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36886 results in Cambridge Textbooks

Page 1632 of 1845

  • Menexenus

  • Edited by Malcolm Schofield, University of Cambridge
  • Translated by Tom Griffith
  • Book:
    Plato: Gorgias, Menexenus, Protagoras
    Published online:
    28 May 2018
    Print publication:
    19 November 2009, pp 115-136

  • Summary

    Dramatis personae

    MENEXENUS With his cousin Ctesippus became a member of Socrates' intimate circle, to judge from their presence in the prison on the day the hemlock was administered (Phaedo 59b). In the Lysis Menexenus (again in Ctesippus's company) and his friend Lysis are boys of twelve or thirteen. In the Menexenus he is evidently a few years older. Socrates suggests that he came from a prominent political family – but history has left no clues enabling us to identify the public figures Plato might have had in mind.

    SOCRATES (469–399) Sustains throughout the dialogue the teasing pretence that he is currently a student of rhetoric, with Pericles' mistress Aspasia for his teacher. What purpose Plato had in representing him in this alien and improbable guise is discussed in the Introduction.

    Analysis

    234a–236d – Introductory conversation

    236d–249c – Speech of Aspasia

    236b–237b Introduction

    237b–238b Good birth and upbringing: Athenian autochthony and how it shapes the life of the population

    238b–239a Good upbringing: the Athenian political system

    239a–246b Noble exploits: Athenian history

  • 239b–c: Athens' very earliest military exploits – the subject of poetry

  • 239c–240e: The rise of Persian imperialism; the Athenian victory at Marathon, and what it taught the Greeks

  • 240e–241c: The Athenian naval victories at Salamis and Artemisium – further lessons for the Greeks

  • 241c–e: Further victories over the Persians instil fear in the Great King

  • […]

  • 1 - Introduction

  • David Muir Wood, University of Bristol
  • Book:
    Soil Mechanics
    Published online:
    28 May 2018
    Print publication:
    28 September 2009, pp 1-11

  • Summary

    Introduction

    In this chapter, we set the scene for the rest of the book. It may be helpful to remind readers of the relevance and importance of soil mechanics for all civil engineering construction: everything we construct sits on the ground in some way or other at some stage in its life. Even aircraft land on runways, and cars drive along roads; in each case there is some stiff layer (pavement) between the wheels and the prepared ground underneath. This stiff layer will help to spread the vehicular load but, in the end, this load must still be supported by the ground. Some examples of typical geotechnical design problems are presented in the next sections.

    The term soil mechanics refers to the mechanical properties of soils; the term geotechnical engineering refers to the application of those mechanical properties to the design and construction of those parts of civil engineering systems which are concerned with the active or passive use of soils. Soils are the materials that we find in the ground: the term ground engineering is somewhat equivalent to geotechnical engineering. We will talk a little about the nature of soils in Chapter 3.

    The term soil means different things to different people. To an agricultural engineer, the soil is the upper layer of the ground which the farmer ploughs and harrows and in which crops are sown.

  • 9 - Soil-structure interaction

  • David Muir Wood, University of Bristol
  • Book:
    Soil Mechanics
    Published online:
    28 May 2018
    Print publication:
    28 September 2009, pp 208-229

  • Summary

    Introduction

    Soil-structure interaction is one of those interface topics which cannot be treated successfully either as a purely structural problem or as a purely geotechnical problem. A holistic approach is required to the modelling – the identification of the essential details of the problem – and to the subsequent analysis. The geotechnical system in this case is the sum of all the geotechnical and structural elements, and the response of the system will certainly depend on some combination of properties of both the soil and the structure. If the ground and the structure are both behaving elastically, then simple configurations lead to exact analyses. While it has to be admitted that the problems that can be analysed are somewhat idealised, there is sufficient realism to demonstrate and support the important messages of soil-structure interaction.

    Let us start with a thought experiment that will seem quite remote from soil-structure interaction. Suppose that we have a quarter kilogram (or half pound) packet of butter (unwrapped) on a plate. We also have a penknife or some other knife with a short, stiff blade, and a palette knife with a rather flexible blade. We place the flat side of the blades of the knives on the block of butter in turn and try to make an impression in the surface. The short, stiff blade will penetrate without difficulty (Fig. 9.1a); the palette knife blade will just bend (Fig. 9.1b).

  • 2 - Stress in soils

  • David Muir Wood, University of Bristol
  • Book:
    Soil Mechanics
    Published online:
    28 May 2018
    Print publication:
    28 September 2009, pp 12-39

  • Summary

    Introduction

    In this chapter, we introduce the concept of stress and demonstrate how we can calculate stresses in the ground, recalling that we are only concerned with configurations that can be described as one-dimensional. Initial sections rehearse some of the ideas of mechanics – Newton's First Law, the distinction between mass and weight, and the idea of gravity. The single dimension of our problems allows us to impose some notions of symmetry which are helpful in simplifying our calculations of stresses in soils.

    We need then to introduce the possible presence of water in the ground. Some background discussion of basic hydrostatics is required in order that we may describe the pressures that exist in the water. We end with a powerful hypothesis about the way in which stresses are shared between the water and the soil.

    Equilibrium

    Newton's First Law of Motion says that an object will remain in its state of rest or of uniform motion in a straight line unless acted upon by an out-of-balance force. We need not concern ourselves here with the possibility of motion – our soils are expected to be rather stationary or at least to move only very slowly as a result of some construction process. The condition of rest or stasis therefore requires that the forces acting on an object should be in balance.

  • 3 - Density

  • David Muir Wood, University of Bristol
  • Book:
    Soil Mechanics
    Published online:
    28 May 2018
    Print publication:
    28 September 2009, pp 40-66

  • Summary

    Introduction

    In Chapter 2 we calculated profiles of vertical stress in the ground on the assumption that we knew the value of the density of each of the several layers of soil. We also noted that soils consist of individual particles packed together in such a way that there will generally be spaces between them – voids – which may contain air or water or a combination of air and water (or other fluid). Knowing the relative proportions of space occupied by solid and liquid and gas, and knowing the densities of the individual components, we can estimate the density of the overall mixture that is the soil.

    Density is obviously essential for the calculation of stress, but the mechanical behaviour of soils is also strongly influenced by the way in which the soil particles are packed together. It seems intuitively obvious that the greater the proportion of the volume of a material that is occupied by “nothing” the lower will be the resistance of that material to imposition of loads, so we will need to explore density and packing in parallel. It is unfortunate that soil mechanics has been endowed with a plethora of different ways of describing aspects of the distribution of materials within the mixture – the effectiveness of the packing of the particles – and, although really only two or three of these are necessary (and indeed sufficient) for the presentation and understanding of the response of soils, some familiarity is required with all of them.

  • 5 - Seepage

  • David Muir Wood, University of Bristol
  • Book:
    Soil Mechanics
    Published online:
    28 May 2018
    Print publication:
    28 September 2009, pp 90-126

  • Summary

    Introduction

    Water is a particular source of geotechnical problems (Figs 5.1, 5.2). It is no coincidence that landslides frequently occur during or after periods of heavy rainfall. We introduced some of the basic principles of hydrostatics in Chapter 2 and used the idea of a water table to calculate pore water pressures in the ground and thus convert total stresses (equilibrium) to effective stresses (which control mechanical response of soils). Hydrostatics is of course concerned with water at rest – here we will allow the water to move through the soil (but not very fast) and introduce principles of one-dimensional seepage.

    Total head: Bernoulli's equation

    There are some basic building blocks that will assist our study of seepage. One is Bernoulli's equation, which describes the steady flow of an incompressible fluid along a streamline, or through a frictionless tube. This is obviously a somewhat idealised situation but the assumption of incompressibility is certainly reasonable for the flow of water under the pressures that are likely to occur in most civil engineering systems. The flow rates in soils will generally be slow.

    A reference diagram is shown in Fig. 5.3 for an element of water of density ρw of cross-section A which is flowing vertically with velocity v and with pressures u acting at its base, at level z above some reference datum, and u + δu at its top, at level z + Δz above the same datum.

  • 4 - Stiffness

  • David Muir Wood, University of Bristol
  • Book:
    Soil Mechanics
    Published online:
    28 May 2018
    Print publication:
    28 September 2009, pp 67-89

  • Summary

    Introduction

    The two principal mechanical properties of all materials that are required for engineering design are some way of knowing how strong the material is: how much stress it will tolerate – its strength – and some indication of the way in which it will change in size when subjected to load – its stiffness. These characteristics essentially form the basis of what are called, respectively, ultimate limit state design and serviceability limit state design. We will take a one-dimensional look at strength in Chapter 8. Here we will explore some aspects of stiffness of soils.

    Linear elasticity

    The standard experiment that can be performed on metal rods or wires to discover their deformation properties consists of the stretching of an appropriate specimen between suitable grips and measuring the link between the load applied and the resulting extension. In fact, the sort of experiment that can be performed at home might use a metal wire fixed to the ceiling and loaded by means of weights on a small pan (Fig. 4.1): the force transmitted to the wire is visibly obvious and, if we have sufficiently accurate position measuring devices – perhaps some optical system to magnify the displacement – we can have direct information about the extension as well (Fig. 4.1a).

    For most metals, provided the loads that are applied are not excessive, the relationship between load, P, and extension, Δℓ, of such a wire is more or less linear (Fig. 4.1b).

  • 6 - Change in stress

  • David Muir Wood, University of Bristol
  • Book:
    Soil Mechanics
    Published online:
    28 May 2018
    Print publication:
    28 September 2009, pp 127-137

  • Summary

    Introduction

    In Chapter 4 we introduced the concept of the stiffness of soils under one-dimensional loading and were able to calculate the change in vertical strain, and hence the change in thickness of a soil layer that might occur as a result of a change in effective stress. In Chapter 5, we encountered the concept of permeability of soils and noted in particular the huge range of values of permeability for soils, broadly, of different particle sizes (but also influenced by the mineralogy and shape of the particles). The permeability of clays is many orders of magnitude lower than the permeability of sands and gravels. Change in effective stress implies change in vertical dimension of the soil layers, which implies the squeezing out or the sucking in of water (assuming that the soil is saturated). In a soil of very low permeability this cannot happen rapidly, and, in this chapter, we will make deductions about the short-term and long-term conditions that must apply. The analysis of the process that spans between the short term and the long term is called consolidation and is the subject of Chapter 7.

    Stress change and soil permeability

    Figure 6.1 provides an analogy for the behaviour of a soil with low permeability when it is subjected to a change in external stresses. The spring represents the soil, and the loads taken by the spring represent the effective stress carried by the soil particles.

  • Preface

  • David Muir Wood, University of Bristol
  • Book:
    Soil Mechanics
    Published online:
    28 May 2018
    Print publication:
    28 September 2009, pp ix-x

  • Summary

    This book has emerged from a number of stimuli.

    There is a view that soils are special: that their characteristics are so extraordinary that they can only be understood by a small band of specialists. Obviously, soils do have some special properties: the central importance of density and change of density merits particular attention. However, in the context of teaching principles of soil mechanics to undergraduates in the early years of their civil engineering degree programmes, I believe that there is advantage to be gained in trying to integrate this teaching with other teaching of properties of engineering materials to which the students are being exposed at the same time.

    It is a fundamental tenet of critical state soil mechanics – with which I grew up in my undergraduate days – that consideration of the mechanical behaviour of soils requires us to consider density alongside effective stresses, thus permitting the unification of deformation and strength characteristics. This can be seen as a broad interpretation of the phrase critical state soil mechanics. I believe that such a unification can aid the teaching and understanding of soil mechanics.

    There is an elegant book by A. J. Roberts which demonstrates in a unified way how a common mathematical framework can be applied to problems of solid mechanics, fluid mechanics, traffic flow and so on.

  • 7 - Consolidation

  • David Muir Wood, University of Bristol
  • Book:
    Soil Mechanics
    Published online:
    28 May 2018
    Print publication:
    28 September 2009, pp 138-168

  • Summary

    Introduction

    In previous chapters, we have noted that soils of low permeability – typically, clayey soils – will not be able to respond rapidly to changes in stresses which require deformation, which in turn implies, for our one-dimensional systems, change in volume. We suggested in Section 6.2 that there would be a transient process between time t = 0 and time t → ∞ during which the temporary disequilibrium of pore pressures would disappear as deformation of the soil spring permitted stresses to be transferred from pore pressure to effective stresses supported by the soil itself. The detail of this process was not considered: we merely looked at the two extremes of the immediate aftermath of the change in external stress (at t = 0) and the eventual equilibrium at infinite time (t → ∞). In this chapter, we will explore various aspects of the analysis of the transient process between these two extremes. The transient process is known as consolidation.

    We will first produce an approximate solution which forces us to concentrate on the important physical aspects of the problem. However, the governing differential equation – the diffusion equation – is one that is common to many problems which involve gradient driven flow: heat flows down a temperature gradient, pollution flows down a concentration gradient, pore water flows down a gradient of total head (Sections 5.2, 5.4).

  • 8 - Strength

  • David Muir Wood, University of Bristol
  • Book:
    Soil Mechanics
    Published online:
    28 May 2018
    Print publication:
    28 September 2009, pp 169-207

  • Summary

    Introduction

    In the context of our chosen one-dimensional approach to the mechanics of soils, we are somewhat limited in what we can say about the strength of soils but there are some ideas which can usefully be presented. Stiffness is concerned with the deformations of geotechnical systems – the serviceability limit states under operational or working loads. Strength is concerned with the collapse of geotechnical systems – the ultimate limit states for which failure of the geotechnical system will occur. Classically, it has always been easier to make statements about ultimate collapse conditions than about deformations, and geotechnical design often proceeds by starting with a collapse calculation and then factoring down the loading sufficiently that, from experience, the resulting reduced load would not be expected to produce excessive displacements. This is always a rather uncertain route by which to control those displacements, especially if the nature of the problem under consideration is more than somewhat different from those previously experienced – a proper understanding of stiffness is really more satisfactory. However, it does emphasise the traditional importance of understanding the strength of soils and the modes of failure of geotechnical systems.

    Failure mechanisms

    Figure 8.1 shows a schematic picture of a pile foundation. A pile is a long slender stiff structural member which is used to transfer loads from some surface structure through more or less soft soils to a certain depth in the ground (Fig. 1.9).

  • 10 - Envoi

  • David Muir Wood, University of Bristol
  • Book:
    Soil Mechanics
    Published online:
    28 May 2018
    Print publication:
    28 September 2009, pp 230-231

  • Summary

    Summary

    Each chapter has ended with a summary of the key points. Here it is appropriate to reiterate the primary intentions of this book and to point the way towards the next stages of soil mechanics education.

    There are two themes which have been developed in this book:

  • The model of soil stiffness and strength links effective stresses and density. Changes in mechanical behaviour of soils can only be properly understood when the stresses and volumetric packing are considered in parallel. The role that history plays in changes in density – which tend to be locked into soils as loads are applied and then removed – is key for the subsequent understanding of the strength of soils. There is then a link with permeability and the ease with which water (or other pore fluid) can move through the voids of the soil, and thus the ability of the soil to respond rapidly to changes in stress. The concepts of drained and undrained response again bring together the thoughts about effective stresses and volumetric packing. This is the essence of critical state soil mechanics, which at its simplest level (Fig. 10.1) tells us that we cannot hope to understand the behaviour of soils unless we think all the time in parallel of the changes in effective stress and of density.

  • […]

  • 8 - The local Universe

  • Bernard F. Burke, Massachusetts Institute of Technology, Francis Graham-Smith, Jodrell Bank, University of Manchester
  • Book:
    An Introduction to Radio Astronomy
    Published online:
    28 May 2018
    Print publication:
    17 September 2009, pp 148-173

  • Summary

    The Universe that we observe had its beginning in the big bang, the cosmic fireball. After an initial phase of element formation, this settled into a primeval plasma of protons and electrons, helium nuclei and a trace of lithium nuclei. When the primeval plasma became optically thin at an age of about 370 000 years (the era of decoupling), electromagnetic radiation could reach the Earth, and appears as the cosmic microwave background (CMB), discovered by Penzias and Wilson (1965) and observable only in the radio and far-infrared parts of the spectrum. Observations of the CMB and their implications are described in Chapter 14; a discussion of anisotropies in the CMB follows in Chapter 15. Here, we discuss the local aftermath, our Milky Way Galaxy and its surroundings.

    Stars and galaxies

    Our home Galaxy, the Milky Way system, has stars as its most visible component; but radio astronomy is usually more concerned with the interstellar medium (ISM). The ISM is composed principally of hydrogen and helium, with a trace of heavier elements, having a mass fraction of about 1%. These occur in both atomic and molecular form, including larger aggregates referred to generically as dust. In addition there is a third, more tenuous component, the high-energy medium, composed mostly of energetic particles, principally protons and electrons, with energies extending well beyond 1018 electron-volts (cosmic rays in the energy range 1019-1020 electron-volts cannot be contained by the Galactic magnetic field, and may come from extragalactic sources).

Page 1632 of 1845