Styles Of Folding

Styles Of Folding

Mechanics And Mechanisms Of Folding Of Natural Elastic Materials

1st Edition - January 1, 1977

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  • Author: Arvind Johnson
  • eBook ISBN: 9780444601438

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Description

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

About the Author

Arvind Johnson

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