The University of Maine DigitalCommons@UMaine Electronic Theses and Dissertations Fogler Library 2003 Crevassing and Calving of Glacial Ice James Patrick Kenneally Follow this and additional works at: http://digitalcommons.library.umaine.edu/etd Part of the Glaciology Commons, and the Physics Commons Recommended Citation Kenneally, James Patrick, "Crevassing and Calving of Glacial Ice" (2003). Electronic Theses and Dissertations. 318. http://digitalcommons.library.umaine.edu/etd/318 This Open-Access Dissertation is brought to you for free and open access by DigitalCommons@UMaine. It has been accepted for inclusion in Electronic Theses and Dissertations by an authorized administrator of DigitalCommons@UMaine. CREVASSING AND CALVING OF GLACIAL ICE By James Patrick Kenneally B.S. Rensselaer Polytechnic Institute, 1995 M.S. University of California San Diego, 1998 A THESIS Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy (in Physics) The Graduate School The University of Maine August, 2003 Advisory Committee: Terence Hughes, Professor of Geological Sciences, Advisor James Fastook, Professor of Computer Science Roger Hooke, Research Professor of Geological Sciences Peter Kleban, Professor of Physics Donald Mountcastle, Associate Professor of Physics External Reader: Brian Hanson, Associate Professor of Geography, University of Delaware CREVASSING AND CALVING OF GLACIAL ICE By James Patrick Kenneally Thesis Advisor: Dr. Terence Hughes An Abstract of the Thesis Presented in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy (in Physics) August, 2003 Calving of ice is a relatively new area of research in the still young field of glaciol- ogy. In the short time that calving has been studied, it has been mainly treated as an afterthought, with the predominant mode of thinking being that it will happen so to concern oneself with why is not important. Many studies dealt with observations of calving front positions over time vs. ice velocity in an attempt to quantify the calving rate as the difference between the two, while others have attempted to deduce some empirical relationship between calving rate and variables such as water depth or tem- perature. This study instead addresses the question of why, where, and when ice will first become crevassed, which is an obviously necessary condition for a later calving event to occur. Previous work examining the causes of calving used ideas put forth from a variety of fields, including civil engineering, materials science, and results from basic physics and mechanics. These theories are re-examined here and presented as part of a larger whole. Important results from the field of fracture mechanics are utilized frequently, and these results can be used as a predictor of ice behavior and intrinsic properties of ice, as well as properties like back stresses induced by local pinning points and resistive shears along glacial ice boundaries. A theory of fracture for a material experiencing creep is also presented with applications to ice shelves and crevasse penetration. Finally, a speculative theory regarding large scale iceberg formation is presented. It is meant mainly as an impetus to further discussion on the topic, with the hope that a model relating crevasse geometries to flow parameters can result in crevasse spacings that could produce the tabular icebergs which are so newsworthy. The primary focus of this thesis is to move away from the "after the fact" studies that are so common in calving research, and instead devote energy to determining what creates the conditions that drive the calving of ice in the first place. PREFACE The ice age is coming. but I have no fear. -The Clash The most real things in the world are those that neither children nor men can see. -Francis P. Church Even the fool sometimes has sage insights. -Chinese fortune cookie ACKNOWLEDGEMENTS A project of this type always requires the support of a great many people. It would be difficult to name everyone that has aided me during my time at the University of Maine, but there are several people that I would like to mention. I would like to thank my parents, sister, and brother for always supporting the decisions I make. I would like to thank Jesse Johnson for introducing me to glaciology during my first visit to this campus. Jesse and I shared an office for three years, and his friendship and assistance have been greatly appreciated. I would also like to thank Simon Krughoff, who has rescued me from the many computer disasters in which I found myself, usually of my own creation. Simon was also never averse to a trip to the Dome or playing a round of golf in the driving rain. I would like to acknowledge the members of my committee for their valuable insights and suggestions, and their understanding when progress was slow. Peter Kleban and Don Mountcastle were brave enough to assist in a project with which they had little familiarity and approached it with much enthusiasm. Jim Fastook was always encouraging, and seemed to know something about everything. Roger Hooke provided solid advice at all times and was extraordinarily considerate and thorough in reviewing this thesis. Finally, I would like to thank Terry Hughes, who has patiently guided me through my time at Maine. The education I received from Terry was not relegated to only glaciology. Terry was more than willing to pass on to me knowledge he has gained from a lifetime of first-hand experience. His willingness to entertain new ideas is invaluable in an advisor, and his gentle prodding allowed me to discover things on my own, without ever straying too far from the herd. TABLE OF CONTENTS .. PREFACE ................................... 11 ACKNOWLEDGEMENTS ......................... iii LIST OF TABLES .............................. viii LIST OF FIGURES ............................. ix Chapter 1 INTRODUCTION ............................ 1 1.1 Why Study Calving? ........................... 1 1.2 Previous Work .............................. 4 1.3 Why This Study? ............................. 5 1.4 Organization ............................... 6 1.5 What to Take Away ........................... 8 2 FRACTURE OF ELASTIC MATERIALS .............. 9 2.1 Linear Elastic Fracture Mechanics: Background ............ 9 2.2 The Stress Intensity Approach ..................... 12 2.3 Stress Intensity Factors For Various Geometries ............ 15 2.3.1 Center Crack ........................... 15 2.3.2 Single Edge Crack ........................ 16 2.3.3 Parallel Edge Cracks in a Half-Plane .............. 16 2.3.4 Single Edge Crack Subject to a Varying Load ......... 17 2.4 Practical Applications of Fracture Mechanics ............. 19 2.4.1 Single Crack in an Ice Field ................... 20 2.4.2 Water Filled Crevasses ..................... 2.4.3 A Field of Evenly Spaced Crevasses .............. 2.5 The Rate of Crack Growth ....................... 2.5.1 The Mott Formulation ..................... 2.5.2 The Dulaney and Brace Formulation .............. 2.5.3 Discussion ............................ 2.6 Limitations ................................ 2.6.1 The Plastic Zone ......................... 2.6.2 Numerical Limitations ...................... 2.7 An Alternate Approach: Dislocation Theory .............. 2.8 Dislocation Density ............................ 2.9 Stress and Dislocation Density Solutions ................ 2.10 Applications ............................... 2.10.1 The Weertman Constant Density Model ............ 2.10.2 Opening Displacements ..................... 2.10.3 Improvements to the Weertman Model ............ 2.11 Discussion ................................. 3 DUCTILE CRACK GROWTH .................... 3.1 Overview ................................. 3.2 Stresses in a Material .......................... 3.3 Crack Growth Law ............................ 3.4 Applications to Ice Shelves ....................... 3.4.1 Modeling a Typical Glacier ................... 3.4.2 Results .............................. 3.5 Discussion ................................. 4 FRACTUREANDBACKSTRESS .................. 4.1 Overview ................................. 4.2 Stresses in Floating Ice .......................... 4.3 Back Stresses in Floating Ice ...................... 4.4 Fracture Mechanics ............................ 4.5 Back Stress: Byrd Glacier ........................ 4.6 Calculation ................................ 4.6.1 Basal Crevasses ......................... 4.6.2 Instability of Water Filled Crevasses .............. 4.7 Constant Parameters With Depth .................... 4.8 Crevasse Initiation ............................ 4.9 Discussion ................................. 5 LARGE SCALE ICEBERG FORMATION ............. 5.1 Background ................................ 5.2 Strains in Floating Ice .......................... 5.3 A New Assumption ............................ 5.3.1 Enhancement Factors and Observation ............ 5.3.2 Stochastic Modeling ....................... 5.4 Discussion ................................. 6 CONCLUSION .............................. 6.1 Overview ................................. 6.2 Validity of Work ............................. 6.3 Shortcomings ............................... 6.4 The Future ................................ 6.4.1 Mixed-Mode Cracking ...................... 6.4.2 Sub-critical Crack Growth ................... vii 6.4.3 Fracture and Calving in Ice Sheet Models ........... 108 6.5 What to Make of it All? ......................... 109 REFERENCES ...............................