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## Über dieses Buch

This textbook offers a superb introduction to theoretical and practical soil mechanics. Special attention is given to the risks of failure in civil engineering, and themes covered include stresses in soils, groundwater flow, consolidation, testing of soils, and stability of slopes.

Readers will learn the major principles and methods of soil mechanics, and the most important methods of determining soil parameters both in the laboratory and in situ. The basic principles of applied mechanics, that are frequently used, are offered in the appendices. The author’s considerable experience of teaching soil mechanics is evident in the many features of the book: it is packed with supportive color illustrations, helpful examples and references. Exercises with answers enable students to self-test their understanding and encourage them to explore further through additional online material. Numerous simple computer programs are provided online as Electronic Supplementary Material.

As a soil mechanics textbook, this volume is ideally suited to supporting undergraduate civil engineering students.

## Inhaltsverzeichnis

### Chapter 1. Introduction

In this introductory chapter some of the characteristic properties of soils are described, and the reasons for soil mechanics as a separate subject of engineering are given.

Arnold Verruijt

### Chapter 2. Classification

In this chapterClassification the basic physical properties of the main types of soils are defined, with the methods to measure them. Some elementary classification systems are considered.

Arnold Verruijt

### Chapter 3. Particles, Water, Air

Soils usually consist of particles, water and air. 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.

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### Chapter 4. Stresses in Soils

In this chapter the separation of the stresses in soils into pressures in the fluid and stresses in the granular mass is presented. Special attention is paid to the definition of the effective stress, and its relation to the deformations.

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### Chapter 5. Stresses in a Layer

This chapter presents some examples for the determination of the vertical stresses (effective stresses and pore pressures) in a layer with a horizontal surface.

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### Chapter 6. Darcy’s Law

InDarcy this chapter Darcy’s law for the flow of groundwater through a porous medium (a soil) is presented. Special attention is paid to the permeability and its unit.

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### Chapter 7. Permeability

In this chapter the determinationPermeability of the permeability of a soil sample by laboratory tests is presented. The two tests considered are Darcy’s original test and the falling head test, which is better suited for soils of small permeability.

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### Chapter 8. Groundwater Flow

In the previous chapters the relation of the flow of groundwater and the fluid pressure, or the groundwater head, has been discussed, in the form of Darcy’s law. In order to solve problems of groundwater flow another equation is needed. This is provided by the principle of conservation of mass. ThisConservation of mass principle will be discussed in this chapter, and some elementary problems will be solved.

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### Chapter 9. Flotation

In the previous chapter it has been seen that under certain conditions the effective stresses in the soil may be reduced to zero, so that the soil looses its coherence, and a structure may fail. Even a small additional load, if it has to be supported by shear stresses, can lead to a calamity.

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### Chapter 10. Flow Net

Two dimensional groundwaterFlow net flow through a homogeneous soil can often be described approximately in a relatively simple way by a flow net, that is a net of potential lines and stream lines.

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### Chapter 11. Flow Towards Wells

In this chapter some examples are presented in which the groundwater flows to a well or a system of wells. Direct applications include the drainage of a building pit, or the production of drinking water by a system of wells.

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### Chapter 12. Stress Strain Relations

As stated in previous chapters, the deformations of soils are determined by the effective stresses, which are a measure for the contact forces transmitted between the particles.

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### Chapter 13. Tangent Modulus

The difference in soil behavior in compression and in shear suggests to separate the stresses and deformations into two parts, one describing compression, and another describing shear. This will be presented in this chapter. Dilatancy will be disregarded, at least initially.

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### Chapter 14. One-Dimensional Compression

In the previous chapters the deformation of soils has been separated into pure compression and pure shear. Pure compression is a change of volume in the absence of any change of shape, whereas pure shear is a change of shape, at constant volume. Ideally laboratory tests should be of constant shape or constant volume type, but that is not so simple. An ideal compression test would require isotropic loading of a sample, that should be free to deform in all directions. Although tests on spherical samples are indeed possible, it is more common to perform a compression test in which no horizontal deformation is allowed, by enclosing the sample in a rigid steel ring, and then deform the sample in vertical direction. In such a test the deformation consists mainly of a change of volume, but some change of shape also occurs. The main mode of deformation is compression, however.

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### Chapter 15. Consolidation

In the previous chapters it has been assumed that the deformation of a soil is uniquely determined by the stress. This means that a time dependent response has been excluded. In reality the behavior is strongly dependent on time, however, especially for clay soils. In compression of a soil the porosity decreases, and as a result there is less space available for the pore water. This pore water can be expelled from the soil, but in clays this may take a certain time, due to the small permeability. This process is called consolidationConsolidation. Its basic equations are considered in this chapter.

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### Chapter 16. Analytical Solution

In this chapter an analytical solution of the one dimensional consolidation problem is given. In soil mechanics this solution was first given by Terzaghi (1923). Terzaghi, K. In mathematics the solution had been known since the beginning of the $$\mathrm{19{th}}$$ century. Fourier developed the solution to determine the heating and cooling of a metal strip, which is governed by the same differential equation. Terzaghi knew that solution, and adapted the parameters to the case of consolidation.

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### Chapter 17. Numerical Solution

The dissipation of the pore water pressures during the consolidation process can be calculated very simply by a numerical solution procedure, using the finite difference method. This is presented in this chapter, keeping the method as simple as possible. Many more advanced, and more powerful numerical methods have been developed. They can be found on the internet.

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### Chapter 18. Consolidation Coefficient

In this chapter two methods to determine the coefficient of consolidation $$c_{v}$$ are described. They are based on measurements in a one-dimensional test. However, inaccuracies in the description of the deformations in such tests require modifications in the measured displacements.

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### Chapter 19. Creep

As mentioned in the previous chapter, in a one dimensional compression test on clay, under a constant load, the deformation usually appears to continue practically forever, even if the pore pressures have long been reduced to zero. Similar types of behavior are found in other materials, such as plastics and concrete. The phenomenon is usually denoted as creepCreep.

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### Chapter 20. Shear Strength

One ofShear strength the main characteristics of soils is that the shear deformations increase progressively when the shear stresses increase, and that for sufficiently large shear stresses the soil may eventually fail. In nature, or in engineering practice, dams, dikes, or embankments for railroads or highways may fail by part of the soil mass sliding over the soil below it. In this chapter the states of stresses causing such failures of the soil are described. In later chapters the laboratory tests to determine the shear strength of soils will be presented.

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### Chapter 21. Triaxial Test

The failure of aTriaxial test soil sample under shear could perhaps best be investigated in a laboratory test in which the sample is subjected to pure distortion, at constant volume. The volume could be kept constant by taking care that the isotropic stress $$\sigma _{0}=\frac{1}{3}(\sigma _{1}+\sigma _{2}+\sigma _{3})$$ remains constant during the test, or, better still, by using a test setup in which the volume change can be measured and controlled very accurately, so that the volume change can be zero. In principle such a test is possible, but it is much simpler to perform a test in which the lateral stress is kept constant, the triaxial test. In order to avoid the complications caused by pore pressure generation, it will first be assumed that the soil is dry sand. The influence of pore water pressures will be considered later.

Arnold Verruijt

### Chapter 22. Shear Test

The notion thatShear test failure of a soil occurs by sliding along a plane on which the shear stress reaches a certain maximum value has lead to the development of shear tests. In such tests a sample is loaded such that it is expected that one part of the sample slides over another part, along a given sliding plane. It is often assumed that the sliding plane is fixed and given by the geometry of the equipment used, but it will appear that the deformation mode may be more complicated.

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### Chapter 23. Pore Pressures

InPore pressure a previous chapter the main principles of triaxial tests have been presented. For simplicity it was assumed that the material was dry soil, so that there were no pore pressures, and the effective stresses were equal to the applied stresses. In reality, especially for clay soils, the sample usually contains water in its pores, and loading the soil may give rise to the development of additional pore pressures. The influence of these pore pressures will be described in this chapter.

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### Chapter 24. Undrained Behaviour of Soils

If no drainage is possible from a soil, because the soil has been sealed off, or because the load is applied so quickly and the permeability is so small that there is no time for outflow of water, there will be no consolidation of the soil. This is the undrained behaviorofUndrained behavior a soil. This chapter contains an introduction to the description of this undrained behavior.

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### Chapter 25. Stress Paths

AStress path convenient way to represent test results, and their correspondence with the stresses in the field, is to use a graph of the stresses. In this technique the stresses in a point are represented by two (perhaps three) characteristic parameters, and they are plotted in aStress path diagram. This diagram is called a stress path.

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### Chapter 26. Elastic Stresses and Deformations

An important class of soil mechanics problems is the determination of the stresses and deformations in a soil body, by the application of a certain load. TheElasticity load may be the result of construction of a road, a dyke, or the foundation of a building. The actual load may be the weight of the structure, but it may also consist of the forces due to traffic, wave loads, or the weight of the goods stored in a building. The stresses in the soils must be calculated in order to verify whether these stresses can be withstood by the soil (i.e. whether the stresses remain below the failure criterion), or in order to determine the deformations of the soil, which must remain limited.

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### Chapter 27. Boussinesq

In this chapter some useful solutions for the stresses in an elastic half space are given. TheseBoussinesq solutions were first obtained by the French scientist Joseph Boussinesq in 1885, and can be found in many books on the theory of elasticity.

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### Chapter 28. Newmark

ThisNewmark chapter presents an ingenious method for the determination of the vertical normal stresses at a certain depth, caused by some arbitrary load distribution on the surface, developed by Nathan M. Newmark, Professor at the University of Illinois.

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### Chapter 29. Flamant

On theFlamant basis of Boussinesq’s solution the French scientist A. Flamant obtained in 1892 the solution for a vertical line loadLine load on a homogeneous isotropic linear elastic half space.

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### Chapter 30. Layered Soil

An important problemDeformationsLayered soil of soil mechanics practice is the prediction of the settlements of a structure built on the soil. For a homogeneous isotropic linear elastic material the deformations could be calculated using the theory of elasticity. That is a completely consistent theory, leading to expressions for the stresses and the displacements. However, solutions are available only for a half space and a half plane, not for a layered material (at least not in closed form). Therefore in this chapter an approximate solution is considered.

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### Chapter 31. Lateral Stresses

In the previous chapters some elastic solutions of soil mechanics problems have been given. It was argued that elastic solutions may provide a reasonable approximation of the vertical stresses in a soil body loaded at its surface by a vertical loadLateral stress. Also, an approximate procedure for the prediction of settlements has been presented. In the next chapters, the analysis of the horizontal stresses will be discussed. This is of particular interest for the forces on a retaining structure, such as a retaining wall or a sheet pile wall.

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### Chapter 32. Rankine

The possible stresses in aRankine soil are limited by the Mohr–Coulomb failure criterion. In 1857 the Scottish engineer W.J.M. RankineRankine, W.J.M. used this criterion to establish limiting values for the stresses in the interior of a soil mass. This will be shown to lead to limits for the lateral stress coefficient K in this chapter. For simplicity the considerations will be restricted to dry soils at first. The influence of pore water will be investigated later.

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### Chapter 33. Coulomb

Long before the analysis of Rankine the French scientist CoulombCoulomb presented a theory on limiting states of stress in soils (in 1776), which is still of great value. The theory enables to determine the stresses on a retaining wallRetaining wall for the cases of active and passive earth pressure. The method is based upon the assumption that the soil fails along straight slip planes.

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### Chapter 34. Tables for Lateral Earth Pressure

The computationLateral earth pressure of lateral earth pressure against retaining walls is such an important problem of soil mechanics that tables have been produced for its solution, all on the basis of Coulomb’s method. These tables can be found in many handbooks, such as the German “Grundbau Taschenbuch”, edited by Prof. Smoltczyk (1980).

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### Chapter 35. Sheet Pile Walls

An effective way to retainSheet pile wall a soil mass is by installing a vertical wall consisting of long thin elements (steel, concrete or wood), that are being driven into the ground. The elements are usually connected by joints, consisting of special forms of the element at the two ends. Compared to a massive wall (of concrete or stone), a sheet pile wall is a flexible structure, in which bending moments will be developed by the lateral load, and that should be designed so that they can withstand the largest bending moments. Several methods of analysis have been developed, of different levels of complexity. The simplest methods, that will be discussed in this chapter, are based on convenient assumptions regarding the stress distribution against the sheet pile wall. These methods have been found very useful in engineering practice, even though they contain some rather drastic approximations.

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### Chapter 36. Blum

In the previous chapter a procedure has been presented for the determination of the minimum length of a sheet pile wall, neededSheet pile wall to ensure equilibrium. This method is such that whenever the wall is shorter thanBlum that minimum length, no equilibrium is possible, and the wall will certainly fail. This suggests that it is advisable to choose the length of the wall somewhat larger than the minimum length, as a total failure of the wall would be disastrous. If the length is taken somewhat larger than required, the bending moments may perhaps be somewhat reduced. A method of analyzing the deformation and bending of the wall has been developed in the 1950s by the German engineerBlum H. Blum. This method is presented in this chapter, including a simple computer program.

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### Chapter 37. Sheet Pile Wall in Layered Soil

In this chapterLayered soil the analysis of a sheet pile wall, as presented in previous chapters, is generalized to a sheet pile wall in a layered soil.

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### Chapter 38. Limit Analysis

Coulomb’sLimit analysis method for the analysis of soil pressures considers extreme conditions, in which the soil is on the verge of failure. This type of analysis can be given a firm theoretical basis by the theory of plasticity. ThisPlasticity also enables to generalize the method, and to investigate the possible limitations and the validity of the method.

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### Chapter 39. Strip Footing

OneStrip footing of the simplest problems for which lower limits and upper limits can be determined is the case of an infinitely long strip load on a layer of homogeneous cohesive material.

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### Chapter 40. Prandtl

In this section a solution is given for the problem of a strip load on a half plane that is both statically admissible and kinematically admissible. ThisPrandtl solution must therefore give the true failure load. The solution was found by the German scientist Ludwig Prandtl (Mathematisch-physikalische Klasse, 1920:74–85) in 1920.

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### Chapter 41. Limit Theorems for Frictional Materials

In the previous chapters the limitFrictional materialsLimit theorems theorems have been applied to determine failure loads for a purely cohesive material ($$\phi =0$$). For materials with internal friction there is a fundamental difficulty, namely that the basic theorems of the theory of plasticity (the upper and lower bound theorems) are not valid, see Appendix C. This difficulty will be illustrated in this chapter.

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### Chapter 42. Bearing Capacity

InBearing capacity this chapter the case of a strip footing on cohesive material, considered in Chaps. 39 and 40, is extended to a general type of shallow foundation, on a soil characterized by its cohesion c, friction angle $$\phi$$ and volumetric weight $$\gamma$$. The soil is assumed to be completely homogeneous. Although the formulas were originally intended to be applied to foundation strips of buildings, at a shallow depth below the soil surface, they are also applied to large caisson foundations used in offshore engineering for the foundation of huge oil production platforms. Although many scientists have contributed to the analysis, the usual reference is to the DanishBrinch Hansen, J. geotechnical engineer Brinch Hansen, (A revised and extended formula for bearing capacity, Danish Geotechnical Institute, Copenhagen, 1970).

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### Chapter 43. Vertical Slope in Cohesive Soil

AExcavationSlopeVertical cutoff classical problem of soil mechanics is the case of a vertical cutoff in a purely cohesive material ($$\phi =0$$), as occurs when making a vertical excavation, or a vertical slope. The problem to be considered in this chapter is the determination of a lower bound or an upper bound for the maximum possible height $$h_{c}$$ of the slope, for a material having a constant cohesive strength c, and a constant volumetric weight $$\gamma$$.

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### Chapter 44. Stability of Infinite Slope

The evaluation of theStabilitySlope stability of a slope, of an embankment or a dyke, is an important problem of applied soil mechanics. In the previous chapter this problem has been considered for a vertical slope in a purely cohesive material ($$c>0$$, $$\phi =0$$). As a preparation for the general case, which will be considered in the next chapter, this chapter will present some solutions for slopes of infinite extent, in a homogeneous frictional material, without cohesion ($$c=0$$, $$\phi >0$$).

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### Chapter 45. Slope Stability

For theSlope stability analysis of the stability of slopes of arbitrary shape and composition various approximate methods have been developed. Many of these assume a circular slip surface. Using a number of simplifying assumptions a value for the safety factor F, the ratio of strength and load, is determined. The circle giving the smallest value of F is considered to be critical. The multitude of methods (developed by FelleniusFellenius, W., TaylorTaylor, D.W., BishopBishop, A.W., MorgensternMorgenstern, N.R. -PricePrice, V.E., SpencerSpencer, E., among others) in itself illustrates that none of them is exact. The results should always be handled with care. A value $$F=1.05$$ gives no absolute certainty that the slope will stand. In this chapter two of the simplest methods will be presented.

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### Chapter 46. Soil Exploration

In this chapterSoil exploration some of the most effective or popular methods for soil exploration, or soil investigations in the field will be described.

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### Chapter 47. Model Tests

A usefulModel tests tool in engineering is the analysis of the behavior of a structure by doing a model test, at a reduced scale. The purpose of the test may be just to investigate a phenomenon in a qualitative way, but more often its purpose is to obtain quantitative information. In that case the scale rules must be known. For a soil a special difficulty is that the mechanical properties often depend upon the state of stress, which is determined to a large extent by the weight of the soil itself. This means that in a scale model the soil properties are not well represented, because in the model the stresses are much smaller than in reality (the prototype).

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### Chapter 48. Pile Foundations

InPile foundation Deltaic areas in the world, for instance the western part of the Netherlands, the soil consists of layers of soft soil (clay and peat), on a rather stiff sand layer, of pleistocene origin. The bearing capacity of the sand layer below the soft soil is derived for a large part from its deep location, with the soft layers acting as a surcharge. And the properties of the sand itself, a relatively high density, and a high friction angle, also help to give this sand layer a good bearing capacity. The system of soft soils and a deeper stiff sand layer is very suitable for a pile foundation. In this chapter a number of important soil mechanics aspects of such pile foundations are briefly discussed.

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### Backmatter

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