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2011 | Buch

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Physical Soil Mechanics

verfasst von: Gerd Gudehus

Verlag: Springer Berlin Heidelberg

Buchreihe : Advances in Geophysical and Environmental Mechanics and Mathematics

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

Soil is matter in its own right. Its nature can be captured by means of monotonous, cyclic and strange attractors. Thus material properties are defined by the asymptotic response of sand- and clay-like samples to imposed deformations and stresses. This serves to validate and calibrate elastoplastic and hypoplastic relations with comparative plots. Extensions capture thermal and seismic activations, limitations occur due to localizations and skeleton decay.Attractors in the large characterize boundary value problems from model tests via geotechnical operations up to tectonic evolutions. Validations of hypoplastic calculations are shown with many examples, possible further applications are indicated in detail. This approach is energetically justified and limited by critical points where the otherwise legitimate continuity gets lost by localization and decay. You will be fascinated by the fourth element although or just as it is so manifold.

Inhaltsverzeichnis

Frontmatter

1. Introduction

Abstract

Ever since continuum approaches for soils were questioned as far as these are visibly particulate matter. One may be tempted to simulate granular aggregates grain by grain with a computer in order to understand their mechanical properties. On the other hand, engineers are inclined to take over continuum models from solids to soils, so they work with notions like stiffness and strength.

Gerd Gudehus

2. Simple psammoids

Abstract

How to catch essentials of granular soils in a simple way? Allegedly Einstein said ‘theories should be as simple as possible, but not simpler’, so what is adequately simple? One can read in the Internet that Einstein’s philosophy of science was more subtle. He wrote ‘Our experience hitherto justifies us in trusting that nature is the realization of the simplest that is mathematically conceivable’, and ‘But what remains unsatisfactory in this is always the arbitrariness in the choice of those elements that one designates as a priori’ (translated by Howard 2004).

Gerd Gudehus

3. Simple peloids

Abstract

Mach (1912) stated ‘The economy of communication and perception belongs to the essence of science’. Which are the essentials of soils like clay, and how can they be captured in Mach’s sense? Which properties and concepts can be taken over from psammoids, what should be added in the first place, and what could be left aside?

Gerd Gudehus

4. Psammoids with reversals

Abstract

It was shown at length in Chap. 2 that the behaviour of psammoids with reversals cannot generally be captured without internal state variables. But how to introduce and justify hidden quantities? Babuska and Oden (2006) show that the uniaxial anelastic response of metals with some hundred cycles is not satisfactorily captured by widely used elastoplastic relations with internal variables. It is not my intention to overcome this misery for solids in Sect. 4.1, but to prepare more geometrico a way out for soils. The hidden state can be related with the spatial fluctuation of internal forces, this is called force-roughness. This oriented quantity is particularly indicated by the asymptotic response to strain cycles and ratcheting (cf. Sect. 2.1). The proposed additional attractors of force-roughness are inevitably heuristic, but may help to secure objectivity.

Gerd Gudehus

5. Peloids with reversals

Abstract

This fourth chapter on constitutive relations is more comprehensive and should therefore be longer than the preceding ones, but it is not and is still possibly too long. Peloids with reversals exhibit viscosity and require hidden variables as skeleton stress and void ratio do not suffice in general to characterize their state.

Gerd Gudehus

6. Pore fluid

Abstract

For saturated soils the interaction of skeleton and pore water can be captured by the effective stress principle and by means of Darcy’s law. In case of partial saturation it is convenient to work again with a kind of pore fluid, and with partial stresses and a permeability relation. A moist soil is glued by capillary water which can scarcely flow. Terzaghi (1920) observed that water in narrow slits between glass plates is less mobile. He called it bound pore water and proposed later that this glues particles in saturated clay (Terzaghi 1931). Derjaguin and Churaev (1973) postulated a denser and more viscous ‘polywater’ in narrow gaps. The DLVO-theory by Derjaguin, Landau, Verwey and Overbeck explains equilibria with interparticle attraction and repulsion in colloids. The interactions of soil particles are more complicated and beyond the present reach of thermodynamics, molecular dynamics and microscopy. So there is no way around heuristic approaches with pore fluid, partial stresses and transport relations, but caution is required.

Gerd Gudehus

7. Bridging gaps

Abstract

The title of this chapter was chosen for two reasons. Solid particles can stick together by net attraction (Sect.7.1), and similarly by capillary (Sect. 7.2) or solid bridges (Sect. 7.3), this attraction enables macropores. In spite of higher skeleton pressures the limit void ratios can be higher by net attraction. The influence and evolution of particle bridges can be captured by extended constitutive models, these will but briefly be indicated as there are only few validations.

Gerd Gudehus

8. Localization

Abstract

Localized shearing, cracking and decay were mentioned in previous chapters as limitations of constitutive models. How far could they be captured by extended continuum models, and on which physical base? As throughout this book attractors will be presented more geometrico for this purpose, we will see that some critical phenomena can thus be indicated or even predicted.

Gerd Gudehus

9. Fabric

Abstract

The notion ‘fabric’, which is often used instead of ‘structure’ for geo-materials, has two different meanings. If a skeleton is homogeneous with respect to the kind of solid particles these can be differently arranged according to the state of an RSE. The outline in Sect. 9.1 deals with the issue of remoulded, reconstituted and undisturbed samples. It may help to understand limitations of constitutive relations and of microscopic approaches.

Gerd Gudehus

10. Boundary conditions

Abstract

Given a system composed of psammoids and/or peloids with pore fluid and of solids, the evolution of its shape and state can be considered as a boundary value problem. For setting the scene imagine marked skeleton and solid particles (Sect. 1.2) at nods of a finite element mesh which indicate displacements and deformations, and transducers between neighboured markers which indicate skeleton or solid stresses and pore pressures. An evolution can be represented as a succession of snapshots of positions and state fields which are ordered by time t. t = 0 may be taken for an onset with an initial state field including the void ratio e _o. This onset is chosen at will and not physically distinguished, i.e. the skeleton does not start at a state limit or at the verge of a suspension in general. Changes of position and shape are thus referred to arbitrary initial configurations.

Gerd Gudehus

11. One-dimensional evolutions

Abstract

Except for the desired uniformity of RSEs the highest symmetry is given if all quantities depend only on one co-ordinate. This is the case with so-called soil columns and with radially symmetric evolutions. For preparation the coupling of skeleton and pore water is first considered with foam rubber (Sect. 11.1), Terzaghi’s (1925) theory of consolidation is thus introduced. The subsequent sections are focussed on attractors in the large. Fields of state limits and state cycles serve to justify simplified calculations, whereas critical phenomena delimit the range of applicability.

Gerd Gudehus

12. Plane-parallel evolutions without SSI

Abstract

Evolutions which are equal in parallel planes are called plane-parallel, this is not always the same as plane strain. Soil-structure interactions (SSIs) are left aside in this chapter, solids occur only as rigid base. Initial and boundary conditions are more complex than in Chap. 11 and more specific than in Chap. 10. Attractors in the large help to justify approaches by calculations and model tests, or at least to delimit their range of validity. Other than with RSEs such asymptotes are non-uniform fields of state variables, but they are again driven (exogeneneous) and/or thermally activated (endogeneous). According to the involved RSEs they belong to monotonous deformations (SOM-states and state limits) or cyclic ones and ratcheting (asymptotic state cycles). As state fields are at best compounds of such states our attractors in the large cannot be treated with mathematical rigour. The generic term ‘strange attractor’ will sometimes be used for the spontaneous loss of symmetry by localization or diffuse bifurcation.

Gerd Gudehus

13. Plane-parallel evolutions with SSI

Abstract

Soil structure interactions (SSIs) are rarely plane-parallel, but often assumed so for calculations. This chapter leads beyond conventional models, and is more an outline of what could be done than a report on successful applications. Plane-strain model tests with structures are spoiled by parasitary wall forces, structures and ground in situ have rarely the same cross section over lengths which suffice for plane-parallelity. Attractors in the large are employed with the assumed symmetry, but how they can be attained or get lost cannot be judged within this frame (cf. the introduction of Chaps. 12 and 15).

Gerd Gudehus

14. Axi-symmetric evolutions

Abstract

Axi-symmetric evolutions can occur in the lab and in situ, they are important for validation, design and technologies. Using again attractors in the large, this chapter is less a report on successful applications than an outline of what could further be done. Axial symmetry can arise with suitable initial and boundary conditions and can get lost with bifurcations towards critical phenomena. Axi-symmetric solutions will also serve as a support of interpolations for evolutions with two symmetry planes (Sects. 15.1 and 15.2).

Gerd Gudehus

15. Less symmetric evolutions

Abstract

Vertical symmetry planes may be assumed for a number of natural and technical evolutions. With two of them interpolations between plane-parallel and axial symmetry can be of use, this is shown without (Sect. 15.1) and with interactions of soil and structures (SSI, Sect. 15.2). More often a single symmetry plane may be justified, therein SSIs can be simple (Sect. 15.3) or complex (Sect. 15.4). Some validations can be presented for such cases, further simulations will be rewarding.

Gerd Gudehus

16. Critical phenomena

Abstract

As announced in the Prologue it was shown in several chapters how and when monotonous and cyclic attractors (which were called SOM states, state limits and state cycles) can serve to capture the nature of soils. A comparable outline of methods for critical phenomena, i.e. pattern formation and deterministic chaos, cannot be offered. This last chapter is to convey what is meant without a unified concept, so my book has an open end and not a finale like a symphony.

Gerd Gudehus

Backmatter

Titel: Physical Soil Mechanics
verfasst von: Gerd Gudehus
Verlag: Springer Berlin Heidelberg
Electronic ISBN: 978-3-540-36354-5
Print ISBN: 978-3-540-36353-8
DOI: https://doi.org/10.1007/978-3-540-36354-5