- Email: [email protected]
The techniques of modern structural geology, volume 3: Applications of continuum mechanics in structural geology
Tectonophysics 344 (2002) 307 – 310 www.elsevier.com/locate/tecto
Book review The techniques of modern structural geology, volume 3: Applications of continuum mechanics in structural geology J.G. Ramsay and R.J. Lisle, Academic Press, London, Sept. 2000. ISBN 0-12-576923-7. US$65, softback Keeping up with the inimitable standard set by ‘‘The Techniques of Structural Geology’’ volumes 1 and 2 and making a subject like continuum mechanics relevant to a wider geological audience would not be easy tasks, yet that is what John Ramsay and Richard Lisle do in the third and final volume of this wellknown series. The key phrase that describes the work is ‘‘Applications in Structural Geology’’ since it is exclusively concerned with the problems of geological deformation at micro- to macro-scale. As such, it is one of the first texts to comprehensively explore the use of continuum mechanics in this field and has little overlap with standard classical works, which are mostly concerned with engineering and geomechanics applications. The book is essentially about understanding structures through models, chiefly ductile flow structures, though also brittle and semi-brittle ones. Models are constantly compared with and often inspired by a diverse range of well-illustrated natural structures. However, the writers frequently remind us of the limitations of a purely model-driven approach, which underscores their philosophy that there is at least as much to learn from careful examination of nature as there is from model theory. Volume 3 maintains the unpretentious, even anti-jargon, writing style of the earlier volumes. This will be a bonus for readers with little previous background in the theory, considering that continuum mechanics is a subject often shrouded by its own specialist nomenclature. Readers who are more familiar with the general subject matter will notice several new topics or ones not discussed to the same extent in a textbook before. Banded strucPII: S 0 0 4 0 - 1 9 5 1 ( 0 1 ) 0 0 2 7 0 - 0
tures, strain in superposed folds and the idea of flow sheets are just some examples. Recognition of separate strains for first- and second-generation superposed structures — a problem at the heart of many field studies — is a further welcome addition in this volume. As you would expect in a book of this subtitle, there is an analytical treatment of elastic deformation and viscous flow theory. It is developed in a straightforward manner from first principles and can be followed without reference to external sources. However, a significant new feature (for a geological text) is the presentation of numerical methods. The treatment is at an introductory level but covers both the finite difference (FD) and finite element (FE) methods and a broad range of applications to problems in statics and finite ductile flow, including materials with mechanical anisotropy. Although more advanced texts and procedures are available, the book provides a good starting point to gain experience with these techniques and, for geologists, has the attraction of being directed towards geological problems. Best of all, executable and source codes for both the FD and FE methods are available on an accompanying compact disk, as well as codes for most of the other procedures described in the book. (The programs can be run directly from Windows 3.1+ on a PC or with QuickBasic on a Macintosh. Graphical output requires a plotting program such as Surfer.) This ready availability removes a significant deterrent for first-time users: the need to compile and verify lengthy computer codes. In my estimation, the disk alone makes the book easily worth its price though the price is reasonable for the text as well. The book is primarily concerned with techniques and guidance on how to apply them. It is thus best suited to a foundation study in structural geology mechanical modelling or as a sourcebook for mathematical models. Because of this approach, it does not attempt to set out the results of previous studies in a systematic way. Indeed, it frequently branches into new and little-explored areas. Readers will neverthe-
308
Book review
less find an up-to-date bibliography that covers relevant earlier work together with explanatory notes about the main sources. As in earlier volumes of the series, most of the sessions or chapters are set out in a theory – question –answer/comment format or (in this volume) as worked examples, a format that teachers and independent users will find helpful. The book is divided into twelve sessions following on from volume 2. The first, Session 28, moves quickly into heterogeneous stress, with applications to fracture patterns. This is followed by Sessions 29 – 31 which deal with analytical, FD and FE methods and solutions to a variety of static and quasi-static problems (fault patterns, possible pressure-solution effects, pressure-shadows, inclusions, strain-refraction, crack propagation, en echelon cracks, indentation and crenulation). Session 32 provides an introduction to paleostress analysis of fault-slip data using some new approaches (clusters and trihedra). Sessions 33 – 36 describe the geometrical patterns of finite strain, with many insights into such structures as similar-type folds, banded structures, apparent rotations of porphyroblasts, transecting cleavage, superposed cleavages, coaxial and other types of refolds, three-dimensional flow sheets (lavas, slumps, glaciers, nappes and de´collement sheets) and even hackle marks. Problems of flow in viscous materials are introduced by means of stream functions in Session 37. Polynomial functions are used to describe homogeneous and simple heterogeneous flows (e.g., pure shear, extrusion and gravity flow), while transcendental functions are used for velocity patterns in incompetent material around buckle folds, boudins and load casts and for special flows with singularities. Stream functions also appear in a brief treatment of viscous single-layer buckling theory in Session 38 and are found by FD methods in the first part of Session 39. Finally, the latter part of Session 39 applies time-step FE modelling of viscous flow to finite amplitude folds, vein-bridges, boudins and inclusions: an appropriate culmination for the book and for the series as a whole. In a book with so many mathematical expressions, it is perhaps inevitable that some typographical irregularities would occur. The ones I found are mainly in Session 37 and a few in Sessions 29, 33 and 39.1 The 1 Visit http://www.es.mq.edu.au/geology/research/durney/ for typographical errors found so far (RLcorrections.htm).
unconventional use of bold type (normally reserved for symbolic representation of vectors and tensors) for scalar components was also noted in parts of Sessions 33 and 36 – 39, and the lack of punctuation after equations was a general feature of most sessions. However, the irregularities or errors are localized and do not affect results derived later on. They can be easily tracked by working through the derivations. Despite its possible appearance as a well-ordered discipline, continuum mechanics provides scope for terminological disputation. In some works, there can be abstraction to such a degree as to render the physical meaning of particular terms incomprehensible (as in ‘deformation gradients’, which are really just ‘deformations’). On the whole, Ramsay and Lisle present the terminology in a more cognitive style suitable for readers who are interested in applications. Nevertheless, some inconsistencies do occur. An example is the dual use of the term displacement in the introductory session on finite strain. In places, this means a transformation (as in a ‘displacement’ or ‘displacement gradient matrix’ M: the finite Lagrangian tensor [a,b,c,d] for the stretch with rotation where a = 1 + qu/qx, etc.; see also volume 1), and elsewhere, it has the more usual meaning of a change of position (u,v) and gradients (qu/qx, etc.) and gradient matrices (strain with rotation) thereof. Similarly, strain is used in the engineering sense (a change in relative position of particles measured by a change of length over old length as in ‘strain rate’), as a stretch (new length over old length as in ‘finite strain ellipse’ and ‘strain ratio’ derived from the semi-axes of this ellipse) and as a displacement gradient tensor (as in ‘rotational component of strain’). Although some of these expressions have been used for a long time, I feel there is justification for questioning their internal consistency. On the other hand, an old term whose transmutation I could not help lamenting is ‘pressure shadow.’ The writers use this term for diffuse augen-like regions of crystal growth in the microlithon matrix material near a rigid object, in line with the current fashion in metamorphic literature (which may have stemmed from an arbitrary redefinition by Spry, 1969). Its original use in English was for the related but distinct effect of sharply defined regions of entirely new crystal growth (Pabst, 1931). While on the subject of pressure-shadows (sensu Pabst) and pressure-shadows (sensu Spry), the work
Book review
on FD and FE elastic stress modelling of these structures and other cases of heterogeneous mass transfer (Sessions 29 – 31) should be noted. This is part of what the writers, as a way of acknowledging the pioneering work by H.C. Sorby, refer to as ‘pressure solution’ (which they use in the sense of dissolution plus diffusive mass transport and precipitation rather than just dissolution alone). Modelling of these effects is barely covered in other texts, apart from Price and Cosgrove (1990), and in a broad way, Ramberg (1952). In addition, Session 34 discusses P- (pressure-solution) band structure in terms of geometrical models and describes the general nature of mass transfer effects in rocks. Although the stress models provide an intuitive idea of the directions of mass transfer (see also Ghosh and Sengupta, 1973; Stro¨mga˚rd, 1973 for example), perhaps the writers’ sagacious advice elsewhere in the book, about not being overly satisfied with one’s models, could have some application here. Two difficulties in applying the classical mechanics of continua to mass transfer are: (1) the theories of elasticity and viscosity incorporate an assumption that mass does not change; (2) growth or dissolution of solid at specific interfaces, for example in pressure-shadows (sensu Pabst), represents a discontinuity in displacement, which is at odds with the assumption of a continuum. Turning now to practical matters, an important consideration is the functionality of the software on the accompanying disk. I report here on the FE programs, which I tested against known solutions for simple shear stress and accumulated simple shear strain on a Windows platform. There are three core programs: Fe2ddat, which prepares the input data, Fe2d, which runs a single-step elastic solution, and Fe2dfin, which works out finite displacements from multiple increments. They all worked fine. In fact, the procedures are very simple, and the programs do not even require setting up. You just double-click the relevant application icon in Explorer, then follow the prompts. Keeping track of the input and output is made simple by labels for all of the parameters and plain text file formats. Of course, there are some restrictions on the number of elements and nodes (200 and 102, respectively), and a little more effort is required to plot the results. However, this is acceptable for learning purposes anyway. The only idiosyncrasies encountered were: (a) a mixed boundary
309
condition required specifying an arbitrary force component first, then overwriting it with the displacement, (b) angles are in degrees for principal directions but in radians for rigid body rotation, (c) a minor rounding error appeared in the file output from program Fe2d but not from program Fe2dfin, and (d) the ‘strain ratio’ (stretch ratio) output parameter of Fe2d did not seem particularly useful since it is a quantity that should be theoretically close to unity. Much checking and scenario testing with very simple models is advisable when first using the finite element method, in order to familiarize oneself with the limitations. One of these is that the method is designed only for small or infinitesimal strains. Although the programs allow the user to produce large strains and displacements in one step, as done for clarity in some of the figures in Session 30, such results are best viewed as ‘magnified’ small strains. For example, the principal strains for pure shear and simple shear are always given as e3 = e1, whereas the finite values would be e3 = 1/(1 + e1) 1. (Session 39 describes how finite strains and displacements can be obtained using Fe2dfin.) This restriction applies to many of the analytical methods, too. In Session 37, for example, instantaneous displacement rate fields calculated from stream functions have been plotted using arbitrary scale factors so that the patterns can be clearly seen in the diagrams. (The vectors can be thought of as infinitesimal displacements developed over an infinitesimal period of time and magnified for plotting.) Finding exact finite displacements from stream flows over a finite time period is more difficult and, in fact, has not been attempted in the book. However, approximate solutions can be found by the successive application of small increments2 (ironically, the smaller the better). Overall, volume 3 provides many challenging examples and detailed insights into the structural deformation processes that will engage both the newcomer and the experienced practitioner in a fascinating journey of exploration. Above all, it is a book that promotes wider participation in quantitative modelling. This is in tune with today’s computing power and the inevitable consequence that computationally 2
Visit http://www.es.mq.edu.au/geology/research/durney/ for viewing progressive deformation for some Ramsay and Lisle polynomial stream functions (StreamF.htm).
310
Book review
intensive procedures, such as FE, are bound to be used more and more in the future. The no-nonsense approach of this book will not only guide the uninitiated through the basic principles and assumptions that underlie such methods but, with careful application, should help to accelerate the development of physically realistic reconstructions of geological deformation. Perhaps the only question is: ‘‘can we afford not to keep up with these developments?’’
References Ghosh, S.K., Sengupta, S., 1973. Tectonophysics 17, 133 – 175. Pabst, A., 1931. Am. Mineral. 16, 55 – 61.
Price, N.J., Cosgrove, J.W., 1990. Analysis of Geological Structures. Cambridge Univ. Press. Ramberg, H., 1952. The Origin of Metamorphic and Metasomatic Rocks. Univ. Chicago Press. Spry, A., 1969. Metamorphic Textures. Pergamon, Oxford. Stro¨mga˚rd, K.-E., 1973. Tectonophysics 16, 215 – 248.
David W. Durney Department of Earth and Planetary Sciences, Macquarie University, Sydney, Australia E-mail address: [email protected]
Book review The techniques of modern structural geology, volume 3: Applications of continuum mechanics in structural geology J.G. Ramsay and R.J. Lisle, Academic Press, London, Sept. 2000. ISBN 0-12-576923-7. US$65, softback Keeping up with the inimitable standard set by ‘‘The Techniques of Structural Geology’’ volumes 1 and 2 and making a subject like continuum mechanics relevant to a wider geological audience would not be easy tasks, yet that is what John Ramsay and Richard Lisle do in the third and final volume of this wellknown series. The key phrase that describes the work is ‘‘Applications in Structural Geology’’ since it is exclusively concerned with the problems of geological deformation at micro- to macro-scale. As such, it is one of the first texts to comprehensively explore the use of continuum mechanics in this field and has little overlap with standard classical works, which are mostly concerned with engineering and geomechanics applications. The book is essentially about understanding structures through models, chiefly ductile flow structures, though also brittle and semi-brittle ones. Models are constantly compared with and often inspired by a diverse range of well-illustrated natural structures. However, the writers frequently remind us of the limitations of a purely model-driven approach, which underscores their philosophy that there is at least as much to learn from careful examination of nature as there is from model theory. Volume 3 maintains the unpretentious, even anti-jargon, writing style of the earlier volumes. This will be a bonus for readers with little previous background in the theory, considering that continuum mechanics is a subject often shrouded by its own specialist nomenclature. Readers who are more familiar with the general subject matter will notice several new topics or ones not discussed to the same extent in a textbook before. Banded strucPII: S 0 0 4 0 - 1 9 5 1 ( 0 1 ) 0 0 2 7 0 - 0
tures, strain in superposed folds and the idea of flow sheets are just some examples. Recognition of separate strains for first- and second-generation superposed structures — a problem at the heart of many field studies — is a further welcome addition in this volume. As you would expect in a book of this subtitle, there is an analytical treatment of elastic deformation and viscous flow theory. It is developed in a straightforward manner from first principles and can be followed without reference to external sources. However, a significant new feature (for a geological text) is the presentation of numerical methods. The treatment is at an introductory level but covers both the finite difference (FD) and finite element (FE) methods and a broad range of applications to problems in statics and finite ductile flow, including materials with mechanical anisotropy. Although more advanced texts and procedures are available, the book provides a good starting point to gain experience with these techniques and, for geologists, has the attraction of being directed towards geological problems. Best of all, executable and source codes for both the FD and FE methods are available on an accompanying compact disk, as well as codes for most of the other procedures described in the book. (The programs can be run directly from Windows 3.1+ on a PC or with QuickBasic on a Macintosh. Graphical output requires a plotting program such as Surfer.) This ready availability removes a significant deterrent for first-time users: the need to compile and verify lengthy computer codes. In my estimation, the disk alone makes the book easily worth its price though the price is reasonable for the text as well. The book is primarily concerned with techniques and guidance on how to apply them. It is thus best suited to a foundation study in structural geology mechanical modelling or as a sourcebook for mathematical models. Because of this approach, it does not attempt to set out the results of previous studies in a systematic way. Indeed, it frequently branches into new and little-explored areas. Readers will neverthe-
308
Book review
less find an up-to-date bibliography that covers relevant earlier work together with explanatory notes about the main sources. As in earlier volumes of the series, most of the sessions or chapters are set out in a theory – question –answer/comment format or (in this volume) as worked examples, a format that teachers and independent users will find helpful. The book is divided into twelve sessions following on from volume 2. The first, Session 28, moves quickly into heterogeneous stress, with applications to fracture patterns. This is followed by Sessions 29 – 31 which deal with analytical, FD and FE methods and solutions to a variety of static and quasi-static problems (fault patterns, possible pressure-solution effects, pressure-shadows, inclusions, strain-refraction, crack propagation, en echelon cracks, indentation and crenulation). Session 32 provides an introduction to paleostress analysis of fault-slip data using some new approaches (clusters and trihedra). Sessions 33 – 36 describe the geometrical patterns of finite strain, with many insights into such structures as similar-type folds, banded structures, apparent rotations of porphyroblasts, transecting cleavage, superposed cleavages, coaxial and other types of refolds, three-dimensional flow sheets (lavas, slumps, glaciers, nappes and de´collement sheets) and even hackle marks. Problems of flow in viscous materials are introduced by means of stream functions in Session 37. Polynomial functions are used to describe homogeneous and simple heterogeneous flows (e.g., pure shear, extrusion and gravity flow), while transcendental functions are used for velocity patterns in incompetent material around buckle folds, boudins and load casts and for special flows with singularities. Stream functions also appear in a brief treatment of viscous single-layer buckling theory in Session 38 and are found by FD methods in the first part of Session 39. Finally, the latter part of Session 39 applies time-step FE modelling of viscous flow to finite amplitude folds, vein-bridges, boudins and inclusions: an appropriate culmination for the book and for the series as a whole. In a book with so many mathematical expressions, it is perhaps inevitable that some typographical irregularities would occur. The ones I found are mainly in Session 37 and a few in Sessions 29, 33 and 39.1 The 1 Visit http://www.es.mq.edu.au/geology/research/durney/ for typographical errors found so far (RLcorrections.htm).
unconventional use of bold type (normally reserved for symbolic representation of vectors and tensors) for scalar components was also noted in parts of Sessions 33 and 36 – 39, and the lack of punctuation after equations was a general feature of most sessions. However, the irregularities or errors are localized and do not affect results derived later on. They can be easily tracked by working through the derivations. Despite its possible appearance as a well-ordered discipline, continuum mechanics provides scope for terminological disputation. In some works, there can be abstraction to such a degree as to render the physical meaning of particular terms incomprehensible (as in ‘deformation gradients’, which are really just ‘deformations’). On the whole, Ramsay and Lisle present the terminology in a more cognitive style suitable for readers who are interested in applications. Nevertheless, some inconsistencies do occur. An example is the dual use of the term displacement in the introductory session on finite strain. In places, this means a transformation (as in a ‘displacement’ or ‘displacement gradient matrix’ M: the finite Lagrangian tensor [a,b,c,d] for the stretch with rotation where a = 1 + qu/qx, etc.; see also volume 1), and elsewhere, it has the more usual meaning of a change of position (u,v) and gradients (qu/qx, etc.) and gradient matrices (strain with rotation) thereof. Similarly, strain is used in the engineering sense (a change in relative position of particles measured by a change of length over old length as in ‘strain rate’), as a stretch (new length over old length as in ‘finite strain ellipse’ and ‘strain ratio’ derived from the semi-axes of this ellipse) and as a displacement gradient tensor (as in ‘rotational component of strain’). Although some of these expressions have been used for a long time, I feel there is justification for questioning their internal consistency. On the other hand, an old term whose transmutation I could not help lamenting is ‘pressure shadow.’ The writers use this term for diffuse augen-like regions of crystal growth in the microlithon matrix material near a rigid object, in line with the current fashion in metamorphic literature (which may have stemmed from an arbitrary redefinition by Spry, 1969). Its original use in English was for the related but distinct effect of sharply defined regions of entirely new crystal growth (Pabst, 1931). While on the subject of pressure-shadows (sensu Pabst) and pressure-shadows (sensu Spry), the work
Book review
on FD and FE elastic stress modelling of these structures and other cases of heterogeneous mass transfer (Sessions 29 – 31) should be noted. This is part of what the writers, as a way of acknowledging the pioneering work by H.C. Sorby, refer to as ‘pressure solution’ (which they use in the sense of dissolution plus diffusive mass transport and precipitation rather than just dissolution alone). Modelling of these effects is barely covered in other texts, apart from Price and Cosgrove (1990), and in a broad way, Ramberg (1952). In addition, Session 34 discusses P- (pressure-solution) band structure in terms of geometrical models and describes the general nature of mass transfer effects in rocks. Although the stress models provide an intuitive idea of the directions of mass transfer (see also Ghosh and Sengupta, 1973; Stro¨mga˚rd, 1973 for example), perhaps the writers’ sagacious advice elsewhere in the book, about not being overly satisfied with one’s models, could have some application here. Two difficulties in applying the classical mechanics of continua to mass transfer are: (1) the theories of elasticity and viscosity incorporate an assumption that mass does not change; (2) growth or dissolution of solid at specific interfaces, for example in pressure-shadows (sensu Pabst), represents a discontinuity in displacement, which is at odds with the assumption of a continuum. Turning now to practical matters, an important consideration is the functionality of the software on the accompanying disk. I report here on the FE programs, which I tested against known solutions for simple shear stress and accumulated simple shear strain on a Windows platform. There are three core programs: Fe2ddat, which prepares the input data, Fe2d, which runs a single-step elastic solution, and Fe2dfin, which works out finite displacements from multiple increments. They all worked fine. In fact, the procedures are very simple, and the programs do not even require setting up. You just double-click the relevant application icon in Explorer, then follow the prompts. Keeping track of the input and output is made simple by labels for all of the parameters and plain text file formats. Of course, there are some restrictions on the number of elements and nodes (200 and 102, respectively), and a little more effort is required to plot the results. However, this is acceptable for learning purposes anyway. The only idiosyncrasies encountered were: (a) a mixed boundary
309
condition required specifying an arbitrary force component first, then overwriting it with the displacement, (b) angles are in degrees for principal directions but in radians for rigid body rotation, (c) a minor rounding error appeared in the file output from program Fe2d but not from program Fe2dfin, and (d) the ‘strain ratio’ (stretch ratio) output parameter of Fe2d did not seem particularly useful since it is a quantity that should be theoretically close to unity. Much checking and scenario testing with very simple models is advisable when first using the finite element method, in order to familiarize oneself with the limitations. One of these is that the method is designed only for small or infinitesimal strains. Although the programs allow the user to produce large strains and displacements in one step, as done for clarity in some of the figures in Session 30, such results are best viewed as ‘magnified’ small strains. For example, the principal strains for pure shear and simple shear are always given as e3 = e1, whereas the finite values would be e3 = 1/(1 + e1) 1. (Session 39 describes how finite strains and displacements can be obtained using Fe2dfin.) This restriction applies to many of the analytical methods, too. In Session 37, for example, instantaneous displacement rate fields calculated from stream functions have been plotted using arbitrary scale factors so that the patterns can be clearly seen in the diagrams. (The vectors can be thought of as infinitesimal displacements developed over an infinitesimal period of time and magnified for plotting.) Finding exact finite displacements from stream flows over a finite time period is more difficult and, in fact, has not been attempted in the book. However, approximate solutions can be found by the successive application of small increments2 (ironically, the smaller the better). Overall, volume 3 provides many challenging examples and detailed insights into the structural deformation processes that will engage both the newcomer and the experienced practitioner in a fascinating journey of exploration. Above all, it is a book that promotes wider participation in quantitative modelling. This is in tune with today’s computing power and the inevitable consequence that computationally 2
Visit http://www.es.mq.edu.au/geology/research/durney/ for viewing progressive deformation for some Ramsay and Lisle polynomial stream functions (StreamF.htm).
310
Book review
intensive procedures, such as FE, are bound to be used more and more in the future. The no-nonsense approach of this book will not only guide the uninitiated through the basic principles and assumptions that underlie such methods but, with careful application, should help to accelerate the development of physically realistic reconstructions of geological deformation. Perhaps the only question is: ‘‘can we afford not to keep up with these developments?’’
References Ghosh, S.K., Sengupta, S., 1973. Tectonophysics 17, 133 – 175. Pabst, A., 1931. Am. Mineral. 16, 55 – 61.
Price, N.J., Cosgrove, J.W., 1990. Analysis of Geological Structures. Cambridge Univ. Press. Ramberg, H., 1952. The Origin of Metamorphic and Metasomatic Rocks. Univ. Chicago Press. Spry, A., 1969. Metamorphic Textures. Pergamon, Oxford. Stro¨mga˚rd, K.-E., 1973. Tectonophysics 16, 215 – 248.
David W. Durney Department of Earth and Planetary Sciences, Macquarie University, Sydney, Australia E-mail address: [email protected]