Fundamental Aspects of Unsaturated Soil Mechanics and its Basic Principles

Summary

This lecture from NPTEL IIT Guwahati delves into the principles of unsaturated soil mechanics, exploring its fundamental importance and application in geotechnical engineering. The instructor discusses key reference textbooks, principles such as the Coulombs friction law and Terzaghi's effective stress principle, and provides insights into real-world applications like slope stability, erosion control, and nuclear waste disposal. Important concepts like osmotic suction and volume change are highlighted, emphasizing their relevance to engineering challenges. This lecture sets the stage for understanding how unsaturated soil mechanics is crucial for solving complex engineering problems involving soil and water interactions.

Highlights

• Discover how unsaturated soil mechanics bridges the gap between the theory of mechanics and real-world soil problems 🌍.
• Terrific textbook recommendations to dive deeper into soil mechanics concepts 📚.
• Learn the secrets of soil strength through principles like Coulomb's law and Terzaghi's effective stress principle 🤓.
• Understand how osmotic and matric suction contribute to soil stability and can prevent engineering disasters 🚧.
• Explore fascinating real-world applications such as in geotechnical engineering, slope stability, and nuclear waste management ⚠️.
• The lecture gives an in-depth view on controlling erosion with unsaturated soil mechanics, vital for environmental conservation 🌳.

Key Takeaways

• Unsaturated soil mechanics explores the behavior of soils that aren't fully saturated with water, vital for geotechnical engineering 🌱.
• Reference textbooks such as the ones by Ng & Lycos, and Fredlund offer foundational insights into the field 📚.
• Key principles discussed include the Coulombs friction law and Terzaghi's effective stress principle, which explain soil behavior under various conditions ⚙️.
• Applications of soil mechanics are vast, including slope stability, and addressing challenges in areas like nuclear waste disposal and erosion control ⚠️.
• Understanding concepts like osmotic and matric suction can greatly enhance soil strength predictions and engineering solutions 💪.
• Practical engineering issues such as landslides, foundation failures, and infrastructure stability can be addressed with these principles 🏗️.

Overview

In this enlightening lecture on unsaturated soil mechanics, the key concepts and applications in geotechnical engineering are explored. The instructor highlights fundamental principles that help professionals design and analyze structures involving partly saturated soils. Reference textbooks by authors such as Lou and Lycos are discussed as essential materials to gain a deeper understanding of the topic.

The lecture thoroughly covers principles like Coulombs friction law and Terzaghi's effective stress principle, which form the backbone of soil mechanics studies. Such principles explain how soil strength and stability can be analyzed under various environmental conditions and applied stresses. This depth of knowledge is crucial for professionals tackling complex engineering challenges.

Applications of unsaturated soil mechanics come alive as the instructor delves into practical scenarios where these principles are essential. From preventing landslides to managing erosion and maintaining infrastructure integrity, understanding the mechanics of unsaturated soils is shown to be indispensable for sustainable engineering solutions.

Chapters

• 00:30 - 05:30: Introduction and Course Scope The 'Introduction and Course Scope' chapter begins with an introductory theme, indicated by background music, setting the tone for what appears to be an educational course. The music serves as a transition or thematic introduction, likely aimed at engaging the audience's attention at the start of the course. Specific details about the course content, key objectives, and scope may follow in the chapters, though the provided transcript is incomplete.
• 05:30 - 15:30: Unsaturated Soil Mechanics and Key Texts The chapter introduces the course on saturated soil mechanics, emphasizing its scope and applications within geotechnical engineering. It briefly touches upon the available reference textbook by Ningaloo and William Lycos on the subject.
• 15:30 - 20:30: Foundations of Soil Mechanics The chapter "Foundations of Soil Mechanics" discusses the significant contributions to the field of unsaturated soil mechanics. It highlights Fred Allen, recognized as the 'father of unsaturated soil mechanics,' for his pioneering work in the area. His early book, 'Soil Mechanics for Unsaturated Soils' published in 1993, is considered a landmark publication in the field, followed by another popular book on the topic in 2004. The chapter underscores Fred Allen's key role and invaluable contributions to advancing the understanding and development of unsaturated soil mechanics.
• 20:30 - 38:50: Consolidation Predictions and Physical Laws The chapter discusses the contributions of a professor at the University of Saskatchewan in Canada to the field of soil mechanics, specifically focusing on unsaturated soils. The professor has integrated concepts from soil physics and soil science into engineering. His work is compiled into the textbook 'Soil Mechanics for Unsaturated Soils' published in 1993. The chapter also mentions that many concepts from this textbook are extensions of previous works by authors Low and Lycos.
• 38:50 - 64:00: Practical Implications and Advanced Topics This chapter focuses on the practical implications and advanced topics pertaining to unsaturated soils. It highlights how earlier concepts preferred in the field of land and 'Rajas' have been sourced, notably from two initial books. Furthermore, it mentions another significant contribution by L. Louie with their 2010 work, 'Mechanics of Unsaturated Geomaterials', which delves into advanced topics of unsaturated soils. Key concepts such as osmotic suction, matric suction, and the osmotic component are discussed.
• 64:00 - 64:30: Conclusion and Further Studies The chapter titled 'Conclusion and Further Studies' discusses various textbooks considered essential for the course. It highlights 'Soil Physics' by Marshall Holmes and Rose as a comprehensive resource for understanding the physical chemistry of soils. Additionally, 'Soil Physics with Hydrous' is mentioned for its valuable concepts on modeling flow behavior. These resources are crucial for advancing knowledge and research in soil-related studies.
• 64:30 - 90:00: Phenomenon Prediction and Mathematical Representation This chapter discusses the application of Hydra software in modeling the flow behavior of unsaturated soils. It highlights the use of various textbooks, including a physical chemistry book by Atkins and Pola, to explain fundamental concepts such as Kelvin's equations, cavitation, condensation, and vapor pressure lowering. The chapter focuses on the prediction of phenomena related to unsaturated soils and their mathematical representation.
• 90:00 - 130:00: Consolidation of Clays The chapter on "Consolidation of Clays" begins by highlighting the foundational theories and concepts in soil mechanics, specifically focusing on the contributions of Coulomb. It discusses the principles underlying friction loss by illustrating with a basic model of a block sliding down a ramp, emphasizing the weight components and resulting mechanisms. This discussion sets the stage for a deeper exploration into soil behavior and its complexities, paving the way for understanding the consolidation processes of clay soils, which are pivotal in civil engineering and construction projects.
• 130:00 - 148:00: Mass Conservation and Constitutive Relationships The chapter discusses the concepts of mass conservation and constitutive relationships, focusing on frictional forces and normal forces in relation to a block. It introduces the friction law, stating that the frictional force is proportional to the normal force. Additionally, it touches upon material constraints that are independent of the normal force or the weight of the block.
• 148:00 - 187:00: Understanding Settlements and Observations In this chapter, the concept of understanding settlements and observations is explored, focusing on the mechanics of sliding and shearing. The chapter describes scenarios such as sliding on a ramp, a block moving against a surface, and individual grains shearing along a plane or a lump of particles shearing along a shear plane. These examples illustrate a failure along the shear plane when a normal load is applied, and the application of Coulomb's principle in understanding these phenomena is emphasized. This forms the motivation for developing further concepts in the study of settlements and observations.
• 187:00 - 240:00: Soft Soils and Special Considerations The chapter discusses the shear box test, a method used to analyze soil samples by applying a normal load and shearing along a predefined plane.

Fundamental Aspects of Unsaturated Soil Mechanics and its Basic Principles Transcription

• 00:00 - 00:30 [Music] you you
• 00:30 - 01:00 hello everyone welcome to the course on saturated 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 Lou and Lycos these are the two authors Ningaloo and William Lycos they have developed a book on this
• 01:00 - 01:30 particular topic called unsaturated soil mechanics in 2004 which is a very popular book and earlier book was soil mechanics for unsaturated soils by Fred Allen and Rajas Oh in 1993 and this is the probably the first book available on this particular topic and ferd lands contribution in unsaturated soil mechanics is significant and often fertile and is considered to be the father of unsaturated soil mechanics for his contribution in this particular
• 01:30 - 02:00 topic during his tenure as professor at the University of Saskatchewan Canada he has developed many concepts for on saturated 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 low and Lycos are extended from the earlier
• 02:00 - 02:30 topics that were earlier concepts are preferred land and Rajas oh and for this particular course most of the concepts are taken from this first two books and you have another book by la Louie on mechanics of unsaturated geo materials in 2010 which contains most advanced topics of unsaturated soils some concepts like osmotic suction matric suction and osmotic component of
• 02:30 - 03:00 pneumatic 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 with hydrous contains many concepts on modeling the flow behavior in
• 03:00 - 03:30 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 Pola there's a excellent book on physical chemistry many fundamental concepts like kelvins equations the cavitation condensation vapor pressure lowering
• 03:30 - 04:00 roles law and many other concepts are taken from this textbook and explained in this course let us begin in 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 sliding on a ramp which has a weight component and
• 04:00 - 04:30 there's a frictional weight component and there's a resistance that is offered there 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 constraint which is independent of the normal force or weight of the block either a block
• 04:30 - 05:00 sliding on a ramp or a block is moving aganist surface are two individual grains shearing along this plane are 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 coulombs principle is applied so this is a motivation for developing
• 05:00 - 05:30 the shear box test operators where you have a soil sample which 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 tau F equal to MU Sigma Sigma is normal stress and tau F is shear stress at failure these are the shear box test results for the same normal stress as given soil behaves in
• 05:30 - 06:00 this manner either in this manner or in this manner soil shear stress gradually increases with increase in the shear strain and reaches a critical value or the shear stress 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 two they exhibit this behavior are loose
• 06:00 - 06:30 sands are normally consolidated clays exhibit this behavior if when you conduct tests with different Sigma by changing the normal stress you will get the relationship between tau F versus Sigma so therefore using the Frick coulombs principle you will get a material constant called angle of internal friction that is tan Phi here either mu or it could be represented with tan Phi this is angle Phi this
• 06:30 - 07:00 angle of internal friction at critical state if you take peak data the shear stress at peak values and plot you may get five peak the angle of internal friction using peak values as this value can change with initial condition this does not represent the metal constant but five critical would represent the metal constant because for whatever the densities you use whatever be the initial condition this is constant so
• 07:00 - 07:30 therefore Phi critical represents a material constant which is often used in the design so all this knowledge is from coulombs friction law however here we will utilize you have a two-phase system you have a soil solids and air in the pore space 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 a counter
• 07:30 - 08:00 thrust that is acting acting from the pore fluid so therefore this is the force that is acting at equilibrium and this is the force acting at equilibrium this is given by terzaghi who has given this effective stress principle and then we modify the Coulomb spring Coulomb's law by changing the normal force
• 08:00 - 08:30 changing the normal force to effective value n minus u we add this counter thrust so essentially you get a tau F that is a shear stress at failure is equals to Sigma dash and effective stress times tan Phi dash so because of this soil exhibits different strength during so soil exhibits different
• 08:30 - 09:00 strength depending on the drainage condition whether you allow the drainage to take place during the shearing our drain ez is not allowed during the shearing would influence the shear strength property of the soil so we get different strengths therefore and interaxial tests we are able to control the drain ease and we conduct consolidated undrained and consolidated
• 09:00 - 09:30 drain test where wherein we get strength parameters in drain condition and undrained 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 a so according to Ted's Aggie in his infamous theoretical soil mechanics textbook he says that the soil mechanics
• 09:30 - 10:00 he's defined as the application of the laws of mechanics and hydraulics to engineering problems dealing with sediments and other consolidated accumulations of solid particles produced by the mechanical and chemical and disintegration of rocks regardless of whether or not they contain an admixture of organic constituents so in this description he's defining what is soil and here he is defining what is
• 10:00 - 10:30 soil mechanics essentially the application of mechanics and hydraulics for understanding the soil mechanics that is what is soil mechanics but however innate in nature you have unsaturated soil the geological media between ground surface and regional ground water table you have a thick are depth varying geological media which is
• 10:30 - 11:00 partly saturated essentially you will have three-phase system so you will have you have pore air space pore water and soil solids so this is a volume of failed volume of water and volume of solids so this is volume of voids within the wide space you have two phases one is air one is generally water are sometimes even have oil or any other thing so this is most natural more
• 11:00 - 11:30 natural most natural case so if this 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 be other Shore we make
• 11:30 - 12:00 sand castles on the shore here with sand you can achieve steep angles 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 is present in the pore space due to the presence of two phase system 2 additionals due to presence of air and water if you go to the sand castle sand
• 12:00 - 12:30 castles where you find that the angles are steep enough to make it to be molded into different shapes and this angles are much steeper than the angle of internal friction if you dump a sand dump sand from a truck it assumes an angle which is equal to the angle of repose steeper than this you cannot make a lesson till there is an additional strength that is coming from the surface tension or negative pore water pressure
• 12:30 - 13:00 so in the sand castles we are able to make structures with 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 are able to get additional strength therefore in natural slopes they may be steeper than the the
• 13:00 - 13:30 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 this 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
• 13:30 - 14:00 phases in the pore space so this is all fine so this we analyzed using conventional stability analysis where each slice is analyzed for force and moment equilibrium and then we find out the factor of safety 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
• 14:00 - 14:30 pour ate space will be replaced with water and you may have an essentially 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 Berto the disaster in agonda this is due to rainfall induces flow failure and this is another landslide in Sikkim in Mizoram where during the
• 14:30 - 15:00 monsoons is a new often see these landslides this is because soil has sufficient strength when it is partly saturated are due to the negative pore water pressure but this additional strength disappears has water imbibes into the soil system this is another disaster we had uh seen recently in India so essentially in these cases we need to answer these two questions what is a water flow rate through unsaturated
• 15:00 - 15:30 slope in our traditional soil mechanics we only learned the flow behavior through saturated soil system using Darcy's law whether Darcy Silla is valid or not here is one cushion because you have eighths's to eight air space through which water will not pass through but it may saturate eventually at time with time so what exactly the flow behavior through unsaturated soils is one question another question the shear strength definitely changes with
• 15:30 - 16:00 change in the moisture content but how does it change these two questions we need to address if we are analyzing the slow behavior due to rainfall infiltration this is another situation where where in the unsaturated soil mechanics is very useful this is a Brahmaputra Bank in Bangladesh here the bank's got eroded and here you could see
• 16:00 - 16:30 the vertical cut vertical cut in the bank this is all because the soil is not fully saturated it's partly saturated therefore it is able to maintain well nearly vertical cut here the slope stability 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
• 16:30 - 17:00 where we're in the soil mass beneath the foundation either swells which we call heave are collapses depending on the type of soil during saturation so initially in 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 decrease in the shear
• 17:00 - 17:30 strength and either building fails in shear or depending if you have an expansive soil the soil may expand or if you have a collapsible soil soil will collapse due to waiting this causes collapse of the entire structure the whole structure may sink into the ground or the entire structure will be uplifted or there will be cracks that may be appearing or this whole thing will fail in shear all these
• 17:30 - 18:00 problems are due to the change in the moisture content of the foundation soil due to seasonal effects which causes changing 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 and other applied loading apart from these two questions which we addressed for slope stability there is an important issue
• 18:00 - 18:30 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 2,000
• 18:30 - 19:00 meters below the ground surface by making tunneling and reaching the reaching the prescribed location where which is much below the ground surface which is nearly several hundred meters below the ground surface where the canisters are these are the canisters which contains the radioactive waste this is placed these canisters are
• 19:00 - 19:30 placed and which is back filled with pinto net material a bundle it is a highly expands you click high plastic clay so which is back filled with so essentially the 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 bin tonight's in unsaturated in the unsaturated condition are as low as 10 power minus 16 10 power minus 18 meter
• 19:30 - 20:00 square meter 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 window net that would take 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 bentonite here this is called buffer and here you have a bank Bend on it backfill so back filling and bin
• 20:00 - 20:30 buffering requires the mentorian material to be used and the properties of these better--it materials or the characteristics of these meteorites are important and moreover the mechanical behavior of this bentonite in this particular condition is very important in this particular situation when it is buff when the winter it is used as a buffer material here and back filled elsewhere now there there could be a water which which may be penetrating from the surrounding saturated rock mass into the
• 20:30 - 21:00 buffer material so in that particular case the unsaturated flow through winter and material is important and secondly there will be thermal gradients across the window net layer so thermal flow thermal conduction is important and the mechanical behavior when the bentonite is saturated from the saturated Rock mass water which is coming from the saturated Rock mass bentonite applies
• 21:00 - 21:30 Hue's pressure on the surroundings so this mechanical pressure could be as high as 40 mega Pascal's depending it depends on 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 is acting at that particular depth from
• 21:30 - 22:00 the ground surface so the mechanical behavior such as this swelling pressure with dry density and similarly the swelling pressure with water content are important for different soils for understanding the mechanical behavior so this is a typical data from butcher and Muller one Mo's here for mx8 Eve internet and Monticello Internet these are highly plastic place where the soil
• 22:00 - 22:30 is compacted to very high densities nearly 2 gram per centimeter cube dry density and it exhibits a swelling pressure of nearly 40 mega Pascal's 40,000 kilo Pascal's so the thermo hydro mechanical behavior because you have a thermal gradient across some internet you have a hydraulic gradient across the bentonite and the pressure which is generated due to the saturation because
• 22:30 - 23:00 of which the coupled analysis of thermo hydro mechanical behavior of the internal barrier is important and also th and behavior of host rock is important airfield and hydro-mechanical myriad of shafts and tunnels seals are also required so THM analysis contains heat transport water flow air flow vapor diffusion mechanical behavior thermal equilibrium between different phases all these need to be coupled and then solved
• 23:00 - 23:30 the expressions for understanding the window read behavior in that particular situation there's another situation where you have buried pipelines buried pipe lines are used for carrying the natural gas or any other material from one point 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
• 23:30 - 24:00 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
• 24:00 - 24:30 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 a excess of drying that
• 24:30 - 25:00 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 this 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
• 25:00 - 25:30 important permeability of the unsaturated soil is important and the slope stability is also important this is another aspect which is not addressed in basic soil mechanics there is osmotic effect expansive soils such as bintang eighths and blackett on soils on the clay particle surface they have negative charge surface due to isomorphous of situation so that attract positive ions under the surface and they had the cation there are exchangeable cations on
• 25:30 - 26:00 the surface when there is a moisture that is 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 diffuse double layer where the electrostatic potential varies from 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
• 26:00 - 26:30 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 some behavior of fine-grained soils are place so such as positive effects are not addressed in basic soil mechanics the beauty of
• 26:30 - 27:00 unsaturated solid mechanics is that the osmotic 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 chain behavior and shear some behavior so these are the noticeable points what shishun parameters we use for the slope stability analysis 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
• 27:00 - 27:30 saturated state then it may lead to unrealistic stability analysis and slope may fail much for the soil approaches the full saturation if it is going from the dry drying to 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
• 27:30 - 28:00 instability and the third aspect is the volume change behavior during infiltration of water under given normal stress normal load and development of cracks due to volume changes these issues can be well addressed using the 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
• 28:00 - 28:30 mechanics the additionally interfacial physics so you can expand 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 fine grained soil behavior to engineering problems dealing with partly saturated soils with this I'll stop here and I'm sure this would
• 28:30 - 29:00 provide enough motivation for studying this subject now we'll discuss some fundamental principles that are essential for understanding the unsaturated soil mechanics in this lecture we'll discuss about the prediction of a phenomenon how a phenomenon can be prediction predictor for that it is important to recognize what are the governing equations need to be invoked the constitutive
• 29:00 - 29:30 relationships for understanding the constitutive relationship you need to identify what are the state variables and build the constitutive relationships based on some experimental observations and determine the material constraints and we predict the phenomenon will try to understand two for any prediction of a phenomenal for phenomena prediction prediction requires mathematical representation of a given
• 29:30 - 30:00 problem so for example a simple problem you have there where in object is falling 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 our a mass of sphere which is oscillating which is attached to a spring and which is oscillating which is having a
• 30:00 - 30:30 displacement of Y and prediction of this phenomenon requires a mathematical representation of this problem when it comes to the geotechnical engineering we are interested in understanding the consolidation settlements of structure which is resting on soil and see base prediction underneath a dam or it could be a shear values of slopes foundations
• 30:30 - 31:00 or any other structures let us try to understand we have governing equations such as conservation of mass we have conservation of linear momentum
• 31:00 - 31:30 and conservation of angular momentum second law of thermodynamics and Maxwell's equations
• 31:30 - 32:00 these are fundamental governing governing equations we need to invoke for understanding any phenomenon mathematically mathematically represent mathematically to represent and for understanding any phenomenon we need to invoke these governing equations now readers are advised to refer the audience are advised to refer any standard textbook on continuum mechanics for more explanation on these physical laws these are physical laws the
• 32:00 - 32:30 audience are advised to refer any standard textbook on continued mechanics for more explanation on these physical laws so these physical laws need to be invoked far mathematically represented representing any phenomenon and prediction of phenomena one of the best textbook could be malwan on
• 32:30 - 33:00 introduction to the mechanics of a continuum medium continuous medium apart from this physical loss we also require additional equations to solve the problem uniquely for satisfying the
• 33:00 - 33:30 constituents it is material dependent equations we require cost equations therefore explain the interdependency of different state variables it is stress strain wide ratio effective stress etcetera the proportionality constants of the constitutive relationships are called material constraints that represent the fundamental constituents of the system material constants may also depend on
• 33:30 - 34:00 the state variables the dependency of material constraints on the state variables and one state variable on another state variable through cost or equations is required for understanding the behavior let us identify the governing equations state variables and material constraints in the basic soil mechanics such identification exercise is important for the prediction of physical phenomena or simply the engineering behavior of soils let us take the problem of consolidation consolidation of clays is a very
• 34:00 - 34:30 important subject area in solid mechanics and also which is very important for prediction of settlements and settlement rates ultimate settlements and rate of settlement of any structure which is existing on soil Chile the soil samples from the field are brought to the laboratory and then studied studied in the laboratory on in Auto Meter cells barometer cells illustration is given here so in this slide it is shown the clay sample which
• 34:30 - 35:00 is sandwiched between a porous stone top porous stone and bottom porous stone and this is a fully submerged in water so the sample is in fully saturated condition and you apply a normal load P and generally the cross sectional area the diameter of the sample would be six centimeter and the thickness of the sample is two centimeter so the load is P applied then the stress existing on a
• 35:00 - 35:30 sample is P by cross section area which is the load by the cross section area which is the total stress that is acting is Sigma 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's a hydraulic gradient
• 35:30 - 36:00 that is developed because of excess pore water pressure at the boundaries are zero and at the middle 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
• 36:00 - 36:30 using terzaghi's one dimensional consolidation theory this consists of considering a one elemental volume by representative volume a representative volume and the flow through this volume could be considered volume of the sample is Delta V and the thickness is Delta Z
• 36:30 - 37:00 if you consider the volumetric flow rate Q which is in the four direction and the volumetric flow rate which is coming out which is Q Z plus Delta Z so the change in the volumetric flow rate can be understood the Q Z in terms of unit discharge or flux is small Q Z times the
• 37:00 - 37:30 cross section area if the length of this elemental cross section area is Delta X then this is Delta x times Delta Y in the in-plane direction Y similarly Q Z plus Delta Z is small Q Z there is a flux plus change in flux with distance into Delta Z into
• 37:30 - 38:00 Delta X into Delta Y so the change in the discharge volumetric flow rate is nothing but Delta Q is dou Q by dou Z times Delta X Delta Y Delta Z which is nothing but dou Q Z by dou Z times Delta
• 38:00 - 38:30 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 zero 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 ringing
• 38:30 - 39:00 place this quantity is equal to the rate of change of volume of whites because the flux is changing the flux is changing because the volume of the element is getting
• 39:00 - 39:30 compressed so therefore this is nothing but the volume of whites here is nothing but n that is whoa that is porosity which is forest is equal to volume of widespread total volume so therefore porosity times total volume is your volume of whites and rate of change dou by dou T of NV so therefore so these two quantities should be equal this is first
• 39:30 - 40:00 equation this is second equation and this can be written as so the dou by dou T of n into Delta V can be written in terms of void ratio has dou by dou T of void ratio by 1 plus y ratio times Delta
• 40:00 - 40:30 V so Delta V is a small elemental volume and one plus c represents total volume so for small strains one can assume one can approximate this as Delta V by 1 plus C e times dou by dou T of e so if
• 40:30 - 41:00 when you equate this expression the second expression and first expression you get dou Q Z by dou Z times Delta V is equal to Delta V times Delta V by 1 plus e times dou u by dou T this expression is a mass conservation
• 41:00 - 41:30 expression conservation of mass is considered here here the conservation of mass is considered so whatever the change in the flux is due to the change in the pore volume with respect to time so this is conservation of mass mass conservation principle so if the ones conservation of mass is satisfied then this equation should be satisfied so here physical law is applied for
• 41:30 - 42:00 deriving next expression now we can simplify these expressions in terms of known state variables this left-hand side expression of this expression left-hand side of the equation 3 can be written as dou by dou Z daf if Darcy's law is valid then Q's it can be represented as K Z into B H by D Z so
• 42:00 - 42:30 because when the load is applied the gradient is available only on one side in one direction that is either up upward direction or downward downward direction so you have gradient that is available only in vertical direction that is Z direction so which is equal to KZ times dou square H by Dow Z square if we assume that the hydraulic
• 42:30 - 43:00 conductivity does not change with space that is an assumption for small strains and consolidation operators this could be shown for low plastic soils etcetera and then this assumption should be valued assumption is valid so then representing the head in terms of this is a hydraulic head representing in terms of pressure this becomes K Z by gamma W into dou square u by dou Z
• 43:00 - 43:30 square because U is equal to H into gamma W so this is equation number 4 if you consider RHS right-hand side of the equation 3 here we require constitutive relationship because it is with respect to void ratio 1 plus C into dou V by dou T here we require 1 constitutive relationship need to be invoked here we use the costal relationship between constitute the relationship between void
• 43:30 - 44:00 ratio and effective stress so far normal scale this plots somewhat like this so the slope of this if you consider a small change in Delta Sigma - and what is the change in Delta e this can be obtained from different loadings when you load the sample load the sample
• 44:00 - 44:30 then change in the void ratio at equilibrium when Sigma is equal to Sigma - can be obtained when excess pore water pressure is nearly zero then Sigma is equal to Sigma - and you get the change in void ratio with respect to Sigma - this is a one cost relationship which is a relationship between one state variable called wide ratio and another
• 44:30 - 45:00 state variable is effective stress so we assumed that the slope is constant we assumed that this is linear for a small increment of delta sigma then the coefficient of compressibility AV is written as Delta e over delta sigma - with negative sign because increase in
• 45:00 - 45:30 the effective stress decreases the void ratio and if you divide so now this expression if you substitute AV here so you get AV by - CV by 1 plus e into Delta dou Sigma - by dou T so this is
• 45:30 - 46:00 nothing but Delta e by 1 plus C which is strain divided by stress so this is a 1 over bulk modulus called coefficient of volume compressibility times so dou Sigma - by dou T the left-hand side expression he's in terms of excess pore water pressure excess pore water pressure here also we try to represent in terms of excess pore water pressure for that we need to invoke the effective stress principle
• 46:00 - 46:30 that is a terzaghi's effective stress principle says that Sigma Dash is Sigma - u effective stress is Sigma total stress - excess pore water pressure our pore water pressure so here the change in Delta Sigma is change in Delta Sigma sorry change in Delta Sigma - if you take consider then it is equal to minus Delta u because the consolidation is
• 46:30 - 47:00 taking place under the applied normal stress the total stress is not changing only the pore water pressure is getting dissipated and which is replaced the poro excess pore water pressure becomes equal to the effective stress therefore Delta Sigma Dash is equal to minus Delta U if you substitute in this expression you get MV times dou u by dou T so if
• 47:00 - 47:30 you equate the expressions four and five you get the transacts one dimensional consolidation equation that is a K by M V comma W into dou square u by dou Z square is equals to dou u by dou T so this quantity we write it as C V so C
• 47:30 - 48:00 V times dou square u by dou Z square is equal to dou u by dou T this is terzaghi's one dimensional consolidation equation so this is a governing equation which a is derived using a physical law that is mass conservation principle so this is the mass conservation principle that is used and we invoked the effective stress principle and we use Darcy's law here to represent this
• 48:00 - 48:30 expression in terms of state variable excess pore water pressure so the governing equations are generally represented in terms of the governing equations are generally in terms of state variables so this to derive this governing equation we require additional equations such as the constitutive relationship that is U versus Sigma H which has a relationship between two
• 48:30 - 49:00 state variables so here now identify the constitutive relationship state variables and metal constants in this derivation the equation three the equation three is a governing equation based on the mass conservation principle equation three is the physical law which is mass conservation using that record the governing X governing equation
• 49:00 - 49:30 we utilized a versus Sigma - relationship which is a costed relationship the state variables are here wide ratio and Sigma - even pore water pressure excess pore water pressure is also a
• 49:30 - 50:00 state variable so these are the state variables the material constants are a V coefficient of compressibility coefficient of volume compressibility which is nothing but 1 over the bulk modulus even CV these are material constants
• 50:00 - 50:30 as we don't measure the excess pore-water pressure in the odometer tests we represent the solution of equation as we do not measure the excess pore water pressure in the water meter tests we represent equation 6 to estimate the material constant one requires to solve this equation six as we do not measure the pore water pressure in the water meter tests we represent the solution of equation six in terms of average degree of
• 50:30 - 51:00 consolidation and versus time factor T V and due to in unique nature of this relationship and similarity between measured the settlement versus time the settlement versus time relationship because these two are similar using this similarity due to the similarity between u average versus T V and settlement versus time we use we utilize either
• 51:00 - 51:30 Taylor's method that is square root of time fitting method or logarithm of fitting method to estimate the time factors tv9 T and T V 50 respectively and we estimate the CV from the expression we use expression T V equals
• 51:30 - 52:00 to C V times T by hit square where T V is estimated from the graphical technique so time is known at what time you achieve a given T V is known and drainage path length is known so one estimate CV indirectly so essentially we narky estimate CV from Equation 6 using graphical techniques so here the phenomena is predicted so once CV is
• 52:00 - 52:30 known one can estimate the rate of settlement in the field and one can estimate the total settlement ultimate settlement from this expressions this is possible because we use the physical law as mass conservation and we identify the state variables and we represented a cost relationship that is he versus Sigma - and we utilized that and we estimated the material constant which only depends on the constituents or the material property so
• 52:30 - 53:00 therefore we can predict any given phenomena we see another example where similarly for steady state flows the equation one that is a dou Q Z by dou Z equation 1 this expression should be equal to 0 for steady state flows if it
• 53:00 - 53:30 is for two-dimensional flows this is nothing but K X dou square H by Dow X s square plus K Z dou square H by Dow Z square he is equals to 0 for isotropic for isotropic case the KX and K are the same this is simply dou square H by Dow X s square plus dou square H by Dow Z square this we solved by invoking velocity potential and stream function and
• 53:30 - 54:00 knowing that these two functions satisfy the Laplace expression Laplace equation we graphically solve this for estimating the seepage rates underneath a dam if you have a dam or sheet pile wall so this is the water which is behind the sheet pile wall and what is the flow that is taking place can be estimated
• 54:00 - 54:30 they confined environment very easily graphically we can estimate and this one we have already learnt in basic soil mechanics so here also we utilized mass conservation principle so there is a physical law so the head here is the state variable all the governing equations are always represented in terms of state variables similarly for estimating the shear strain characteristics of we invoke stress-strain relationship our
• 54:30 - 55:00 stress versus stream stress versus strain relationship indirect here we get the shear stress versus shear strain relationship where for normally consorted where normally
• 55:00 - 55:30 consolidated clays they exhibit this behavior normally consolidated clays are loose and exhibit this behavior and were consolidated clays and dense OC soils are dense sands exhibit a peak behavior and after that the stress decreases and CR loose sands so here we obtain the
• 55:30 - 56:00 failure shear stress at failure for critical state and from this this is a stress strain relationship and this is a shear stress versus shear stress at failure versus Sigma at failure this whole test is conducted at one Sigma and for different Sigma's if you conduct different shear stresses you get and from that you can obtain either straight
• 56:00 - 56:30 line joining from origin or with some intercept so these are the material constants Phi critical and cohesion these are the metal constants and Sigma F tau F are the state variables similarly tau and shear strain these are state variables so the cost relationships are two versus Sigma if it
• 56:30 - 57:00 is a drain test interaction test then it could be Sigma dash also and tau versus gamma or in track shell test you get Delta Sigma versus stream so these are the cost relationships we have so therefore for the phenomenal
• 57:00 - 57:30 prediction you require fast physical observation for example in case of consolidation this is a settlement versus time settlement versus time and you have governing equations which are derived from the physical laws here it is a mass conservation this is for
• 57:30 - 58:00 consolidation problem then after getting the observation settlement versus time you invoke the mass conservation principle and to derive the governing equation and you identify the state variables here the state variables are Sigma rash wide
• 58:00 - 58:30 ratio you etcetera you identify the state variables then construct a casted relationship using experimentation so you build wide ratio versus Sigma - so this is a constant relationship which is obtained from the experiment observations iwere says Sigma - then identify the metal constants such as a V or MV and finally C V then you predict the
• 58:30 - 59:00 phenomenon because once CV is known CV is obtained you predict at what rate the settlement is taking place you get a theoretical settlement versus theoretical settlement versus time so once you theoreticaly once you theoretically obtain the settlement versus time you compare with the
• 59:00 - 59:30 measured or observed physical observation that is settlement versus time if that does not match so then you need to refine whether you have considered all the physical laws for building the governing equation or not you need to check are are there any anymore state variables need to be recognized and costed relationships need to be built that you need to check for
• 59:30 - 60:00 example in one case that is a consolidation settlement of soft soils which is of concern in many applications like mine tailing applications and other applications and phosphate clays are tailings deposition in all these situations the soft soil sedimentation our soft soil settlement is very important in such situations the terzaghi's
• 60:00 - 60:30 vanishing consolidation theory or estimates the settlement rates that is because the soft soils would settle even because of its own weight here the conservation of momentum that is 4c clipper me is not invoked here because we are assuming that sample size is very small Puu centimeter thick and we are ignoring the effect of self weight so when we invoke the sulfide when we invoke the
• 60:30 - 61:00 conservation of momentum principle that is force equilibrium then we can predict the behavior very well that is done by Gibson and also in this particular derivation one also need to express another cost relationship that is k vs e the hydraulic conductivity in the sample so if this is the consolidation sample you have a porous stones at the top and
• 61:00 - 61:30 bottom are sand which is at the top and bottom now as soon as the load is applied from the soil sample you have pore pressure at any given point at time T equal to zero at time T equal to zero pore pressure at any given depth is equal to the applied stress but just
• 61:30 - 62:00 after time T equal to zero the pore pressure at z equal to 0 and Z equal to L it becomes zero and this is a pore water pressure distribution you get pore pressure is excess pore water pressure is maximum at the center and they are 0 at the boundaries so this is the condition if the excess pore water pressure is 0 at the boundaries - boundaries then the Sigma dash Sigma
• 62:00 - 62:30 dash should be maximum here and from the expression of Sigma dash vs. Yi relationship and minashi is maximum the void ratio is minimum so if the wide ratio plot is made with the depth here so the wide ratio should be smaller here and larger here and smaller here so this is how the wide ratio changes if the wide ratio
• 62:30 - 63:00 changes in this manner the hydraulic conductivity also changes similarly hydraulic conductivity way should be smaller when the wide ratio is small and should be higher when the white ratio is large so K also changes accordingly so therefore this expression is also invoked this constant relationship is also built sorry this relationship is also obtained from the consolidation tests and this is also used in the analysis and finally the
• 63:00 - 63:30 Gibson's model which considers the lagrangian coordinate system where the element also changes the element the element to initially be considered this also changes with time that is also concerned by considering the Lagrangian coordinates and it considers the another physical order is conservation of linear conservation of momentum that is
• 63:30 - 64:00 considered so that means for cyclamen is considered and the expression for Sigma dash versus C and K versus C both are invoked and Gibson's expression predicts very well the consolidation behavior of soft soils thank you [Music]
• 64:00 - 64:30 you [Music]