Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Fundamentals of rock failure physics
- 3 Laboratory-derived constitutive relations for shear failure
- 4 Constitutive laws for earthquake ruptures
- 5 Earthquake generation processes
- 6 Physical scale-dependence
- 7 Large earthquake generation cycles and accompanying seismic activity
- List of illustration credits
- References
- Index
6 - Physical scale-dependence
Published online by Cambridge University Press: 05 April 2013
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Fundamentals of rock failure physics
- 3 Laboratory-derived constitutive relations for shear failure
- 4 Constitutive laws for earthquake ruptures
- 5 Earthquake generation processes
- 6 Physical scale-dependence
- 7 Large earthquake generation cycles and accompanying seismic activity
- List of illustration credits
- References
- Index
Summary
Introduction
As described in Chapter 1, fracture (or failure) phenomena are observed over a very broad range of size scales, from atomistic-scale to microscopic-scale to macroscopic-scale fractures. A shear failure (or rupture) of laboratory-scale encompassed by continuum mechanics would be roughly of the order of 10–3 to 1 m. In contrast, shear rupture phenomena occurring in the Earth's interior, including microearthquakes and huge earthquakes, encompass a much broader range of size scales from 10–1 to 106 m. Rupture phenomena over such a broad scale range covering both laboratory-scale and field-scale encompassed by continuum mechanics, are characterized by scale-dependent physical quantities inherent in the rupture.
In general, physical quantities inherent in rupture phenomena can be categorized into two groups: scale-dependent physical quantities, and scale-independent physical quantities. As shown in previous chapters, the scale-dependent quantities include the breakdown zone length Xc, the breakdown time Tc (or its reciprocal fsmax), the nucleation zone length Lc, and the fault-slip acceleration D̈. Thus, it is an unavoidable fact that rupture phenomena are scale-dependent. As noted earlier, therefore, it is essential that the constitutive law must be formulated in such a way that the scaling property inherent in the rupture breakdown is incorporated into the law; otherwise, scale-dependent physical quantities inherent in the rupture over a broad scale range cannot be treated consistently and quantitatively in a unified manner in terms of a single constitutive law.
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- The Physics of Rock Failure and Earthquakes , pp. 179 - 199Publisher: Cambridge University PressPrint publication year: 2013
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