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2010 | Buch

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Stress Field of the Earth’s Crust

verfasst von: Priv.-Doz. Dr. Arno Zang, Prof. Ove Stephansson

Verlag: Springer Netherlands

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik"

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Über dieses Buch

Stress Field of the Earth’s Crust is based on lecture notes prepared for a course offered to graduate students in the Earth sciences and engineering at University of Potsdam. In my opinion, it will undoubtedly also become a standard reference book on the desk of most scientists working with rocks, such as geophysicists, structural geologists, rock mechanics experts, as well as geotechnical and petroleum en- neers. That is because this book is concerned with what is probably the most pe- liar characteristic of rock – its initial stress condition. Rock is always under a natural state of stress, primarily a result of the gravitational and tectonic forces to which it is subjected. Crustal stresses can vary regionally and locally and can reach in places considerable magnitudes, leading to natural or man-made mechanical failure. P- existing stress distinguishes rock from most other materials and is at the core of the discipline of “Rock Mechanics”, which has been developed over the last century. Knowledge of rock stress is fundamental to understanding faulting mechanisms and earthquake triggering, to designing stable underground caverns and prod- tive oil fields, and to improving mining methods and geothermal energy extraction, among others. Several books have been written on the subject, but none has atte- ted to be as all-encompassing as the one by Zang and Stephansson.

Inhaltsverzeichnis

Frontmatter

Introduction

Chapter 1. Introduction

Abstract

This book is about the stress field of the Earth’s crust and consists of three major parts. Part I is dedicated to the definition and terminology of rock stress (Chaps. 2–4) resulting in simple Earth stress models (Chap. 5). Part II is an overview of the various stress-measuring methods from a physical point of view (Chap. 6) and a rock mechanics point of view (Chaps. 7 and 8). Rock mechanics and rock engineering techniques for determining stress are divided into borehole (Chap. 7) and corebased methods (Chap. 8). In Part III, stress data are interpreted at the local scale (Chap. 9) and at the global scale in terms of plate tectonics (Chap. 11). A generic stress approach relates local to global data through stress-scaling relations and the best estimated rock stress model (Chap. 10).

Arno Zang, Ove Stephansson

Definition and Terminology

Frontmatter

Chapter 2. Stress Definition

Abstract

This chapter presents the fundamental concept of stress as it is defined from a mathematical, physical and continuum mechanics point of view. The stress tensor defining the state of stress at a point is introduced using the continuum concept of a stress vector (traction) defining the state of stress on a plane (Sect. 2.1). Principal stresses and their orientations are deduced from solving the eigenvalue problem (Sect. 2.2). The Mohr circle of stress is a way of visualizing normal and shear stress components for traction vectors associated with all possible planes through one point (Sect. 2.3). Since elastic stress is a fictitious term, the display of stress involves some mathematical gimmicks (Sect. 2.4).

Arno Zang, Ove Stephansson

Chapter 3. Rock Fracture Criteria

Abstract

When stresses in the Earth’s crust exceed the crustal strength, the rock fractures and fails (Brace 1964; Hoek 1968; Obert 1972). A fracture criterion describes the conditions for which failure occurs in a material. In principle, one distinguishes between phenomenological and mechanistic failure theories. Phenomenological theories (Coulomb, Coulomb-Mohr, Mohr or Hoek-Brown) quantify the spatial orientation of fracture planes with respect to the stress field producing the discontinuities. Mechanistic theories (Griffith, McClintock & Walsh, fracture mechanics models) start from the premise that fracture initiates from existing flaws acting as stress concentrators through which the brittle fracture process in rock is controlled. Both theories are used to determine the stress state in the Earth’s crust and to evaluate the stresses for some of the stress measurement techniques.

Arno Zang, Ove Stephansson

Chapter 4. Rock Stress Terminology

Abstract

There is no internationally agreed terminology for words describing the state of stress in a rock mass (Hudson et al. 2003). In Fig. 4.1 we present a terminology for the classification of rock stress modified from a diagram published by Amadei and Stephansson (1997). The diagram is a structured compilation of terms used earlier (Bielenstein and Barron 1971; Lindner and Halpern 1978; Hyett et al. 1986; Cornet 1993) and in the discussion of descriptive stress terms by Harrison and Hudson (2000). For didactic reasons, we modified two aspects of the diagram. First, each type of rock stress is symbolized by a pictogram illuminating a typical cause of the stress component shown. Second, the term structural stresses (Jaeger and Cook 1979) is added to account for the influence of material properties (anisotropy, heterogeneity) on the in-situ state of rock stress.

Arno Zang, Ove Stephansson

Chapter 5. Crustal Stress Models

Abstract

The stress field of the Earth’s crust is often described by three compressive principal stress components, namely the minimum horizontal, S_h, the maximum horizontal tectonic stress, S_H and the vertical stress due to the weight of the overburden, S_V. Depending on the depth variation of principal stresses assumed, different, simplified crustal stress models can be distinguished. When the vertical direction is not a principal stress direction, assuming that one principal component of the stress tensor is equal to the weight of overburden is of course wrong (cf. Sect. 4.1).

Arno Zang, Ove Stephansson

Measuring Stress

Frontmatter

Chapter 6. Physics of Stress Measurements

Abstract

Stresses cannot be measured directly. Stress determination is made indirectly, e.g. by the measurement of strain. Deformation values obtained from an unbalanced body approaching equilibrium in combination with theoretical knowledge about constitutive behaviour (stress-strain relationship) allows us to evaluate the state of stress existing in any deformable body. The physics of stress measurements can be subdivided into six methodologies (see Table 6.1 ). For rocks and minerals, some modifications of these techniques used in material sciences are required.

Arno Zang, Ove Stephansson

Chapter 7. Measuring Crustal Stress: Borehole Methods

Abstract

Stresses within the Earth’s crust are “measured” indirectly by coring, slotting and loading a piece of rock with subsequent analysis of re-equilibrium deformations. This action requires assumptions about constitutive behaviour of the rock, i.e. the relationship between measured strain and inferred stress (Eq. (4.2) for anisotropic, Eq. (4.8) for isotropic rock). In addition, Eq. (4.8) includes the effect of temperature on mechanical stresses. If the location of stress measurement is chosen to be close to natural discontinuities (fracture, fault) or excavation (borehole, tunnel) boundaries, near-field stresses are determined (Sect. 4.4). The virgin or in-situ stress field can only be observed at distances of two to three times the size of the excavation discontinuity or any other stress concentrator (inclusion).

Arno Zang, Ove Stephansson

Chapter 8. Measuring Crustal Stress: Core-Based Methods

Abstract

In-situ stresses are important for many processes in tight gas reservoirs, ranging from siting the well, to drilling, completion and long-term production. The orientation of the stress field, which controls the azimuth of the hydraulic fracture (Sect. 7.2), is important for field development as optimum drainage in a tight reservoir will depend on the drainage from a hydraulic fracture. If wells are not sited properly, drainage patterns will overlap and production may be uneconomic. Stress magnitudes are important for wellbore stability and hydraulic fracturing. For fracturing, in particular, the stress difference between lithologies in a geological sequence is the major control on fracture-height growth. The focus of this chapter is shifted from borehole methods to core-based methods for in-situ stress estimates. As pointed out in Sect. 7.1, the crucial assumption in core-based stress estimates is that the dominating portion of the stress-relief cracks observed in deep drill cores is caused by the relief of present-day stresses. Only with this assumption, the azimuth of relief-crack populations can be related to in-situ stress azimuth, and the closing pressure of relief cracks to in-situ stress magnitudes.

Arno Zang, Ove Stephansson

Interpreting Stress Data

Frontmatter

Chapter 9. Local Stress Data

Abstract

Local stress data are usually tied to underground excavations (mines, tunnels) or boreholes which are drilled into the Earth’s crust. The most important reasons for designing excavations and drilling holes are withdrawal of natural materials like hydrocarbon or mineral resources, deposit of human waste materials like nuclear waste or CO₂, and geothermal energy as well as pure scientific purpose. We choose three sites to show different applications of stresses in the Earth’s crust and facets in stress determination involved.

Arno Zang, Ove Stephansson

Chapter 10. Generic Stress Data

Abstract

In this chapter we present and discuss in-situ stress data in terms of magnitudedepth profiles (Sect. 10.1) and stress-orientation maps (Sect. 10.2). We refer to the relationship of stress-state scaling (Sect. 10.3) and how to find the Best Estimated Stress Model for a study area (Sect. 10.4). In this sense, generic means commonly used mathematical relationships to present stress data and their general agreement to this relationship for different sites selected.

Arno Zang, Ove Stephansson

Chapter 11. Global Stress

Abstract

In this last chapter of the book we present and interpret stress data in Europe (Sect. 11.1). In the following, stress orientations from the World Stress Map data set are displayed as a hybrid stress map and are interpreted based on global mantle flow (Sect. 11.2) and in terms of plate-tectonic sources (Sect. 11.3).

Arno Zang, Ove Stephansson

Backmatter

Titel: Stress Field of the Earth’s Crust
verfasst von: Priv.-Doz. Dr. Arno Zang
Prof. Ove Stephansson
Verlag: Springer Netherlands
Electronic ISBN: 978-1-4020-8444-7
Print ISBN: 978-1-4020-8443-0
DOI: https://doi.org/10.1007/978-1-4020-8444-7

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