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The Deformation Cf Inhomogenous Materials and Consequent Geological Inflications

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The Deformation Cf Inhomogenous Materials and Consequent Geological Inflications THE DEFORMATION CF INHOMOGENOUS MATERIALS AND CONSEQUENT GEOLOGICAL INFLICATIONS by NICHOLAS CHARLES GAY A thesis submitted for the degree of Doctor of Philosophy at the University of London August, 1966. (±) ABSTRACT This thesis is a theoretical and experimental study of the deformation of inhomogenous materials by- simple and pure shear. The model adopted is that of a homogenous, Newtonian fluid matrix, in which are embedded rigid or deformable inclusions. The inclusions are ellipsoidal or elliptical in shape and the deformable ones are also assumed to be Newtonian bodies, but they may differ from the matrix in coefficient of viscosity. Published work on rock deformation is reviewed to show that rock does, in certain geological environments, approxi- mate closely to a Newtonian body. Equations are derived to describe the motion and changes in shape of the inclusions (or particles as they are called) during deformation of-the model. These equations are checked experimentally and, within the limits of the experimental error, the results agree satisfactorily with the theory. The behaviour of systems containing a large number of particles is discussed and the strains developed in the matrix around the inclusions are examined. The application of the theoretical concepts to certain problems in structural geology, such as the rotation of crys- tals, the development of preferred orientations and the deformation of conglomerates, is considered. Particular emphasis is laid on the use of the theoretical equations to determine the finite strain in rock. (ii) TABLE OF CONTENTS Page CHAPTER I INTRODUCTION A. GENERAL STATEMENT 1 B. ACKNOWLEDGEMENTS 5 C. LIST OF SYMBOLS 6 CHAPTER II VISCOSITY AND THE VISCOUS FLOW OF ROCKS' A. INTRODUCTION 9 B. RHEOLOGICAL MODELS -ND THE TIME-STRAIN OF ROCKS 10 C. TERMS USED TO DESCRIBE FLOW IN ROCKS 15 D. CALCULATIONS OF COEFFICIENTS OF VISCOSITY FOR GEOLOGICAL MATERIALS 16 E, THE REYNOLDS NUMBER AND THE TYKE OF VISCOUS FLOW IN ROCKS 25 F. SUMMARY AND CONCLUSIONS 27 CHAPTER III THE EXPERIMENTAL PROGRAMME A. INTRODUCTION 29 B. APPARATUS AND MATERIALS 30 C. THE EXPERIMENTAL PROGRAMME 48 D. ACCURACY AND PRECISION OF THE RESULTS 56 CHAPTER IV THEORETICAL AND EXPERIMENTAL ANALYSIS OF THE MOTION OF PARTICLES DURING DEFORMATION OF THE PARTICTR-MATRIX SYSTEM A. INTRO- 7CTI6N 58 B. THE BEHAVIOUR OF RIGID PARTICLES DURING DEFORMATION BY SIMPT,F, SHEAR 63 C. THE BEHAVIOUR OF RIGID PARTICLES DURING DEFORMATION BY PURE SHEAR 78 D. THE DEFORMATION OF NON-RIGID PARTICLES DURING PURE SHEAR 93 E. PURE SHEAR DEFORMATION OF AN ELLIPTICAL PARTICLE WITH ITS AXES NOT NECESSARILY PARALLEL TO THE STRAIN AXES 106 F. SIMI-LE SHEAR DEFORMATION OF NON-RIGID CIRCULAR PARTICLES 118 G. THE DEFORMATION OF SYSTEMS CONTAINING A LARGE NUMBER OF PARTICLES IN A VISCOUS MATRIX 127 H. STRAINS DEVELOPED IN THE MATRIX AROUND A SINGLE PARTICLE DURING DEFORMATION BY PURE OR SIMPLE SHEAR 140 CHAPTER V GEOLOGICAL APPLICATIONS A. ROTATED CRYSTALS AS QUANTITATIVE STRAIN INDICATORS 146 B. THE DEVELOMENT OF PREFERRED ORIENTATIONS IN ROCKS 159 C. THE USE OF DEFORMED PEBBLES AS QUANTITATIVE STRAIN INDICATORS 171 D. A PROCEDURE FOR ANALYZING DEFORMED CONGLOMERATES 180 E. COMMENTS ON SOME DEFORMED CONGLOMERATES 181 SUMMARY AND CONCLUSIONS 186 REFERENCES 192 APPENDIX I THE EXPERIMENTAL RESULTS 200 - 1 - CHAPTER I INTRODUCTION GEYERLI, ST.i...TEMENT Structural geologists working in both igneous and metamorphic rocks have for many years now recog- nized the importance of small, marker particles such as gas bubbles, phenocrysts, pebbles and fossils in elucidating the state of strain in rocks. This approach is a kinematic one and involves. relating the present geometrical position of particles to possibi:c_movement paths during the deformation of the whole rock mass. In other words, it should be possible to estimate the strain in a body of rock from the changes in shape and position of individual objects in the rock, pro- vided the initial shapes of these objects and the physical properties of the rock and its components during deformation are known. This is no new concept. One hundred and forty years ago Scrope (1825) described gas bubbles in lavas " drawn out, or elongated, in the direction of motion ....". In 1839 Naumann recognized the importance of lineation in lavas and gneisses and made a careful mathematical analysis of changes in the lineattm positions with tilting of the planes in which they are contained. Deformed fossils were described by Ehillips (1843); and Sharpe (1846), Haughton (1856) and Wettstein (1886) used the changes in shape to calculate the amount of strain. Slaty cleavage and its relation to deformed spots, oolites and crinoid stems was studied by Sorby (1653, 1855). The deformation of pebbles was clearly recognized and analyzed by Hitchcock, Hitchcock and Hager (1861). Heim (1878) explained external rotations and orientation of minerals and Reusch (1887) described elongation of pebbles by a rolling mechanism. Moreover, following on these early papers, there is now available a vast amount of literature on the subjects: men- tioned above. Oleos (1946, 1947) reviews r2ost of the work 2 up to 1945; in addition, Knopff and Ingerson (1938), Sander (1930, 1950) and Turner and Weiss (1963) also contain detailed bibliographies. In all this work, no one, so far as. the writer is aware, has suggested a general method using all the available evid- ence for determining the states of strain in rock. The total finite strain has been calculated from objects of known origi- nal shape which have deformed homogenously with the surround- ing material. However, no attempt has been made to relate the degree of preferred orientation of rigid or non-rigid, deformed particles to the finite strain. And, similarly, where there has been a competence difference between an object and its surroundings, the change in shape of the object has not been used. to estimate the finite strain in the rock. This thesis is particularly concerned with finding methods to solve problems such as these. To do so it is assumed that under certain conditions a rock may be consider- ed as an ihhomogenous mass of extremely viscous, fluid. By inhomogenous is meant that the mass of material differs from point to point in its physical properties; in particular the coefficient of viscosity may vary from zero to infinity. In detail, the model is a large body of homogenous viscous material in which are embedded much smaller spherical or ellipsoidal bodies with different physical properties. The bulk of the material will be referred to as the matrix and the inhomogeneities as the particles. The particles may be either rigid or non-rigid with coefficients of viscosity greater than, equal to or less than that of the matrix. The types of deformation assumed are pure shear and simple shear. These are both plane strains in which there is no volume change and both have a triaxial strain ellipsoid with an intermediate axis equal to unity. Simple shear also has a component of rigid body rotation. General strains can always be considered as three mutually perpendicular simple sheara of different magnitudes and so the analysis presented. here can be applied to more complex examples of strain, if necessary. After these opening paragraphs an explanatory list of the more important symbols. appearing in the text is given. In addition to those explained in the list, all symbols are defined when they are first introduced. As far as possible the writer has followed Nadai's. (1950, 1963) symbols for strain analysis. In the second part of this introductory section, some basic concepts of rheology are outlined and applied to the change with environment in the physical properties of rock. In particular, the assumption of rocks behaving as, viscous fluids is examined in the light of published data obtained from field, experimental and theoretical work and an attempt is made to define the physical conditions under which the assumption is valid. Coefficients of viscosity for different rock types are tabulated and expected changes in these values with temperature and pressure discussed. Finally, the kind of flow occurring in extremely viscous materials is discussed The Reynolds Number is used to show that rocks normally deform by laminar flow. Chapters. III and IV form the main part of the thesis. In them the mathematical theory relating the finite strain to the changes in shape and orientation of the particle during pure and simple shear deformations of the particle-matrix system is presented together with its experimental verifi- cation. The theory is based on the fundamental equations of vis- cous fluid dynamics. for slow-motion laminar flow and the mathematical techniques involved are similar to those used by other workers in the fields of suspensions and emulsions. The analysis is divided into sections; the first deals with the behaviour of single, rigid spheres and ellipsoids in the two types of deformation field. Single non-rigid particles are then considered and an analytical solution is obtained. 4 - for the pure shear deformation of an ellipse with its axes parallel to the strain axes. The more general problems of elliptical particles not aligned parallel to the strain axes. during pure shear are solved numerically with the aid of a computer. The behaviour of multiparticle systems is then discussed in the light of this theory. Finally, the strains. in the matrix surrounding the particles are examined. Wherever possible the theoretical equations are plotted as graphs to clarify their meaning and are compared directly with the experimental results. For the sake of convenience, therefore, the basic experimental apparatuses and methods. are described first and followed by the theoretical and experi- mental work. Applications of the theory to geological problems are described in Chapter V of the thesis. Rigid crystals which have rotated during the deformation are used to calculate the amount of finite strain; their use in analyzing styles of folding is.
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