of which there is a change in the vapor pressure. Similarly, when there is a capillary tube which causes a lowering of the vapor pressure. So, you have, say for example, here you are maintaining RH equals 100 percent. So, thenyou have u v sat here in the ambiance, so here the vapor pressure is lower than the saturated vapor pressure u v inside the capillary tube. Even though the vapor pressure inside a capillary tube is lower than saturated vapor pressure, you see that the water accumulates into the capillary tube with time and you see that there is a filling of water within the tube. So, which fills because, a number of water molecules that get trapped in this small cavity, so slowly the water level increases within the capillary tube in order to which is nothing but condensation. So, condensation takes place at a vapor pressurewhich is less than saturated vapor pressure that is the implication of Kelvin’s equation, this has a very important application, important correspondence to our soil mechanics. Because, when you take a soil sample which is kept outside this is initially dry which is the oven-dried, initially at the oven-dried state you take a clay powder, say any clay powder or even soil at oven-dry state if you take and then place it in the cup and in an atmosphere when you leave it the relative humidity of the atmosphere maybe 80 percent or it could be anything, it may vary usually between 60 to 90 are closed to 100 percent depending on the location. So, when you have some particular RH and temperature of the ambiance, then you would see that there is an accumulation of water at the surface of the soil due to condensation. Because, if you consider the force of soil grains hasindividual capillaries you have a number of capillaries attached here which lowers thevapor pressure above this and eventually there is a condensation that takes place at lower vapor pressure which causes accumulation of water at the surface, because of the potential difference from the top surface and the bottom surface there is a diffusion that takes place and water slowly penetrates into the deeper layer of the soil.So, this happens in any type of soil but clays generally the pore size is very small, so therefore easily the condensation takes place and more water will get accumulated. So,the vapor pressure lowering depends on the capillary size, so here in this particular case Kelvin’s equation a simple capillary tube is assumed. Therefore, the pressure drop across the water interface is 2 T s by r surface tension times 2 by the radius of the capillary tube. So, capillary tube diameter or the radius is very important in controlling the vapor pressure and condensation so this is called capillary condensation. This is a very important concept in soil mechanics because this concept is also utilized in the estimation of the specific surface area of fine-grained soil such as Carnuts and other clays not expensive clays like Bentonite etcetera. Because Bentonite generally they have dual porosity system and you have smaller pore fractions that exist this generally used for only for Carnot clays using adsorption isotherms. So, you take a soil sample and you expose the soil sample to a particular temperature and then relative humidity and absorption of. So you would expect that there is an absorption of water molecules around the clay surface and the exchangeable Cations because of the hydration there is waterthat accumulates. So, you would see that the adsorption increases with time for a given RH, and also it increases the adsorption amount of adsorption also increases with an increase in the RH, so using this concept the specific surface area is estimated.
Video 2
As we have seen that there are important state variables such as relative humidity when relative humidity is maintained you would see that there is an accumulation of water so the water content of the soil changes. So, these 2 are important state variables relativehumidity and water content and also they are dependent on each other, you one can establish a constitutive relationship between these 2 state variables also. However, simply the RH is not alone the controlling factor for the water accumulation or water retention in soil mass, there are other factors that would influence the water retention in soils. So, therefore, it is not the RH versus w there is something called soil water potential which is used as an important state variable to relate with the water content. So for example, if you consider if you immerse a soil column in a water reservoir at timet equal to 0 just immersed in a water reservoir after time t equal to 0, you would expect that the lower portion of the soil mass get saturated and the water content increases within the soil mass even above thus this free surface free water surface. So, above thislevel also there is a water diffusion that takes place and then the water content increases above this level due to the capillary mechanism. This is similar to inserting one capillary tube or multiple capillary tubes into soil mass into a water reservoir, therefore there is a rise of water within these capillary tubes which is similar to this.So, therefore, due to the capillary mechanism, there is a rise of water into the soil column. The water content is now related to the capillary mechanism if you have a thincapillary. So, raise is higher if you have larger capillary the raise is smaller. So, the water content depends on here capillary mechanism plays a role in the water content of soil mass, the water content also varies with the height of the soil samples from the free water surface. Similarly, the soil water potential also gets influenced due to the electro Osmotic mechanism. What is this electro Osmotic mechanism let us understand we have seen that if you have a U shaped tube. So, you take a U shaped glass tube so where you have a semipermeable membrane, which separates the water and a salt solution this is water and this is a salt solution. So, you have a number of solutes which is added to the solvent, so in this particular case, we expect that at equilibrium at this is this is at time t equal to 0. Now at time t equal to t greater than 0 the same system if you brought now so you would see that there is an initial height. Now, water from this reservoir would move on to the other side to decrease theconcentration of the salt in the right-hand column. So, there is a head that develops to bring the chemical potential equilibrium which is called a which is the Osmotic head. This is similar to a capillary head we have seen earlier where when a small capillary or thin capillary is immersed in a water reservoir, there is a rise of water in the capillary which is the capillary head similar to the capillary height are raised. You would see an Osmotic head that is developed in when the solute is present in this column and there is asemi-permeable membrane that filters the solute to move from the right-hand side to the left-hand side. So, in this case, water moves from left to right to equilibrate the chemical potential, if the semi-permeable membrane was not present diffusion of the solute takes place from right to left in order to balance the chemical potential. So, this is relevant to our clay system where we have a clay particle which is negatively charged, there is a negative charge in the clay surface because of isomorphous substitution it attracts positive ions on the surface and so there are so many exchanges of cations that are present which are attracted in from the environment and kept it on the surface of course on this side also. So, now when this clay particle is exposed to the water you would see that then when thewater is available or if this clay particle is taken and put it in a beaker of water, we expect that these ions should diffuse from this clay particle surface to the bulk solution because the concentration of these ions is very high here the concentration is c not and here the concentration is 0. So, therefore, there is a concentration gradient that exists from the surface to the bulk solution, therefore there should be a flux diffusion that should take place to equilibrate the concentration of these ions throughout this beaker ofwater. However, clay particles are negatively charged and they would not allow these ions to go away from the surface and this clay particle negative charge acts as a semi-permeable membrane in this particular case. So, therefore, there is an osmotic flow of water takesplace from the bulk solution towards the clay surface, so which causes diffusion of ions distributed in this particular manner. Here the concentration decreases from the particle surface towards the bulk solution in this particular manner. So, you have a denser densely packed exchangeable ion close to the surface and theconcentration decreases, deplete with the increase in the distance from the clay surface. So, this mechanism is just similar to the osmosis that takes place due to the semipermeable membrane. So, therefore, Osmotic mechanism also takes place in clays especially expansive clays, where you have a (Refer Time: 14:47) more led mineral where one more led mineral has a very high surface area and very high cation exchange capacity, therefore, it exhibits the Osmotic mechanism very well. In case (Refer Time:15:00) the specific surface area is low and cation exchange capacity is very low the Osmotic mechanism does not dominate. So, because of the Osmotic mechanism also there is a potential decrease, there is a potential decrease because of the presence of these cations exchangeable cations around the clay surface and because of that there is a change in the potential this Osmotic head or cosmetic potential is also included in soil water potential. Clay particle is just now I said that the clay particle is negatively charged and it has positive ions around the surface when the water molecules are available such as keeping a clay sample oven-dried clay sample in the atmosphere. So, then it attracts the positive ions at the surface it attracts the water molecules on to the surface, so there is hydration of exchangeable cations and hydration of clay surface that takes place. So, there is an electrostatic force that is available around the clay particle surface,therefore there is an additional potential due to the adsorption of water molecules around the clay surface and water molecules, so, therefore, the combination of these 2 is called the electro Osmotic mechanism. So, essentially this is the capillary mechanism andelectro Osmotic mechanism all these mechanisms are included in soil water potential, soil water potential is nothing but it is the potential can be defined as the amount of work done or potential energy stored per unit mass in bringing same mass m from reference tothe point in question. So, the potential is the work done per unit mass. So, this is simply gh or simply presented with h. So, in the case of capillary rise, there is a capillary rise of head h this is a soil water potential it is called and in this particular case this is the h c, so soil water potential includes all of them and which is synonym to total suction soil water potential is synonym to total suction The total suction is nothing but a so u a minus u w, so this is the pressure drop nothing but total suction which has units of kilopascal. So, the potential has units of joule per mass kg, but the total suction has units of kPa soil water potential has units of meter because which is a header. So, soil water potential can be converted to total suction by multiplying with gamma w so this is a meter and this is the kilo Newton per meter cube that gives kilo Newton per meter square or kilopascal. So, the total suction includes matric suction, the matricsuction is consists of the capillary mechanism and os electro Osmotic mechanism. So, the matric suction component includes all of them, matric comes from the matrix due to the soil matrix there is a potential drop or potential change that is indicated with matricsuction and Osmotic suction is due to the presence of salts in pour water. So, this Osmotic suction needs to be clearly distinguished from the Osmotic mechanism that is consisted of in the matric suction. So, generally the clay particles the exchangeable ions the exchangeable cations that are present that cause that providesOsmotic mechanism, that provides some suction which is included in the matric suction. But additional salts if you add a salt solution to the pore water then that is a contribution to the Osmotic suction. So, this contribution can be explained if you consider an oedometer, where you have soil sample soil and you have a porous stone above andbottom you have a reservoir where the whole sample can be merged in which can be connected to a water reservoir or a burette stand. So, such a head is maintained there will be a flow of water flow takes place and you apply some load on this. So, when you consolidate the soil sample by increasing the pressure, so this is an initial void ratio and you would see that it consolidate in thismanner. If this is a normally consolidated soil sample are initially the sample is in a virgin when it follows a virgin compression line. So, this is how the soil consolidates if you take a duplicate sample prepared now this is an initial void ratio. Now if I change thesolution this water with some salt solution, now I put salt solution instead of water under the same pressure you would see that the void ratio drops so this is the new void ratio. So, this void ratio you can obtain by consolidation when you have water by applying apressure of this much. So, this is a pressure so therefore the same void ratio can be achieved by passing through a salt solution that is equivalent to this pressure. So, the addition of salt solution is equivalent to the application of this much pressure on a soil, where the pore system consists of only water so this is called Osmotic pressure or similar to your Osmotic suction. Because there is a change in the potential because of that there is a pressure here matric suction is kPa and this is also kilopascal. So, this is Osmotic suction kPa this should be distinguished clearly from the Osmoticmechanism that is existing in matric suction. So, the total suction and Osmotic suction is important not only in unsaturated soils, which is significantly influencing the soil behavior in the saturated condition as well. But matric suction exists only in unsaturated state Osmotic section exist in both the conditions whether the soil is saturated orunsaturated, but matric suction exists only when the soil is unsaturated. So, this total suction versus the water content is an important constitutive relationship which is called the soil-water characteristic curve or also called the water retention curve.
Video 3
The water retention curve is a terminology used in water resources and soil chemistry, in agriculture, etc. So, whereas the soil-water characteristic curve is a terminology used in soil mechanics geotechnical engineering. So, the soil water characteristic or waterretention curve is an important constitutive relationship of unsaturated soils, which is a psi versus water content here I am writing gravimetric. But generally, we use volumetric water content I will explain why in a bit very soon, which forms a very important constitutive relationship unsaturated soil mechanics forunderstanding the flow behavior or for understanding the shear strength of the soils or volume change, etc, this constitution relationship is very important this is central to the entire soil mechanics. So, let us try to understand how this suction and water content are related. If you consider the simple capillary the single capillary tube initially the water may be completely filled or slightly it may have some meniscus due to the interaction between the water molecules and the capillary tube. So, the adhesive forces woulddictate what is an angle that would that it would have it may 90 degrees or it may be less than that. So, when there is continuous evaporation of water that is taking place, so as there is goodinteraction between the water molecules of the pore fluid and the wall surface a good adhesive forces that exist, so water cannot leave even though there is evaporation that takes place or the energy is applied. So, it changes the curvature of the meniscus so thatsome water can be taken out. So, without losing the interaction between the wall surface and the water phase it loses some water molecules some water, so which is negligible. So, there is a point one initial state and there is a 0.2 that is a state here. So further if you wait for some more time or further energy is given, so the energy that is given is indicated with the suction there is negative pore water. As we have seen earlier that if you consider soil column immersed in a water reservoir you would see that there is a rise of water or water content is increasing, but the water pressure within the soil mass above this level is negative, so water pressure is negative this is less than the atmospheric pressure. So, therefore, there is a negative pressure due to the potential drop, so therefore this is the potential that is increased. So, the evaporation is taking place because it is likesuction you are taking a thin straw and keeping it in a juice glass of juice and sucking you are applying energy and then sucking it. When you are sucking this is what is happening water is lost because of the sucking action that is this is a suction pressure or simply the suction negative pore water pressure, which creates a negative pore waterpressure initially. There is no water pressure inside here you would see that there is a pressure that is build up because, u a minus u w if you see here there is a negative pressure that a that is developed here, this is the atmospheric pressure this is the water pressure is lower than atmospheric pressure. If you consider gas pressure the water pressure is negative that is what is indicated here if this is 0 then the minus u w is plotted here. So, the new w is negative here within the water column, so if you increase the suction further or more water is lost. So, then there is a change of contact angle from earlier angle to the new angle, and further water is lost when the curvature of the meniscus increases, there is more water pressure inside more negative pressure within the column so water pressure here is increasing. So, here this is a water pressure corresponding to the second figure and this is a water pressure corresponding to the third figure and beyond that with a small change in the suction, you would see that the with the same angle the water drops drastically and this particular point is called receding angle theta r. So, therefore, one water is slowly lost from the column of water due to the evaporation. You would see that there is a build-up of negative pressure within the water because there is a concave meniscus that is developed and because of that there is negativepressure and more water is lost u w here increases or more negative pressure that is built up within the system within the soil within the water and beyond that, the water simply decreases by decreasing it is level within the capillary. So, this particular point is also called air entry value, air entry value, or air entry suction the suction corresponding to this particular point is called air entry value or air entry suction. So, because until then the air enters into the system but here air has entered. So, we have air here so you have air here so this is called the air entry value. So, that was the most idealized system where you have a single capillary, but when it comes to the soils you have a network of pores that can be idealized as a capillary network like this. So, you have one capillary which is larger capillary here so you have thick capillary here and there is a thin capillary here, there is a thickest and this is the thinnest capillary and in between, you have these 2 capillaries. If you take such a system where the water is completely present in the capillary, so initially the entire capillarynetwork is completely full of water. So, therefore, here we plotted with respect to the volume of water earlier and again we are plotting with respect to the volume of water per total volume of pore space. If you plot and which is we hear x-axis is plotted with respect to the suction are the negative pore water pressure in log scale, then you would see that initially, the suction would be 0because this is flat. So, this is flat so u a is equal to u w or u a minus u w is cos 90 is 0, sou a is equal to u w or u a minus u w is 0 so the suction is 0. So, however, that particular point cannot be pointed because it is a log scale, but a small value if you consider and the corresponding value is equal to 1 this cannot this could be 1 only at you have u w is u a or u a minus u w is 0. But he because it is a log scale that cannot be represented here this cannot be1 this could be small value here. So, when there is evaporation that is taking place because we have seen that the pressure drop across the air-water interface is inversely proportional to the radius of the capillary tube. So, the pressure drop in the larger capillary tube or the thicker capillary tube would be smaller, therefore water will be lost first from the larger capillary tube and followed by this tube and followed by this tube. So, as they approach the receding angles corresponding to the receding angles the water beyond that it drops and this is the point this particular point, say, water drops beyond this particular point. So, this is this particular point corresponding to the air entry value and beyond that, the water content decreases drastically and when or after some time you would see that all other capillary tubes would be empty, but thinnest capillary still contains some water so that water is remaining here and even some more suction is applied or some more negative pore water pressure is developed then also you havesmall water. So, this is the relationship that is shown between water content or volume of water park total volume, so this is nothing but theta. So, this volume of water part total volume is theta with respect to u a minus u w or if you consider gas pressure, then it is simplyminus u w in log scale this is considered this is a unique relationship for a given material. So, if you consider a soil column in a water reservoir, so then you would see that there is a rise of water or the water content of the soil mass increases with time water contentdecreases with depth. So, you would see that there is up to here the water content within the soil mass will be equals to the saturated water content. So, here in case if you consider volumetric water and this volume of water by total volume. So, this is a nothing but porosity times porosity is the volume of voids by total volume times Sr is volume of water by volume of voids. So, this is n Sr so when degree of saturation is 1 that is fully saturated case equals to porosity and interestingly beyond that also up to some particulardepth the water content equals to the porosity or Sr equals to 1 degree of saturation equals to one up to the second depth Beyond that the water content decreases from theta, so let us understand why this particular soil mass can be idealized as a number of capillary tubes. So, this is 1 capillary tube this is a bigger capillary tube this is another capillary tube, so this is a thinnest capillary tube this is a widest capillary tube and this is in between. So, if this is immersed in a water reservoir, so then you would see that the capillary raise would be smallest in this particular capillary tube and highest in the thinnest 1 you would see that capillary rise is would be highest in the thinnest capillary tube and this would be medium. So, this the condition when you have 3 capillary tubes together when they are immersed in a water reservoir so this is a condition. So here if you see at this particular section atthe free water surface level you would see that the water content within this pore space or the capillary tubes water content is completely full. So, this is fully saturated capillary tubes in this particular case. So, if you consider the volume of the capillary tubes at this particular section is equal to the volume of water. If you ignore the surface of the capillary tubes or walls of the capillary tubes, so above this up to a particular depth, at this particular level where the capillary rise into the larger pore larger capillary tube. Here also it is the same volume of the capillaries equals the volume of water, beyond that if you consider any section the volume is less than the volume of water. So, up to this particular depth, the water content remains the same as below this level also, below the free surface also water content how much you have the same water content you have here.So, similarly here also the water content in this particular zone will be the same as the water current in this particular zone. So, therefore, this is called air entry suction head, air entry suction head is the point corresponding to the suction where air enters into thelargest pores of the soil sample. So, here if you consist if you consider this whole soil mass consists of only 3 capillary tubes, so then the air enters into the largest capillary tube here so that is air entry. So, here this air entry head which can be h AEV is equal tois nothing but the suction corresponding to suction corresponding to the soil-water characteristic on a which is on the saltwater characteristic of. The suction corresponding to which the air enters into the largest pore of the soil system is called the air entry section, so beyond that thinnest pore still has some water. So, water content here is less than theta s here theta equals theta s. So, if you plot the water content versus the suction head because the negative pore-water pressure the pore water pressure within the soil mass if you see that is positive downward and the negative upward. So, with an increase in the depth, the water content, if you see water content depletes like this. So, at some particular depth beyond particular depth, this is completely dry water content is 0, so this particular height is capillary height capillary rise h c in the soil mass. So, if you consider the soil mass a one pore structure, if you consider saturated state thisis the condition of the water phase within the soil mass where you have nearly flatmeniscus. So, the point corresponds to degree of saturation versus suction is here as thesuction, here it is written matric suction, matric suction here is nothing but u a minus uw. So, the matric suction that corresponding matric suction is a close to 0, but this is logscale so this cannot be 0 this is a very small value, here it is a small value as a suctionincreases to one particular value.
Video 4
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