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.

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.

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.

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).

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.

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.

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).

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).

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: