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Fractals in Rock Mechanics

Author: Heping Xie

Publisher: CRC Press

Published: 2020-12-17

Total Pages: 464

ISBN-13: 1000099660

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Important developments in the progress of the theory of rock mechanics during recent years are based on fractals and damage mechanics. The concept of fractals has proved to be a useful way of describing the statistics of naturally occurring geometrics. Natural objects, from mountains and coastlines to clouds and forests, are found to have boundaries best described as fractals. Fluid flow through jointed rock masses and clusterings of earthquakes are found to follow fractal patterns in time and space. Fracturing in rocks at all scales, from the microscale (microcracks) to the continental scale (megafaults), can lead to fractal structures. The process of diagenesis and pore geometry of sedimentary rock can be quantitatively described by fractals, etc. The book is mainly concerned with these developments, as related to fractal descriptions of fragmentations, damage and fracture of rocks, rock burst, joint roughness, rock porosity and permeability, rock grain growth, rock and soil particles, shear slips, fluid flow through jointed rocks, faults, earthquake clustering, and so on. The prime concerns of the book are to give a simple account of the basic concepts, methods of fractal geometry, and their applications to rock mechanics, geology, and seismology, and also to discuss damage mechanics of rocks and its application to mining engineering. The book can be used as a textbook for graduate students, by university teachers to prepare courses and seminars, and by active scientists who want to become familiar with a fascinating new field.

Book Synopsis Fractals in Rock Mechanics by : Heping Xie

Download or read book Fractals in Rock Mechanics written by Heping Xie and published by CRC Press. This book was released on 2020-12-17 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Important developments in the progress of the theory of rock mechanics during recent years are based on fractals and damage mechanics. The concept of fractals has proved to be a useful way of describing the statistics of naturally occurring geometrics. Natural objects, from mountains and coastlines to clouds and forests, are found to have boundaries best described as fractals. Fluid flow through jointed rock masses and clusterings of earthquakes are found to follow fractal patterns in time and space. Fracturing in rocks at all scales, from the microscale (microcracks) to the continental scale (megafaults), can lead to fractal structures. The process of diagenesis and pore geometry of sedimentary rock can be quantitatively described by fractals, etc. The book is mainly concerned with these developments, as related to fractal descriptions of fragmentations, damage and fracture of rocks, rock burst, joint roughness, rock porosity and permeability, rock grain growth, rock and soil particles, shear slips, fluid flow through jointed rocks, faults, earthquake clustering, and so on. The prime concerns of the book are to give a simple account of the basic concepts, methods of fractal geometry, and their applications to rock mechanics, geology, and seismology, and also to discuss damage mechanics of rocks and its application to mining engineering. The book can be used as a textbook for graduate students, by university teachers to prepare courses and seminars, and by active scientists who want to become familiar with a fascinating new field.

Fractals in Rock Mechanics

Author: Heping Xie

Publisher: CRC Press

Published: 2020-12-18

Total Pages: 472

ISBN-13: 1000150348

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Book Synopsis Fractals in Rock Mechanics by : Heping Xie

Download or read book Fractals in Rock Mechanics written by Heping Xie and published by CRC Press. This book was released on 2020-12-18 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Important developments in the progress of the theory of rock mechanics during recent years are based on fractals and damage mechanics. The concept of fractals has proved to be a useful way of describing the statistics of naturally occurring geometrics. Natural objects, from mountains and coastlines to clouds and forests, are found to have boundaries best described as fractals. Fluid flow through jointed rock masses and clusterings of earthquakes are found to follow fractal patterns in time and space. Fracturing in rocks at all scales, from the microscale (microcracks) to the continental scale (megafaults), can lead to fractal structures. The process of diagenesis and pore geometry of sedimentary rock can be quantitatively described by fractals, etc. The book is mainly concerned with these developments, as related to fractal descriptions of fragmentations, damage and fracture of rocks, rock burst, joint roughness, rock porosity and permeability, rock grain growth, rock and soil particles, shear slips, fluid flow through jointed rocks, faults, earthquake clustering, and so on. The prime concerns of the book are to give a simple account of the basic concepts, methods of fractal geometry, and their applications to rock mechanics, geology, and seismology, and also to discuss damage mechanics of rocks and its application to mining engineering. The book can be used as a textbook for graduate students, by university teachers to prepare courses and seminars, and by active scientists who want to become familiar with a fascinating new field.

Fractal Algorithm and Its Application in Rock Mechanics

Author: Dongjie Xue

Publisher: Springer Nature

Published: 2022-02-22

Total Pages: 183

ISBN-13: 9811697167

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This book focuses on learning and adapting nonlinear geometry tool in rock engineering through fractal theories, hypotheses, algorithm, practical understandings, and case studies. Understanding self-similarity and self-affinity is a prerequisite to the fractal model in rock mechanics. The book aims to provide a guide for the readers seeking to understand and build nonlinear model by fractal algorithm. The book is motivated by recent rapid advances in rock engineering in China including application of fractal theory, in addition to percolation theory. It is an essential reference to the most promising innovative rock engineering. Chapters are carefully developed to cover (1) new fractal algorithms (2) five engineering cases. This authored book addresses the issue with a holistic and systematic approach that utilizes fractal theory to nonlinear behavior in rock engineering. The book is written for researchers interested in rock and geological engineering as well as organizations engaged in underground energy practices.

Book Synopsis Fractal Algorithm and Its Application in Rock Mechanics by : Dongjie Xue

Download or read book Fractal Algorithm and Its Application in Rock Mechanics written by Dongjie Xue and published by Springer Nature. This book was released on 2022-02-22 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on learning and adapting nonlinear geometry tool in rock engineering through fractal theories, hypotheses, algorithm, practical understandings, and case studies. Understanding self-similarity and self-affinity is a prerequisite to the fractal model in rock mechanics. The book aims to provide a guide for the readers seeking to understand and build nonlinear model by fractal algorithm. The book is motivated by recent rapid advances in rock engineering in China including application of fractal theory, in addition to percolation theory. It is an essential reference to the most promising innovative rock engineering. Chapters are carefully developed to cover (1) new fractal algorithms (2) five engineering cases. This authored book addresses the issue with a holistic and systematic approach that utilizes fractal theory to nonlinear behavior in rock engineering. The book is written for researchers interested in rock and geological engineering as well as organizations engaged in underground energy practices.

The Implication of Fractal Dimension in Hydrogeology and Rock Mechanics Version 1.1

Author: W. Dershowitz

Publisher:

Published: 1992

Total Pages: 62

ISBN-13:

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Book Synopsis The Implication of Fractal Dimension in Hydrogeology and Rock Mechanics Version 1.1 by : W. Dershowitz

Download or read book The Implication of Fractal Dimension in Hydrogeology and Rock Mechanics Version 1.1 written by W. Dershowitz and published by . This book was released on 1992 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fractals in Geotechnical Engineering

Author: Dimitrios Kolymbas

Publisher:

Published: 2004

Total Pages: 0

ISBN-13: 9783832505837

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Self-similarity is a striking and ubiquitous characteristic of structures in geology. On the other hand, capturing of scale effects is one of the main challenges in geotechnical engineering. There, the usual approach is to extrapo-late laboratory findings toward large scale problems. Whereas this procedure is passable for small grained soils, it proves unrealistic for coarse grained soils and rock, especially jointed one. As a consequence, the prediction of e.g. water inrush into a large tunnel based on the examination of rock samples and spot-wise packer tests proves to be hardly possible. The new branch of fractal analysis encompasses both notions, self-similarity and scale effects. Therefore, it pricks up the geotechnical engineer's ears and evokes the hope that it can help to treat the related problems. A more thorough view, however, shows that the exploitation of fractal analysis in the above sense is not so straightforward. First of all, our limited range of observance over several scales inhibits to check and quantify the scale effect. At that, we lack the mathematical tools to treat problems that exhibit a continuous scale dependence, as this is the case with fractal materials.

Book Synopsis Fractals in Geotechnical Engineering by : Dimitrios Kolymbas

Download or read book Fractals in Geotechnical Engineering written by Dimitrios Kolymbas and published by . This book was released on 2004 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Self-similarity is a striking and ubiquitous characteristic of structures in geology. On the other hand, capturing of scale effects is one of the main challenges in geotechnical engineering. There, the usual approach is to extrapo-late laboratory findings toward large scale problems. Whereas this procedure is passable for small grained soils, it proves unrealistic for coarse grained soils and rock, especially jointed one. As a consequence, the prediction of e.g. water inrush into a large tunnel based on the examination of rock samples and spot-wise packer tests proves to be hardly possible. The new branch of fractal analysis encompasses both notions, self-similarity and scale effects. Therefore, it pricks up the geotechnical engineer's ears and evokes the hope that it can help to treat the related problems. A more thorough view, however, shows that the exploitation of fractal analysis in the above sense is not so straightforward. First of all, our limited range of observance over several scales inhibits to check and quantify the scale effect. At that, we lack the mathematical tools to treat problems that exhibit a continuous scale dependence, as this is the case with fractal materials.

Estimation of Shear Strength Using Fractals as a Measure of Rock Fracture Roughness

Author: Paul C. McWilliams

Publisher:

Published: 1993

Total Pages: 48

ISBN-13:

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Book Synopsis Estimation of Shear Strength Using Fractals as a Measure of Rock Fracture Roughness by : Paul C. McWilliams

Download or read book Estimation of Shear Strength Using Fractals as a Measure of Rock Fracture Roughness written by Paul C. McWilliams and published by . This book was released on 1993 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fractals in Petroleum Geology and Earth Processes

Author: C.C. Barton

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 338

ISBN-13: 1461518156

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In this unique volume, renowned experts discuss the applications of fractals in petroleum research-offering an excellent introduction to the subject. Contributions cover a broad spectrum of applications from petroleum exploration to production. Papers also illustrate how fractal geometry can quantify the spatial heterogeneity of different aspects of geology and how this information can be used to improve exploration and production results.

Book Synopsis Fractals in Petroleum Geology and Earth Processes by : C.C. Barton

Download or read book Fractals in Petroleum Geology and Earth Processes written by C.C. Barton and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this unique volume, renowned experts discuss the applications of fractals in petroleum research-offering an excellent introduction to the subject. Contributions cover a broad spectrum of applications from petroleum exploration to production. Papers also illustrate how fractal geometry can quantify the spatial heterogeneity of different aspects of geology and how this information can be used to improve exploration and production results.

Fractals in the Earth Sciences

Author: C.C. Barton

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 277

ISBN-13: 1489913971

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Fractals have changed the way we understand and study nature. This change has been brought about mainly by the work of B. B. Mandelbrot and his book The Fractal Geometry of Nature. Now here is a book that collects articles treating fractals in the earth sciences. The themes chosen span, as is appropriate for a discourse on fractals, many orders of magnitude; including earthquakes, ocean floor topography, fractures, faults, mineral crystallinity, gold and silver deposition. There are also chapters on dynamical processes that are fractal, such as rivers, earthquakes, and a paper on self-organized criticality. Many of the chapters discuss how to estimate fractal dimensions, Hurst exponents, and other scaling exponents. This book, in a way, represents a snapshot of a field in which fractals has brought inspiration and a fresh look at familiar subjects. New ideas and attempts to quantify the world we see around us are found throughout. Many of these ideas will grow and inspire further work, others will be superseded by new observations and insights, most probably with future contributions by the authors of these chapters.

Book Synopsis Fractals in the Earth Sciences by : C.C. Barton

Download or read book Fractals in the Earth Sciences written by C.C. Barton and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractals have changed the way we understand and study nature. This change has been brought about mainly by the work of B. B. Mandelbrot and his book The Fractal Geometry of Nature. Now here is a book that collects articles treating fractals in the earth sciences. The themes chosen span, as is appropriate for a discourse on fractals, many orders of magnitude; including earthquakes, ocean floor topography, fractures, faults, mineral crystallinity, gold and silver deposition. There are also chapters on dynamical processes that are fractal, such as rivers, earthquakes, and a paper on self-organized criticality. Many of the chapters discuss how to estimate fractal dimensions, Hurst exponents, and other scaling exponents. This book, in a way, represents a snapshot of a field in which fractals has brought inspiration and a fresh look at familiar subjects. New ideas and attempts to quantify the world we see around us are found throughout. Many of these ideas will grow and inspire further work, others will be superseded by new observations and insights, most probably with future contributions by the authors of these chapters.

Boundaries of Rock Mechanics

Author: Meifeng Cai

Publisher: CRC Press

Published: 2008-04-01

Total Pages: 1008

ISBN-13: 0203883209

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Boundaries of Rock Mechanics. Recent Advances and Challenges for the 21st Century contains 180 papers from the International Young Scholars Symposium on Rock Mechanics 2008 (Beijing, China, 28 April-2 May 2008). The symposium was organized by the ISRM Commission on Education, and sponsored by the International Society for Rock Mechanics (ISRM) and

Book Synopsis Boundaries of Rock Mechanics by : Meifeng Cai

Download or read book Boundaries of Rock Mechanics written by Meifeng Cai and published by CRC Press. This book was released on 2008-04-01 with total page 1008 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boundaries of Rock Mechanics. Recent Advances and Challenges for the 21st Century contains 180 papers from the International Young Scholars Symposium on Rock Mechanics 2008 (Beijing, China, 28 April-2 May 2008). The symposium was organized by the ISRM Commission on Education, and sponsored by the International Society for Rock Mechanics (ISRM) and

Fractals in Geophysics

Author: SCHOLZ

Publisher: Birkhäuser

Published: 2013-11-22

Total Pages: 312

ISBN-13: 3034863896

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Reprint from Pure and Applied Geophysics (PAGEOPH), Volume 131 (1989), No. 1

Book Synopsis Fractals in Geophysics by : SCHOLZ

Download or read book Fractals in Geophysics written by SCHOLZ and published by Birkhäuser. This book was released on 2013-11-22 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reprint from Pure and Applied Geophysics (PAGEOPH), Volume 131 (1989), No. 1