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Introduction to Principles of Unsaturated Soil Mechanics

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Video 1
Hello everyone, welcome to the course, Unsaturated Soil Mechanics. Now, in this first lecture, I will take your attention to the scope of this particular course and possible applications in the field of geotechnical engineering. Let us look at some reference textbooks available on this topic. The first one is Lu and Likos, these are the two authors Ningaloo and William Likos. They have developed abook on this particular topic called Unsaturated Soil Mechanics in 2004, which is a very popular book And earlier book was Soil Mechanics for Unsaturated Soils by Fredlund and Rahardjo in1993. And this is probably the first book available on this particular topic. And Fredlund’s contribution to unsaturated soil mechanics is significant and often Fredlund is considered to be the father of unsaturated soil mechanics for his contributions this particular topic. During his tenures as a professor at the University of Saskatchewan, Canada, he has developed many concepts on unsaturated soils. And especially the concepts taken from soil physics and soil science are brought into engineering and he has developed many concepts. And those are all compiled into one textbook that is Soil Mechanics for Unsaturated Soils in 1993. And most of the concepts that are given in Lu and Likos are extended from the earlier topics that were earlier concepts developed by Fredlund and Rahardjo. And for this particular course, most of the concepts are taken from these first two books. And you have another book by Laloui on Mechanics of Unsaturated Geomaterials in 2010 which contains the most advanced topics of unsaturated soils. Some concepts like osmotic suction, matric suction, and the osmotic component of matrix suction such concepts are considered from this textbook for this good course. And the other book is Soil Physics by Marshall, Holmes, and Rose. This is a wonderful book on soil physics many physical chemistry concepts of soils are taken from this textbook and then considered in this course. And the next book is Soil Physics withHydrus contains many concepts on modeling, the flow behavior in unsaturated soils. And the application of hydra software which is a freebie and those are discussed in this particular textbook. And some modeling aspects of unsaturated flow behavior are taken from this book. And the last book is on Physical Chemistry by Atkins and Paula. This is an excellent book on physical chemistry. Many fundamental concepts like Kelvin’s equations, the cavitations, condensation, vapor pressure lowering, Raoult’s law, and many other concepts are taken from this textbook and explained in this course. Let us begin by understanding the shortcomings of our soil mechanics for understanding the soil behavior it all starts with coulomb who proposed the friction loss which can be described by this simple mechanism where a simple block which is slidingon a ramp, which has a weight component and there is a frictional weight component. And there is a resistance that is offered, that is a frictional component, and there is a normal component which is acting on this block this is a free body diagram of the block.According to the friction law, the frictional force is proportional to the normal force. And this is the material constant which is independent of the normal force or weight of the block. Either a block sliding on a ramp or a block is moving against a surface are two individual grains shearing along this plane are a lump of particles which are sheared along this shear plane when there is a normal load. All this would represent a failure along the shear plane and the Coulomb’s principle is applicable. So, this is a motivationfor developing the shear box test operators where you have a soil sample that is sheared along this predefined shear plane by applying some normal load. And the same equation is valid. In terms of stresses, we represent this using τ f equal to mu σ is normal stress, and τ f is shear stress at failure. These are the shear box test results. For the same normal stress as given soil behaves in this manner, either in this manner or in this manner. Soil shear stress gradually increases with an increase in the shear strain, and reaches a critical value or the shear stresses shear stress approaches a peak value and decreases and approaches the critical value. Generally, the dense soils are over consolidated clays where OCR is more than 2, theyexhibit this behavior are loose sands are normally consolidated clays exhibit this behavior. If when you conduct tests with different σ by changing the normal stress, you will get the relationship between τ f versus σ. So, therefore, using the Coulomb’s principle you will get a material constant called the angle of internal friction that is tanphi here either mu or it could be represented with tan phi, this is an angle phi, this is an angle of internal friction at the critical state. If you take peak data, the shear stress at peak values and plot you may get phi peak - the angle of internal friction using peak values, as this value can change with the initial condition this does not represent the material constant. Then comes this effective stress principle; where, in case if you have a pore fluid, in the pore space of the system, when you apply normal force and frictional force there is acounter thrust that is acted acting from the pore fluid. So, therefore, this is the force that is acting at equilibrium; and this is the force act acting at the equilibrium, this is given by Terzaghi who has given this effective stress principle. And then we modify the coulomb spring coulombs law by changing the normal force o effective value N U we add this counter thrust. So, essentially you get a τ f that is shear stress at failure equals to an effective stress times tan phi So, because of this soil exhibits different strength during so soil exhibits different strength depending on the drainage condition; whetheryou allow the drainage to take place during the shearing, or drainage is not allowed during the shearing would influence the shear strength property of the soil. So, we get different strengths, therefore, and in triaxial tests, we control the drainage; and we conduct consolidated un drained and consolidated drain tests wherewherein we get strength parameters in drain condition and un drained condition. So far we have utilized the soils, in considering soils to be a  two-phase system; where either you have soil solids and water, or soil solids and air. So, according to Terzaghi in his infamous theoretical soil mechanics textbook; he says that the soilmechanics, he is defined as the application of the laws of mechanics and hydraulics to engineering problems dealing with sediments and other unconsolidated accumulations of solid particles produced by the mechanical and chemical disintegration of rocks, regardless of whether or not they contain an admixture of organic constituents. So, in this description he is defining what is soil; and here he is defining what is a soil mechanics, essentially the application of mechanics and hydraulics for understanding the soil mechanics that is what is soil mechanics. However, in nature, you have unsaturated soil, the geological media between the ground surface and the regional ground water table. You have a thick or depth varyinggeological media which is partly-saturated, essentially you will have a three-phase system. So, you will have you have pore air space, pore water, and soil solids. This is a volume of air, volume of water, and volume of solids. The volume of voids within the void space you have two phases, one is air; one is generally water, or sometimes you may have oil or any other thing this is the most natural case. So ifthis is the case, then soil within the soil at the air-water interface, you may have surface tension developed at the interface this provides additional strength to the soil, and this can change with change in the water content, change in the air content in the system. So, for example, we make sand castles at beachside on the shore, we make sand castles on the shore. Here, with sand you can achieve steep angles, an angle which is much steeper than the angle of internal friction, this is because of additional strength that is provided from the surface tension; or the negative pore-water pressure which ispresent in the pore space, due to the presence of the two-phase system, two additional due to presence of air and water. If you go to the sand castle, sand castles where you find that the angles are steep enough to make it, to be mould into different shapes; and these angles are much steeper than the angle of internal friction. If you dump sand from a truck; it assumes an angle that is equal to the angle of repose, steeper than this you cannot make unless there is an additional strength that is coming from the surface tension or negative pore water pressure. So, in the sand castles, we can make structures with angles steeper than the angle of internal friction of the soil because of the surface tension effects. So, because you have two phases in the pore space, you can get additional strength. Therefore in natural slopes, they may be steeper than the natural slopes; may be steeper than natural slopes are much steeper. And you may see vertical cuts in many a times that will be withstood that would which stood. Therefore, in natural slopes if you see, often you see a vertical cut which can withstand the slope for a very long time without failure, this is all because it has additional strength due to negative pore water pressure in the system that is because you have two phases in the pore space, so these all fine. So, this we analyzed using conventional stability analysis where each slice is analyzedfor force and moment equilibrium. And then we find out the factor of safety.
Video 2 
However when during the rainfall, water may seep into the ground surface or the slope. And then the air-water interface may disappear, because the pore space will be replaced, pour air space will be replaced with water; , and you may have only essentially a two-phase system that is water and soil solids. In that particular case, the strength may drop and which causes a decrease in the shear strength and which causes a landslide. And we have seen several disasters recently, in the recent past like Bududa disaster inUganda this is due to rainfall induces slope failure. And this is another landslide in Sikkim and Mizoram, where during the monsoons season you often see these landslides, this is because the soil has sufficient strength when it is partly saturated or due to the negative pore-water pressure, but this additional strength disappears as water imbibes into the soil system. This is another disaster we had seen recently in India. So, essentially in these cases, we need to answer these two questions, what is the waterflow rate through unsaturated slope? In our traditional soil mechanics, we only learned the flow behavior through saturated soil system using Darcy’s law; whether Darcy’s law is valid or not here is one question, because you have air space through which water will not pass through, but it may saturate eventually with time. So, what exactly the flow behavior through unsaturated soils is one question.Another question, the shear strength definitely, changes with change in the moisture content, but how does it change? These two questions we need to address, if we are analyzing the slope behavior, due to rainfall infiltration. This is another situation, where in the unsaturated soil mechanics is very useful; this is aBrahmaputra bank in Bangladesh. Here, the banks got eroded, and here you could see the vertical cut, vertical cut in the bank this is all because the soil is not fully saturated, it is partly saturated. Therefore, it is able to maintain a nearly vertical cut. Here the slopestability plays an important role in controlling the erosion of this stream bank. So, the unsaturated soil mechanics principles are again very important, and applicable for addressing such problems. And most frequently we encounter such issues, where in the soil mass beneath foundation either swells which we call heaven, or collapses depending on the type of soil during saturation. So, initially, in a dry state the foundation soil will have sufficient strength to carry the structure, but when rainfall occurs the water seeps into the ground,which causes a decrease in the shear strength. And either building fails in shear; or depending on if you have expansive soil, the soil may expand. Or if you have a collapsible soil, the soil will collapse due to wetting. This causes the collapse of the entire structure. The whole structure may sink into the ground or the entire structure willbe uplifted; , or there will be cracks that may appear; , or this whole thing will fail in shear, all these problems are due to the change in the moisture content of the foundation soil due to seasonal effects, which causes changes in the shear strength and volume change So, addressing in addressing such issues we need to address another issue that is what is the volume change that is either heave or collapse, that may take place due to moisture content variation under the applied loading. Apart from these two questions which weaddressed for slope stability. There is an important issue these days is a nuclear waste disposal even though it is at present India does not require this facility, but then in long term, we require such facilities to address the disposal of nuclear waste high-level nuclear waste. The Swiss, according to the Swiss design, the nuclear waste is kept in a canister, copper canister and which will be dumped or placed at several hundreds to thousand meters below the ground surface by making tunneling. And reaching the prescribed location where which is much below the ground surface which is a nearly several hundred meters below the ground surface wherethe canisters are these are the canisters which contains the radioactive waste. This is placed these canisters are placed and which is back filled with bentonite material. The bentonite it is a highly expensive clay high plastic clay, so which is back filled with.So, essentially the bentonite which is available around the canister would contain the radioactive waste will element by making the permeability very low. The permeability of the bedrock in unsaturate in the unsaturated condition is as low as 10 power minus16, 10 power minus 18 meters per second such a low permeability they create. So, essentially if there is a leakage that happens from the canister radioactive elements would diffuse through the bedrock that would take a nearly very long time. And which is surrounded by a rock mass saturated rock mass. And you have access tunnels which are again back filled by the bedrock here this is called buffer and here you , have a bentonite backfill. So, back filling and bin buffering requires the bentonite material to be used. And the properties of these bentonite materials or the characteristics of these bentonites are important. Moreover, the mechanical behavior of this bentonite in this particular condition is very important. In this particular situation, when it is buff when the bentonite is used as a buffer material here and back filled elsewhere. Now, there could be water that may be penetrating from the surrounding saturated rock mass into the buffer material. So, in that particular case, the unsaturatedflow through bentonite material is important. And secondly, there may be thermal gradients across the bentonite layer. So, thermal flow thermal conduction is important and mechanical behavior. When the bentonite is saturated from the saturated rockmass, water that is coming from the saturated rock mass bentonite applies huge pressure on the surroundings. So, this mechanical pressure could be as high as 40 mega Pascals depending it dependson the type of soil. However, so this swelling pressure, this is called swelling pressure that the bentonite exerts on the surroundings when it is confined and when it is not allowed to swell due to saturation will be nearly equal to the hydrostatic pressure that isacting at that particular depth from the ground surface. So, mechanical behavior such as this swelling pressure with dry density. And similarly, the swelling pressure with water content is important for different soils for understanding the mechanical behavior. So, this is a typical data from butcher and Muller Vonmoos here for MX 80 bentonite and Montigel bentonite these are highly plastic clays, where the soil is compacted to very high densities nearly 2 gram per centimeter  cube dry density and it exhibits a swelling pressure of nearly 40 mega Pascals 40, 000-kilo Pascals. So, the thermo- hydro- mechanical behavior because you have a thermal gradient acrossthe bentonite, you have a hydraulic gradient across the bentonite. And the pressure which is generated due to the saturation because of which the coupled analysis of thermohydro-mechanical behavior of the bentonite barrier is important. And also THM behavior of host rock is important near field; , and hydro-mechanical behavior of shafts and tunnel seals are also required. So, THM analysis contains heat transport, water flow, air- flow, vapor diffusion, mechanical behavior, the thermal equilibrium between different phases, all these needs to be coupled and then solved the expressions for understanding the bentonite behavior in that particular situation. There is another situation where you have buried pipelines that are used for carrying natural gas or any other material from one point to another point. Here the soil which is surrounding the buried pipeline might exert some pressure on the pipes due to change in the moisture content or they may exhibit a volume change behavior due to change in the moisture content which causes additional stresses on the pipes. And if the stability of pipes is not sufficient, then it may break and leakage can occur. So, to address these issues, we require to understand the unsaturated soil mechanics are unsaturated soil behavior. So, another application is a cover design in acid mine drainage, in acid mines, and in landfills. Cover designing plays a very important role in this particular situation where the rainfall percolation into the system should be controlled. Here, the permeability of the cover system should be low enough so that the water generally runs off from the surface and the percolation is minimal. Secondly, if you use directly bentonite type of soils here, it may develop cracks. When there is an excess of drying that takes place or evaporation that is taking place during dry periods, so it should have low permeability, at the same time it should not crack. Otherwise in the next season during monsoon, these cracks would prompt the water to enter directly into the system either acid mine tailings or it could be landfill liners landfills. So, the permeability of the soils are very important permeability of the unsaturated soil isimportant. And the slope stability is also important. This is another aspect that is not addressed in basic soil mechanics. There is an osmotic effect. Expansive soils such as bentonites black cotton soils on the clay particle surface they have negative charge surface due to isomorphism substitution, so that attract positive ions under the surface and they had the cation there are exchangeable cations on the surface. When there is moisture available, the exchangeable cations get hydrated and the external surface and internal surface of the clay particles also would get hydrated. And if there is additional water that is available free water available, then there is a formation of the diffuse double-layer where the electrostatic potential variesfrom the clay surface to one particular distance called diffuse double layer thickness. So, clay particles exist along with the diffuse  double layer, and the this is due to the osmotic effect. And when two different particles come close to each other, there is an osmotic potential that is developed at the interpolate distance. These osmotic effects are important for controlling the flow behavior, for volume change behavior and shear strength behavior of fine-grained soils or clays. So, such osmotic effects are not addressed in basic soil mechanics. The beauty of unsaturated soil mechanics is that theosmotic head and the negative pore-water pressure that we call a matrix suction head. All these heads are considered in the same head and we considered for the flow behavior volume change behavior and shear change behavior. So, these are the noticeable points, what shear strength parameters we use for the slope stability because the shear strength depends on the amount of moisture that is available. If you analyze the soil slope using saturated strength our strength obtained at the saturated state, then it may lead to unrealistic stability analysis. And slope may fail much before for the soil approaches the full saturation if it is going from the dry dryingto full saturation state. And at what rate the water flows through the soil, so that you can couple the flow behavior and the strength or mechanical behavior so that one can analyze rainfall-induced slopes slope instability. And the third aspect is the volume change behavior during the infiltration of water under given normal stress normal load, and development of cracks due to volume changes. These issues can be well addressed using unsaturated soil mechanics. So, therefore, unsaturated soil mechanics should be defined as the application of the laws of mechanics, hydraulics, these are any ways used in basic soil mechanics additionally interfacial physics. So, you can allow the surface tension forces to come in, and then you can explain many things. And Physico-chemical mechanisms so that you can address the fine-grained soil behavior to engineering problems dealing with partly saturated soils. With this, I will stop here. And I am sure this would provide enough motivation for studying this subject 
Video 3  
Now, we will discuss some fundamental principles that are essential for understanding the unsaturated soil mechanic. In this lecture, we will discuss the prediction of a phenomenon, how aphenomenon can be prediction predicted. For that, it is important to recognize what are the governing equations need to be invoked, the constitutive relationships. For understanding the constitutive relationship you need to identify what are the state variables, and build the constitutive relationships based on some experimentalobservations, and determine the material constants and we predict the phenomenon. We will try to understand today that phenomenaprediction requires a mathematical representation of a given problem. So, for example, a simple problem an object is falling from a certain height from a tower. And at what rate how much time it takes to reach the ground is one problem. And or a mass of sphere which is oscillating which is attached to a spring and which is oscillating which is having a displacement of y; and prediction of thisphenomenon requires a mathematical representation of this problem. When it comes to geotechnical engineering, we are interested in understanding the consolidation settlements of structure which is resting on the soil. And seepage prediction underneath a dam, or it could be a shear failures of slopes, foundations, or any other structures. Let us try to understand we have governing equations such as conservation of mass, wehave conservation of linear momentum and conservation of angular momentum, the second law of thermodynamics and Maxwell’s equations. These are fundamental governing equations we need to invoke for understanding any phenomenon mathematically, to represent, and for understanding any phenomenon, we need to invoke these governing equations. Now, readers are advised to refer, any standard textbook on continuum mechanics for more explanation on these physical laws. These are physical laws; the audiences are advised to refer any standard textbook on continuedmechanics for more explanation on these physical laws. So, these physical laws need to be invoked for mathematically representing any phenomenon and prediction of phenomena. One of the best textbooks could be Malvern on Introduction to the Mechanics of a Continuum Medium Apart from these physical laws, we may also require additional equations to solve the problem uniquely for satisfying the constituents, it is material dependent equations we require. Constituent’s equations, therefore, explain the interdependency of different state variables. It is stress, strain, void ratio, effective stress, etc. The proportionality constants of the constitutive relationships are called material constants that represent the fundamental constituents of the system. Material constantsmay also depend on the state variables. The dependency of material constraints on the state variables and one state variable on another state variable through constituent equations is required for understanding the behavior. Let us identify the governing equations, state variables, and material constants in the basic soil mechanics. Such an identification exercise is important for the prediction ofphysical phenomena or simply the engineering behavior of soils. Let us take the problem of consolidation of clays is a very important subject area in solid mechanics and also which is very important for the prediction of settlements and settlement rates, ultimate settlements, and rate of settlement of any structure which is existing on the soil The soil samples from the field are brought to thelaboratory and then studied in the laboratory on in odometer cell illustration is given here. So, in this slide, it is shown the clay sample which is sandwiched between a porous stone top porous stone and bottom porous stone. And this is a fully submerged in water. So, thesample is in a fully saturated condition. And you apply a normal load P and generally, the cross cross-sectional area the diameter of the sample would be 6 centimeters, and the thickness of the sample is 2 centimeters. So, the load is p applied then the stress existing on a sample is P by cross-section area which is the load by the cross cross-section area which is the total stress that is acting is  So, under this particular condition as there are two boundaries where you have highly permeable porous stones are sitting which replicates the situation of clay sample which is sandwiched between sand layers in the field. So, there is a hydraulic gradient that is developed because of excess pore water pressure at the boundaries are 0. And at themiddle of the sample, it has a maximum pore water pressure excess pore water pressure. So, there is a gradient that is developed within the sample and water excess pore water pressure dissipates through the boundaries. So, in turn, the clay sample consolidates with time.So, this phenomenon is theoretically studied using Terzaghi’s one-dimensional consolidation theory. This consists of considering one elemental volume a representative volume and the flow through this volume could be considered. The volume of the sample is and the thickness is ∆delta z. If you consider the volumetric flow rate Q, which is in the flow direction; and the volumetric flow rate which is coming out which is Q So, the change in the volumetric flow rate can be understood as the Q Z in terms of unit discharge or flux is small q z times the cross- section area. If the length of this elemental cross- section area is then this is x times y in the in-plane direction Similarly, Q z plus Z is small q z there is a flux plus change in flux with distance into z into x into y So, the change in the discharge volumetric flow rate is nothing but ∆q is q by z times ∆ x ∆y z which is nothing but ∂z times ∆v. So, this is the volume of the element. So, this quantity is nonzero for transient flows. If it is a steady- state flow this quantities is 0, but because here a transient flow that is taking place or  time-variant that is taking place flow is dependent on time here that is a transient flow that is taking place. This quantity is equal to the rate of change of volume of voids because the flux ischanging because the volume of the element is getting compressed. So, therefore, this is nothing but the volume of voids is nothing but n that is porosity which is porosity is equal to the volume of void spread total volume. So, therefore, porosity times total volume is your volume of voids and rate of change ∂ by ∂t of n v. So, therefore, so these two quantities should be equal this is the first equation; this is the second equation. And this can be written as so the ∂ by ∂ t of n into ∆v can be written in terms of void ratio has ∂ by ∂ t of the void ratio by 1 plus void ratio times v. So, ∆v is a small elemental volume and 1 plus c represents total volume. So, for small strains, one can assume one can approximate this as ∆v by 1 plus e times ∂ by t of e. 
Video 4