Styles Of Folding
Mechanics And Mechanisms Of Folding Of Natural Elastic Materials
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Styles of Folding: Mechanics and Mechanisms of Folding of Natural Elastic Materials, Developments in Geotectonics 11, provides an introduction to theoretical underpinnings of folds in rocks. The book begins with a review of studies which have been most significant to the development of current understanding of folds. It then turns to the development of a theory of folding of multilayered elastic materials. It presents the derivation of linearized equations that describe the incremental deformation of materials with memory; these equations are then used to solve for wavelengths of sinusoidal folds in single layers and multilayers. A theory of kink folding in elastic multilayers is introduced based on the mechanism of plastic yielding between layers. The chapters also include analyses of folds in the Carmel Formation at Arches National Monument in Utah; asymmetric folds in interbedded cherts and shales of the Franciscan Complex; and some folds in Tertiary rocks in the Coast Ranges of California. Finally, the most important mechanisms of folding recognized thus far are summarized for multilayered materials with a wide range of properties.
Table of Contents
Preface
Acknowledgements
Chapter 1. Mechanisms and Mechanics of Folding
Introduction
Mechanisms of folding
Willis
Van Hise
De Sitter Carey
Ramberg
Paterson and Weiss
Ghosh
Biot
Chapple and Spang
Mechanics of folding
Single-layer folds — low amplitude
Single-layer folds — high amplitude
Multilayer folds
References for Chapters 1, 10 and 11 20
Chapter 2. Folding of Bedded Sandstones of the Carmel Formation, Arches National Monument, Utah
Summary
Introduction
Crenulations within Carmel at Arches National Monument
Origins of crenulations
Sources of shortening of Carmel
Areal extent of crenulations in Carmel
Conditions of Carmel at time of folding
Analysis of fold patterns within Carmel Formation
General conditions of rocks
Biot theory of buckling of multilayers
Differential equation of deflection of multilayer
Elastic constants of multilayer
Review of assumptions
Buckling of multilayer between rigid boundaries
Comparison of theoretical folds with folds in the Carmel Formation
Effects of irregularities of bedding on folding
Reason maximum amplitudes of folds are near base of Carmel
Extension of folding into lower part of Entrada
References
Appendix to Chapter 2
Chapter 3. Idealized Fold Forms and Lines of Discontinuity (“Part I”)
Summary
Introduction
Forms of some natural folds
Theoretical characteristic directions
First-order equations
Higher-order equations
Linear elasticity theory
Nonlinear elasticity theory
Lines of discontinuity in ideal folds
Lines of apparent discontinuity in natural and experimental folds
Some natural folds
Some experimental folds
Acknowledgment
References
Chapter 4. Initial Stress and Nonlinear Equations of Equilibrium (“Part II”)
Summary
Introduction
Nonlinear equations of equilibrium
Stress boundary conditions
Initial and incremental stresses
Linearized equilibrium equations and boundary conditions
Discussion
Acknowledgement
References
Chapter 5. Transition from Sinusoidal to Concentric-Line to Chevron Folds (“Part III”)
Summary
Introduction
Buckling of isolated, homogeneous layers
Solution
Experiments
Analysis of experiments
Generalized solutions for multilayered bodies
Folding of a homogeneous stiff layer in a soft medium
Folding of elastic multilayers
Experimental
Theoretical wavelengths of sinusoidal folds
Variations of wavelengths within multilayers
An explanation for the transition from sinusoidal to concentric-like to chevron folds
Discussion
Acknowledgement
References
Chapter 6. Sinusoidal and Reverse Conjugate Kink Folds (Part IV”)
Summary
Introduction
Experiments
Interbedded gelatin and rubber
Grease between rubber layers
Layers with frictional contacts
Theory
Sinusoidal folding of multilayer between rigid confining media
Kink form
Criteria for kink folding and sinusoidal folding
Widths of kink bands
An explanation for sinusoidal and kink folding of multilayers confined by rigid boundaries
Sinusoidal form
Kink form
Acknowledgement
References
Chapter 7. Asymmetric Folding in Interbedded Chert and Shale of the Franciscan Complex (“Part V”)
Summary
Introduction
Forms of folds in the Franciscan cherts and shales
Theory
Experiments with elastic multilayers
Relatively high interlayer contact strength
Low interlayer contact strength
Analysis of superimposed shear
Analysis of folds in interbedded chert and shale
Acknowledgement
References
Chapter 8. Asymmetric Folding and Monoclinal Kinking (“Part VI”)
Summary
Introduction
Experiments
Theory
Sinusoidal folding of interbedded stiff and soft layers subjected to layer-parallel shear
Elementary theory of monoclinal kink folding
Kinking as a process of yielding instability
Experiments by Gay and Weiss
Spacing of monoclinal kink bands
Effect of cohesive strength and pore pressure on kinking
Propagation of kink bands
Summary of kinking processes and conditions of asymmetric folding
Acknowledgement
References
Chapter 9. Development of Concentric-Line and Chevron Folds and Doubly Plunging Folds in Tertiary Rocks in Part of Coast Ranges, California (“Part VII”)
Summary
Introduction
The Huasna syncline
Regional geologic setting
Form of the Huasna syncline
Times of folding
Folds near south end of Huasna syncline
Rock units at south end of Huasna syncline
Forms of the folds
Field evidence for shear in folded rocks
Analysis of folds at south end of Huasna syncline
Ramberg wavelength for multilayer in confining media
Simultaneous folding at different scales
Folds in riverbank exposure
Significance of the ratio of stress to elastic modulus
Folds at The Eagle
Larger folds
Development of doubly plunging folds
Reaction of infinite medium
Folding of single layer within soft media
Folding of multilayer with zero contact strength
Acknowledgement
References
Chapter 10. Folding of Linear Elastic and Power-Law Materials and Revision of Linearized Theory
Introduction
Folding of linear elastic materials
Equilibrium and rheological equations
Boundary conditions
Sinusoidal solutions
Elimination of special assumptions in linearized theory
Sequence of plane-strain deformations
Initial stress state
Incremental stresses for incompressible materials
Equilibrium equations
Boundary conditions
Comparison of predictions of wavelengths in single layers
Comparison of Biot's theory with linearized theory of incompressible Mooney material
Comparison of wavelengths predicted by Biot, Ramberg, Fletcher and linearized theories
Folding of power-law material with memory
Stress—strain relations to first order
Equilibrium equations
General, sinusoidal solution
Approximate, thin-plate solution — single layer
Approximate, thin-plate solution — multilayer
Preliminary evaluation of single-layer and multilayer folding of rock with memory
Appendix
Invariants
Incremental stresses for compressible materials
Relations for initially perturbed boundaries
Chapter 11. Synthesis
Introduction
Mechanisms of folding
Anisotropy due to interlayering of stiff and soft materials or to slip at contacts between layers
Anisotropy due to initial stresses and strains
Yielding within layers
Yielding between layers
Superimposed strain
Instabilities
Mechanics of folding of materials with memory
Folding of incompressible elastic material
Elementary theory of sinusoidal folding of multilayers
Folding of power-law material
Transformation from sinusoidal to concentric-like to chevron folds
Theory of kink folding
Criteria of kink folding
Transformation from sinusoidal to conjugate kink to chevron folds
Asymmetric folding
Doubly plunging folds
Author Index
Subject Index
Product details
- No. of pages: 426
- Language: English
- Copyright: © Elsevier 1977
- Published: January 1, 1977
- Imprint: Elsevier
- eBook ISBN: 9780444601438