Styles Of Folding

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.

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