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Book · January with , Reads The application of the principles of soil mechanics to the design and construction of foundations for various. Proceedings of the Eighth Regional Conference for Africa on Soil Mechanics and as a soil. The mining engineer, the mill manager and the geotechnical. Many books of soil mechanics are available in the market. but you have asked books for JE preparations so i am going to mention some good.


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Pages·· MB·15, Downloads. A companion lab manual is available from the Publisher: Soil Mechanics This book is intended -. Find Soil mechanics books online. Get the best Soil mechanics books at our marketplace. Soil Mechanics and Foundation Engineering deals with its principles in an elegant, yet simplified, manner in this text. It presents all the material required for a.

Personal information is secured with SSL technology. Free Shipping No minimum order. Description Soil Mechanics: Calculations, Principles, and Methods provides expert insights into the nature of soil mechanics through the use of calculation and problem-solving techniques. This informed reference begins with basic principles and calculations, illustrating physical meanings of the unit weight of soil, specific gravity, water content, void ratio, porosity, saturation, and their typical values. This is followed by calculations that illustrate the need for soil identification, classification, and ways to obtain soil particle size distribution, including sizes smaller than 0. The book goes on to provide expert coverage regarding the use of soil identification and classification systems both Unified Soil Classification System and AASHTO , and also includes applications concerning soil compaction and field applications, hydraulic conductivity and seepage, soil compressibility and field application, and shear strength and field application. Key Features Presents common methods used for calculating soil relationships Covers soil compressibility and field application and calculations Includes soil compaction and field application calculations Provides shear strength and field application calculations Includes hydraulic conductivity and seepage calculations.

In the Netherlands the slide of a railway embankment near Weesp, in see Figure 1. Many of the basic principles of soil mechanics were well known at that time, but their combination to an engineering discipline had not yet been completed. The first important contributions to soil mechanics are due to Coulomb, who published an important treatise on the failure of soils in , and to Rank- ine, who published an article on the possible states of stress in soils in In Darcy published his famous work on the permeability of soils, for the water supply of the city of Dijon.

The principles of the mechanics of continua, including statics and strength of materials, were also well known in the 19th century, due to the work of Newton, Cauchy, Navier and Boussi- nesq. The union of all these fundamentals to a coherent discipline had to wait until the 20th century.

Important pioneering contributions to the development of soil mechanics were made by Karl Terzaghi, who, among many other things, has described how to deal with the influence of the pressures of the pore water on the be- havior of soils. This is an essential element of soil mechanics theory. Mistakes on this aspect often lead to large disasters, such as the slides near Weesp, Figure 1.

Aberfan Wales and the Teton Valley Dam disaster. In the Netherlands much pioneering work was done by Keverling Buisman, especially on the deformation rates of clay. A stimulating factor has been the establishment of the Delft Soil Mechanics Laboratory in , now known as GeoDelft. In many countries of the world there are similar institutes and consulting companies that specialize on soil mechanics. Usually they also deal with Foundation engineering, which is concerned with the application of soil mechanics principle to the design and the construction of foundations in engineering practice.

Soil mechanics and Foundation engineering together are often denoted as Geotechnics. A well known Arnold Verruijt, Soil Mechanics : 1. The international organization in the field of geotechnics is the International Society for Soil Mechanics and Geotechnical Engineering, the ISSMGE, which organizes conferences and stimulates the further development of geotechnics by setting up international study groups and by standardization.

In most countries the International Society has a national society. Soil mechanics has become a distinct and separate branch of engineering mechanics because soils have a number of special properties, which distinguish the material from other materials. Its development has also been stimulated, of course, by the wide range of applications of soil engineering in civil engineering, as all structures require a sound foundation and should transfer its loads to the soil.

The most important special properties of soils will be described briefly in this chapter. In further chapters they will be treated in greater detail, concentrating on quantitative methods of analysis. This means that the deformations will be twice as large if the stresses are twice Particles, water, air. Stresses in soils. Stresses in a layer. Groundwater flow. Flow net. Flow towards wells. Stress strain relations. One-dimensional compression.

Analytical solution. Numerical solution. Consolidation coefficient. Secular effect. Shear strength. Triaxial test. Shear test. Cell test. Pore pressures. Undrained behaviour of soils. Stress paths.

Book soil mechanics

Elastic stresses and deformations. Deformation of layered soil. Lateral stresses in soils. Tables for lateral earth pressure.

Sheet pile walls. Sheet pile wall in layered soil. Limit analysis. Strip footing. Limit theorems for frictional materials. Brinch Hansen. Vertical slope in cohesive material. Stability of infinite slope. Slope stability. Soil exploration. Model tests.

Soil Mechanics Book - Vol 1 - Complete Guide of Soils Engineering

Pile foundations. Stress analysis. Theory of elasticity. Theory of plasticity. This book is the text for the introductory course of Soil Mechanics in the Department of Civil Engineering of the Delft University of Technology, as I have given from until my retirement in It contains an introduction into the major principles and methods of soil mechanics, such as the analysis of stresses, deformations, and stability.

The most important methods of determining soil parameters, in the laboratory and in situ, are also described. Some basic principles of applied mechanics that are frequently used are presented in Appendices.

The subdivision into chapters is such that one chapter can be treated in a single lecture, approximately. Comments of students and other users on the material in earlier versions of this book have been implemented in the present version, and errors have been corrected.

The logo was produced by Professor G. Several users, from all over the world, have been kind enough to send me their comments or their suggestions for corrections or improvements. In recent versions of the screenbook it has also been attempted to incorporate the figures better into the text, using the macro wrapfigure, and colors.

In this way the appearance of many pages seems to have been improved. Papendrecht, March Arnold Verruijt. The non-weathered material in this crust is denoted as rock, and its mechanics is the discipline of rock mechanics. In general the difference between soil and rock is roughly that in soils it is possible to dig a trench with simple tools such as a spade or even by hand.

In rock this is impossible, it must first be splintered with heavy equipment such as a chisel, a hammer or a mechanical drilling device. The natural weathering process of rock is that under the long-term influence of sun, rain and wind, it degenerates into stones.

This process is stimulated by fracturing of rock bodies by freezing and thawing of the water in small crevices in the rock. The coarse stones that are created in mountainous areas are transported downstream by gravity, often together with water in rivers.

By internal friction the stones are gradually reduced in size, so that the material becomes gradually finer: In flowing rivers the material may be deposited, the coarsest material at high velocities, but the finer material only at very small velocities.

This means that gravel will be found in the upper reaches of a river bed, and finer material such as sand and silt in the lower reaches. The Netherlands is located in the lower reaches of the rivers Rhine and Meuse.

In general the soil consists of weathered material, mainly sand and clay. This material has been deposited in earlier times in the delta formed by the rivers. Much fine material has also been deposited by flooding of the land by the sea and the rivers. This process of sedimentation occurs in many areas in the world, such as the deltas of the Nile and the rivers in India and China. In the Netherlands it has come to an end by preventing the rivers and the sea from flooding by building dikes.

The process of land forming has thus been stopped, but subsidence continues, by slow tectonic movements. In order to compensate for the subsidence of the land, and sea water level rise, the dikes must gradually be raised, so that they become heavier and cause more subsidence. This process must continue forever if the country is to be maintained. People use the land to live on, and build all sort of structures: It is the task of the geotechnical engineer to predict the behavior of the soil as a result of these human activities.

The problems that arise are, for instance, the settlement of a road or a railway under the influence of its own weight and the traffic load, the margin of safety of an earth retaining structure a dike, a quay wall or a sheet pile wall , the earth pressure acting upon a tunnel or a sluice, or the allowable loads and the settlements of the foundation of a building.

For all these problems soil mechanics should provide the basic knowledge. The need for the analysis of the behavior of soils arose in many countries, often as a result of spectacular accidents, such as landslides and failures of founda- tions.

In the Netherlands the slide of a railway embankment near Weesp, in see Figure 1. Many of the basic principles of soil mechanics were well known at that time, but their combination to an engineering discipline had not yet been completed.

The first important contributions to soil mechanics are due to Coulomb, who published an important treatise on the failure of soils in , and to Rank- ine, who published an article on the possible states of stress in soils in In Darcy published his famous work on the permeability of soils, for the water supply of the city of Dijon.

The principles of the mechanics of continua, including statics and strength of materials, were also well known in the 19th century, due to the work of Newton, Cauchy, Navier and Boussi- nesq. The union of all these fundamentals to a coherent discipline had to wait until the 20th century.

Advanced Soil Mechanics, Fifth Edition

Important pioneering contributions to the development of soil mechanics were made by Karl Terzaghi, who, among many other things, has described how to deal with the influence of the pressures of the pore water on the be- havior of soils.

This is an essential element of soil mechanics theory. Mistakes on this aspect often lead to large disasters, such as the slides near Weesp, Figure 1. Landslide near Weesp, Aberfan Wales and the Teton Valley Dam disaster. In the Netherlands much pioneering work was done by Keverling Buisman, especially on the deformation rates of clay. A stimulating factor has been the establishment of the Delft Soil Mechanics Laboratory in , now known as GeoDelft.

In many countries of the world there are similar institutes and consulting companies that specialize on soil mechanics. Usually they also deal with Foundation engineering, which is concerned with the application of soil mechanics principle to the design and the construction of foundations in engineering practice.

Soil mechanics and Foundation engineering together are often denoted as Geotechnics. The international organization in the field of geotechnics is the International Society for Soil Mechanics and Geotechnical Engineering, the ISSMGE, which organizes conferences and stimulates the further development of geotechnics by setting up international study groups and by standardization.

In most countries the International Society has a national society. Soil mechanics has become a distinct and separate branch of engineering mechanics because soils have a number of special properties, which distinguish the material from other materials. Its development has also been stimulated, of course, by the wide range of applications of soil engineering in civil engineering, as all structures require a sound foundation and should transfer its loads to the soil.

The most important special properties of soils will be described briefly in this chapter. In further chapters they will be treated in greater detail, concentrating on quantitative methods of analysis. Many engineering materials, such as metals, but also concrete and wood, exhibit linear stress-strain-behavior, at least up to a certain stress level.

This means that the deformations will be twice as large if the stresses are twice Soils do not satisfy this law. For instance, in compression soil becomes gradually stiffer. At the This is mainly caused by the increase of the forces This property is used in daily life by the packaging of coffee and other granular materials by a The package becomes very In civil engineering the non-linear property is used to In the sand below a thick deposit of soft clay the stress level is high, due to the weight of This makes the sand very hard and strong, and it is possible to apply large compressive forces to the piles, provided that they are long enough to reach well into the sand.

Figure 1. Pile foundation. Arnold Verruijt, Soil Mechanics: In shear, however, soils become gradually softer, and if the shear stresses reach a certain level, with respect to the normal stresses, it is even possible that failure of the soil mass occurs.

This means that the slope of a sand heap, for instance in a de- pot or in a dam, can not be larger than about 30 or 40 degrees. The reason for this is that particles would slide over each other at greater slopes.

As a consequence of this phenomenon many countries in deltas of large rivers are very flat. It has also. Especially dangerous is that in very fine materials, such as clay, a A positive application of the failure of soils in shear is the construction of guard rails along highways. After a collision by a vehicle the foundation of the guard rail will rotate in the soil due to the large shear stresses between this foundation and the soil body around it. This will dissipate large amounts of Figure 1.

A heap of sand. Of course, the guard rail must be repaired after the collision, which can relatively easily be done with the aid of a heavy vehicle. Loose sand has a tendency to contract to a smaller volume, and densely packed sand can practically deform only when the volume expands somewhat, making the sand looser.

This is called dilatancy, a phenomenon discovered by Reynolds, in This property causes the soil around a human foot The densely packed sand is loaded The expansion of a dense soil during shear is The space between the particles increases when they shear over each other.

On the other hand a very loose assembly of sand particles will have a tendency to collapse when Figure 1. Such volume deformations may be especially dangerous when the soil is saturated with water. The tendency for volume decrease then may lead to a large increase in the pore water pressures.

Many geotechnical accidents have been caused by increasing pore water pressures. During earth quakes in Japan, for instance, saturated sand is sometimes densified in a short time, which causes large pore pressures to develop, so that the sand particles may start to float in the water.

This phenomenon is called liquefaction. In the Netherlands the sand in the channels in the Eastern Scheldt estuary was very loose, which required large densification works before the construction of the storm surge barrier. Also, the sand used to create the airport Tjek Lap Kok in Hongkong had to be densified before the construction of the runways and the facilities of the airport.

This is called creep. Clay and peat exhibit this phenomenon. It causes structures founded on soft soils to show ever increasing settlements. A new road, built on a soft soil, will continue to settle for many years. For buildings such settlements are particular damaging when they are not uniform, as this may lead to cracks in the building.

The building of dikes in the Netherlands, on compressible layers of clay and peat, results in settlements of these layers that continue for many decades. In order to maintain the level of the crest of the dikes, they must be raised after a number of years. This results in increasing stresses in the subsoil, and therefore causes additional settlements. This process will continue forever. Before the construction of the dikes the land was flooded now and then, with sediment being deposited on the land.

This process has been stopped by man building dikes. Safety has an ever increasing price. Sand and rock show practically no creep, except at very high stress levels.

This may be relevant when predicting the deformation of porous layers from which gas or oil are extracted. This water contributes to the stress transfer in the soil. It may also be flowing with respect to the granular particles, which creates friction stresses between the fluid and the solid material. In many cases soil must be considered as a two phase material. As it takes some time before water can be expelled from a soil mass, the presence of water usually prevents rapid volume changes.

In many cases the influence of the groundwater has been very large. In in the Netherlands many dikes in the south-west of the country failed because water flowed over them, penetrated the soil, and then flowed through the dike, with a friction force acting upon the dike material.

The force of the In other countries of the world large dams have sometimes failed also because of rising water Even excessive rainfall may Overflowing dike. It is also very important that lowering the water pressures in a soil, for instance by the production of groundwater for drinking purposes, leads to an increase of the stresses between the particles, which results in settlements of the soil.

This happens in many big cities, such as Venice and Bangkok, that may be threatened to be swallowed by the sea. It also occurs when a groundwater table is temporarily lowered for the construction of a dry excavation.

Buildings in the vicinity of the excavation may be damaged by lowering the groundwater table. The production of natural gas from the large reservoir in Groningen is estimated to result in a subsidence of about 50 cm in the production time of the reservoir. Therefore the initial state of stress is often not uniform, and often even partly unknown. Because of the non-linear behavior of the material, mentioned above, the initial stresses in the soil are of great importance for the determination of soil behavior under additional loads.

These initial stresses depend upon In particular, the initial The initial vertical stresses may be determined by the weight.. This means that the stresses increase with depth, and therefore stiffness and strength also The horizontal stresses, however, usually remain largely unknown.

When the soil has been Together with the stress dependency of the Figure 1. It may also be noted that further theoretical study can not provide much help in this matter.

Studying field history, or visiting the site, and talking to local people, may be more helpful. Even in two very close locations the soil properties may be completely different, for Sometimes the course of an ancient When an embankment..

The variability of soil properties may also be the result of a heavy local load in the past. A global impression of the soil composition can be obtained from geological maps. These indicate the Together with geological knowledge and experience this may Other geological information may also be helpful. Large areas An accurate determination of soil properties can not be made from desk studies.

It requires testing of the actual soils in the laboratory, using samples taken from the field, or testing of the soil in the field in situ. This will be elaborated in later chapters. Problems 1. Is that useful? On which side? What can be the reason? On what side of the tower would that clay layer be thickest? On which side of the tower would that building have been? What is the probable cause, and is there a possible simple technical solution to prevent further leaning?

Chapter 2. In many cases these various types also have different mechanical properties. A simple subdivision of soils is on the basis of the grain size of the particles that constitute the soil. Coarse granular material is often denoted as gravel and finer material as sand.

In order to have a uniformly applicable terminology it has been agreed internationally to consider particles larger than 2 mm, but smaller than 63 mm as gravel. Larger particles are denoted as stones. Sand is the material consisting of particles smaller than 2 mm, but larger than 0.

Particles smaller than 0. Soil consisting of even smaller particles, smaller than 0. In some countries, such as the Netherlands, the soil may also contain layers of peat, consisting of organic material such as decayed plants.

Particles of peat usually are rather small, but it may also contain pieces of wood. It is Soil type min. The amount of carbon in a soil clay 0. The mechanical behavior of the main types of soil, sand, clay and peat, sand 0. Clay usually is much less permeable for water than sand, gravel 2 mm 63 mm but it usually is also much softer.

Peat is usually is very light some times hardly heavier than water , and strongly anisotropic because of the presence Table 2. Grain sizes. Peat usually is also very compressible. Sand is rather permeable, and rather stiff, especially after a certain preloading. It is also very characteristic of granular soils such as sand and gravel, that they can not transfer tensile stresses.

The particles can only transfer compressive forces, no tensile forces. Only when the particles are very small and the soil contains some water, can a tensile stress be transmitted, by capillary forces in the contact points. The grain size may be useful as a first distinguishing property of soils, but it is not very useful for the mechanical properties. The quantitative data that an engineer needs depend upon the mechanical properties such as stiffness and strength, and these must be determined from mechanical tests.

Soils of the same grain size may have different mechanical properties. Sand consisting of round particles, for instance, can have a strength that is much smaller than sand consisting of particles with sharp points. Also, a soil sample consisting of a mixture of various grain sizes can have a very small permeability if the small particles just fit in the pores between the larger particles.

A steep slope of the curve For rather coarse particles, say larger than The usual procedure is to use a system of sieves having Special Figure 2. Grain size diagram. The example shown in Figure 2.

In this case there appear to be no grains larger than 5 mm. The grain size distribution can be characterized by the quantities D60 and D In the case illustrated in Figure 2.

This indicates that the soil is not uniform. This is sometimes denoted as a well graded soil. In a poorly graded soil the particles all have about the same size. For particles smaller than about 0. The amount of particles of a particular size can then be determined much better by measuring the velocity of deposition in a glass of water.

This formula expresses that the force on a small sphere, sinking in a viscous fluid, depends upon the viscosity of the fluid, the size of the sphere and the velocity. Because the force acting upon the particle is determined by the weight of the particle under water, the velocity of sinking of a particle in a fluid can be derived. The formula is. Because for very small particles the velocity may be very small, the test may take rather long. Sand and gravel usually consist of the same minerals as the original rock from which they were created by the erosion process.

This can be quartz, feldspar or glimmer. In Western Europe sand usually consists mainly of quartz. The chemical formula of this mineral is SiO2. Fine-grained soils may contain the same minerals, but they also contain the so-called clay minerals, which have been created by chemical erosion. The main clay minerals are kaolinite, montmorillonite and illite. In the Netherlands the most frequent clay mineral is illite. These minerals consist of compounds of aluminum with hydrogen, oxygen and silicates.

They differ from each other in chemical composition, but also in geometrical structure, at the microscopic level. The microstructure of clay usually resembles thin plates. On the microscale there are forces between these very small elements, and ions of water may be bonded.

Because of the small magnitude of the elements and their distances, these forces include electrical forces and the Van der Waals forces. Although the interaction of clay particles is of a different nature than the interaction between the much larger grains of sand or gravel, there are many similarities in the global behavior of these soils. There are some essential differences, however. The deformations of clay are time dependent, for instance. When a sandy soil is loaded it will deform immediately, and then remain at rest if the load remains constant.

Under such conditions a clay soil will continue to deform, however. It is very much dependent upon the actual chemical and mineralogical constitution of the clay. Also, some clays, especially clays containing large amounts of montmorillonite, may show a considerable swelling when they are getting wetter.

As mentioned before, peat contains the remains of decayed trees and plants. Chemically it therefore consists partly of carbon compounds. It may even be combustible, or it may be produce gas. As a foundation material it is not very suitable, also because it is often very light and compressible. It may be mentioned that some clays may also contain considerable amounts of organic material.

For a civil engineer the chemical and mineralogical composition of a soil may be useful as a warning of its characteristics, and as an indication of its difference from other materials, especially in combination with data from earlier projects.

A chemical analysis does not give much quantitative information on the mechanical properties of a soil, however. For the determination of these properties mechanical tests, in which the deformations and stresses are measured, are necessary.

These will be described in later chapters. It determines whether the soil can easily be handled, by soil moving equipment, or by hand. The consistency is often very much dependent on the amount of water in the soil. This is expressed by the water content w see also chapter 3. It is defined as the weight of the water per unit weight of solid material, When the water content is very low as in a very dry clay the soil can be very stiff,..

It is then said to be in the solid state. Adding water, for instance In order to distinguish between these states Figure 2. Liquid limit.

They are sometimes denoted as the Atterberg limits, after the Swedish engineer who introduced them. The transition from the liquid state to the plastic state is denoted as the liquid limit, wL.

It represents the lowest water content at which the soil behavior is still mainly liquid. As this limit is not absolute, it has been defined as the value determined in a certain test, due to Casagrande, see Figure 2.

In the test a hollow container with a soil sample may be raised and dropped by rotating an axis. The liquid limit is the value of the water content for which a standard V-shaped groove cut in the soil, will just close When the groove closes after less than 25 drops, the soil is too wet, By waiting for some time, and perhaps Then the water content must In this test a steel The cone is then dropped and its penetration.

The liquid limit has been defined as the water content corresponding. Again the liquid limit can be determined by doing the It has also been observed, however, that the penetration Figure 2.

The fall cone. This means that the liquid limit may be determined from a single test, which is much faster, although less accurate. P w wL The transition from the plastic state to the solid state is called the plastic limit, and denoted as It is defined as the water content at which the clay can just be rolled to threads of 3 mm diameter.

Very wet clay can be rolled into very thin threads, but dry clay will break when rolling thick threads. The arbitrary limit of 3 mm is supposed to indicate the plastic limit.

In the laboratory the test is For many applications potteries, dike construction it is especially important that the range of the This is described by the plasticity index PI. It is defined as the difference of the The plasticity index is a useful measure for the possibility to process the clay.

It is important for In all these cases a high plasticity index indicates that the clay can easily be used without too much fear of it turning into a liquid or a solid.

Figure 2. Water content. In countries with very thick clay deposits England, Japan, Scandinavia it is often useful to deter- mine a profile of the plastic limit and the liquid limit as a function of depth, see Figure 2. In this diagram the natural water content, as determined by taking samples and immediately determining the water content, can also be indicated.

Soil Mechanics And Foundation Engineering

This is enhanced by confusion between terms such as sandy clay and clayey sand that may be used by local firms. In some areas tradition may have also lead to the use of terms such as blue clay or brown clay, that may be very clear to experienced local engineers, but have little meaning to others. Uniform criteria for the classification of soils do not exist, especially because of local variations and characteristics.

The soil in a plane of Tibet may be quite different from the soil in Bolivia or Canada, as their geological history may be quite different. The engineer should be aware of such differences and remain open to characterizations that are used in other countries.

Nevertheless, a classification system that has been developed by the United States Bureau of Reclamation, is widely used all over the world. This system consists of two characters to indicate a soil type, see Table 2. A soil of type SM, for instance, is a silty sand, which indicates that it is a sand, but containing considerable amounts of non-organic fine silty particles. This type of soil is found in the Eastern Scheldt in the Netherlands.

A clay of very low plasticity, that is a clay with Character 1 Character 2 a relatively small plasticity index is denoted as CL. The clay in a polder in Holland will often be of the type CH. It has a reasonably large range of G gravel W well graded plastic behavior. S sand P poorly graded The characterization well graded indicates that a granular material con- sists of particles that together form a good framework for stress transfer.

It M silt M silty usually is relatively stiff and strong, because the smaller particles fill well in C clay C clayey the pores between the larger particles.

A material consisting of large gravel particles and fine sand is called poorly graded, because it has little coherence. O organic L low plasticity A well graded material is suitable for creating a road foundation, and is also Pt peat H high plasticity suitable for the production of concrete. Global classifications as described above usually have only little meaning Table 2. There may be some correlation between the classification and the strength, but this is merely indicative.

For engineering calculations mechan- ical tests should be performed, in which stresses and deformations are measured. Such tests are described in later chapters. Chapter 3. In order to describe a soil various parameters are used to describe the distribution of these three components, and their relative contribution to the volume of a soil. These are also useful to determine other parameters, such as the weight of the soil. They are defined in this chapter.

When the porosity is small the soil is called densely packed, when the porosity is large it is loosely packed. It may be interesting to calculate the porosities for two particular cases. The first case is a very This is called a cubic array of particles, see Figure 3. If the diameter of.. The ratio of the volume of the solids. Figure 3. Cubic array. This is the loosest packing of spherical particles that seems possible.

Of course, it is not stable: A very dense packing of spheres can be constructed by starting from layers in which the spheres form a pattern of equilateral triangles, see Fig- ure 3. The packing is constructed by packing such layers such that the spheres of the next layer just fit in the hollow space between three spheres of the previous layer. The axial lines from a sphere with the three spheres that support it from p below Each sphere of thepassembly, with This seems to be the most dense packing of Densest array.

Although soils never consist of spherical particles, and the values calculated above have no real meaning for actual soils, they may give a certain indication of what the porosity of real soils may be. It can thus be expected that the porosity n of a granular material may have a value somewhere in the range from 0.

Practical experience confirms this statement.

Mechanics book soil

The amount of pores can also be expressed by the void ratio e, defined as the ratio of the volume of the pores to the volume of the solids,. In many countries this quantity is preferred to the porosity, because it expresses the pore volume with respect to a fixed volume the volume of the solids.

The porosity can not be smaller than 0, and can not be greater than 1. The void ratio can be greater than 1. The void ratio is also used in combination with the relative density. This quantity is defined as. Here emax is the maximum possible void ratio, and emin the minimum possible value.

These values may be determined in the laboratory. The densest packing of the soil can be obtained by strong vibration of a s ample, which then gives emin. The loosest packing can be achieved by carefully pouring the soil into a container, or by letting the material subside under water, avoiding all disturbances, which gives emax.

The accuracy of the determination of these two values is not very large. After some more vibration the sample may become even denser, and the slightest disturbance may influence a loose packing. It follows from eq. Such a densification can occur in the field rather unexpectedly, for instance in case of a sudden shock an earthquake , with dire consequences.

Of course, the relative density can also be expressed in terms of the porosity, using eqs. To describe the ratio of these two the degree of saturation S is introduced as.

Here Vw is the volume of the water, and Vp is the total volume of the pore space. The density of a substance is the mass per unit volume of that substance. Small deviations from this value may occur due to temperature differences or variations in salt content. In soil mechanics these are often of minor importance, and it is often considered accurate enough to assume that. For the analysis of soil mechanics problems the density of air can usually be disregarded. The density of the solid particles depends upon the actual composition of the solid material.

This value can be determined by carefully dropping a certain mass of particles say Wp in a container partially filled with water, see Figure 3.

The precise volume of the particles can be measured by observing the rise of the water table in the glass. This is particularly easy when using a graduated measuring glass. The rising of the water table indicates the volume of the particles, Vp. Their mass Wp can be measured most easily by measuring the weight of the glass before and after dropping the particles.. The density of the particle material then follows immediately from The principle of this simple test, in which the volume of a body having He had been asked to check the composition of a golden crown, Measuring the density of solid particles with the density of a piece of pure gold, but then he had to determine the precise volume of the crown.

The legend has it that when stepping into his bath he discovered that the volume of a body submerged in water equals the volume of water above the original water table. This can be calculated if the porosity, the degree of saturation and the densities are known. Thus the total weight W is. This formula indicates that the volumetric weight is determined by a large number of soil parameters: In reality it is much simpler to determine the volumetric weight often also denoted as the unit weight directly by measuring the weight W of a volume V of soil.

It is then not necessary to determine the contribution of each of the components. If the soil is completely dry the dry volumetric weight is. This value can also be determined directly by weighing a volume of dry soil.

In order to dry the soil a sample may be placed in an oven. The temperature in such an oven is usually close to degrees, so that the water will evaporate quickly.

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At a much higher temperature there would be a risk that organic parts of the soil would be burned. From the dry volumetric weight the porosity n can be determined, see eq. This is a common method to determine the porosity in a laboratory. In some cases, this may lead to large errors, for instance when the compressibility of the water-air-mixture in the pores must be determined.