Scholars' Mine Masters Theses Student Theses and Dissertations Spring 2018 The role of flexural slip in the development of chevron folds Yuxing Wu Follow this and additional works at: https://scholarsmine.mst.edu/masters_theses Part of the Petroleum Engineering Commons Department: Recommended Citation Wu, Yuxing, "The role of flexural slip in the development of chevron folds" (2018). Masters Theses. 7788. https://scholarsmine.mst.edu/masters_theses/7788 This thesis is brought to you by Scholars' Mine, a service of the Missouri S&T Library and Learning Resources. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact [email protected]. i THE ROLE OF FLEXURAL SLIP IN THE DEVELOPMENT OF CHEVRON FOLDS by YUXING WU A THESIS Presented to the Faculty of the Graduate School of the MISSOURI UNIVERSITY OF SCIENCE AND TECHNOLOGY In Partial Fulfillment of the Requirements for the Degree MASTER OF SCIENCE IN PETROLEUM ENGINEERING 2018 Approved by Andreas Eckert, Advisor John Patrick Hogan Jonathan Obrist Farner ii 2018 Yuxing Wu All Rights Reserved iii ABSTRACT Chevron folds are characterized by straight limbs and narrow hinge zones. One of the conceptual models to initiate and develop chevron folds involves flexural slip during folding. While some kinematical models show the necessity for slip to initiate during chevron folding, recent numerical modeling studies of visco-elastic effective single layer buckle folding have shown that flexural slip does not result in chevron folds. In this study, several 2D finite element analysis models are run, distinguished by 1) geometry of the initial perturbation (sinusoidal and white noise), 2) varying thewavelength of the initial perturbation (10%, 50%, and 100% of the dominant wavelength) and 3) variation of the friction coefficient (high and low friction coefficient between interlayers). All numerical simulations apply 60% of shortening, in order to achieve inter-limb angles of 60 to 70 degrees. The results show that for sinusoidal initial perturbations, systematic and symmetric chevron folds are reproduced when 10% of the dominant wavelength is used for the initial perturbation. Using 50% or 100% of the dominant wavelength results in circular and sinusoidal folds, respectively. Low friction coefficient models result in larger amplitudes and sharper inter-limb angles compared to high friction coefficient models. For white noise initial perturbations, isolated and asymmetric chevron folds are developed when the friction coefficient is low. High friction coefficient models reproduce the dominant wavelength without chevron folds and low friction coefficient models result in a different dominant wavelength. In all chevron folds models, slip initiates at the early stages of folding (i.e. 1% to 5% of shortening). iv ACKNOWLEDGMENTS I would like to thank my advisor, Dr. Andreas Eckert, for giving me the chance to work in the Numerical Geomechanics Research Group. He was an excellent professor and mentor, contributing with my intellectual and personal development. His technical writing guidance was primordial on the development of this work. My gratitude to my committee members, Dr. Hogan and Dr. Obrist Farner that helped me to improve my presentation skills and guide my researches. I would like to also thank to Zhipeng Zhu, Wangchuchu Han, and Yashu Chen going through my hardest days in the USA. We all came from the same university in China and helped each other so far as possible. Because of them, I met lots of friends in Rolla that was my brothers and sisters on the past years, always helping me with whatever I needed. Thanks Weicheng Zhang and Jianbo Liu for the sincere friendship. We had many talks about how to change the world and he also gave me a lot of guide when I start my research. Thanks to my roommates, Kailun Ba, and my good friend, Dongyu Zheng, for being such good friends and companies. My partners in the Numerical Geomechanics Research Group, William Chandonia, Avery Welker, Chao Liu and Nso Petter, they helped me a lot in the research and for the good times. Thanks to my good friend, Wenyu Zhao, he taught me a lot of maintaining a strong body and the correct ways to workout. I am also grateful to all the friends that at some point participated on this journey, even though not listed here. v TABLE OF CONTENTS Page ABSTRACT ....................................................................................................................... iii ACKNOWLEDGMENTS ................................................................................................. iv LIST OF ILLUSTRATIONS ............................................................................................ vii LIST OF TABLES………………………………………………………………………. ix SECTION 1. INTRODUCTION .......................................................................................................... 1 1.1. LITERATURE REVIEW ........................................................................................ 1 1.2. RESEARCH OBJECTIVES AND QUESTIONS ................................................... 4 2. METHODOLOGY ......................................................................................................... 9 2.1. GOVERNING EQUATIONS ................................................................................. 9 2.2. DOMINANT WAVELENGTH .............................................................................. 9 2.3. MODEL SETUPS ................................................................................................. 11 3. RESULTS ..................................................................................................................... 16 3.1. FLEXURAL SLIP FOR EFFECTIVE SINGLE LAYER .................................... 16 3.1.1. Viscosity Contrast. ......................................................................................... 17 3.1.2. Initial Perturbation. ........................................................................................ 18 3.1.3. Friction Coefficient.. ...................................................................................... 20 3.2. FLEXURAL SLIP FOR TRUE MULTILAYER .................................................. 22 3.2.1. Varying s/h for Sinusoidal. ............................................................................ 23 3.2.2. Competence Contrast. .................................................................................... 31 vi 3.2.3. Friction Coefficient. ....................................................................................... 33 3.2.4. Overburden Load. .......................................................................................... 34 4. DISCUSSION ............................................................................................................... 36 4.1. EFFECTIVE SINGLE LAYER SETUPS ............................................................. 36 4.2. TRUE MULTILAYER SETUPS .......................................................................... 38 4.3. POSSIBLE ALTERNATING INFLUENCES ...................................................... 40 4.3.1. Turbidite Setups. ............................................................................................ 41 4.3.2. Initial Wavelength. ......................................................................................... 43 5. CONCLUSIONS........................................................................................................... 45 6. FUTURE WORK .......................................................................................................... 47 APPENDICES A. SLIP TENDENCY DEFINITION…………………………………………….48 B. DERIVATION OF FOLD PROFILES………………………………………. 50 C. RESULTS FOR THE BASED MODEL………………………………………52 BIBLIOGRAPHY ............................................................................................................. 55 VITA …………………………………………………………………………………….60 vii LIST OF ILLUSTRATIONS Figure Page 1.1. Kinematic model of effective single layer. ..................................................................6 2.1. Model sketch. …………………………………………….........................................12 3.1. Slip tendency evolution based on sinusoidal initial perturbations. .............................16 3.2. The relationship between aspect ratio and dip angle at the inflection point featuring varying viscosity contrasts.. ........................................................................17 3.3. Slip tendency evolution featuring sinusoidal, chevron and white noise initial perturbations. ..............................................................................................................19 3.4. The relationship between aspect ratio and dip angle at the inflection point featuring sinusoidal and chevron initial perturbation. ................................................20 3.5. Slip tendency evolution featuring varying friction coefficients based on white noise initial perturbations. ................................................................................21 3.6. The relationship between aspect ratio and dip angle at the inflection point featuring varying friction coefficient based on white noise initial perturbations. ..............................................................................................................22 3.7. Slip evolution based on sinusoidal initial perturbations. ............................................25 3.8. Fold shape