Physics for Geologists, Second edition

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96 Stress and strain In geology, viscosities will be very large, probably of the order of 10 x 10'' Pa s, but even these could lead to catastrophic rates of sliding of perhaps 10m a year on quite small slopes. When Smoluchowski (1909) addressed the problems of sliding he wrote: Suppose a layer of plastic material, say pitch, interposed between the block and the underlying bed; or suppose the bed to be composed of such material: then the law of viscous liquid friction will come into play, instead of the friction of solids; therefore any force, however small, will succeed in moving the block. Its velocity may be small if the plasticity is small, but in geology we have plenty of time; there is no hurry. Bending and folding There are several ways of bending layered material, and it is one of the retarding influences on geology that many seem to think of bending only in terms of lateral compression (Figure 9.5). Carey (1954) in this regard is still worth reading. (Since we are concerned with geology, we shall talk about folding or deformation rather than bending.) Folding is certainly possible by crumpling a thin sheet under lateral compression, but it arises more commonly from mechanical instability in the outer parts of the Earth, and in layered sequences under conditions where gravity plays a part. In an unstable layered system (such as one in which the upper layers are more dense than the lower), deformation will result in folding of the type shown in the upper part of Figure 9.5 - and such folding may be induced in stable layers above and below the unstable layer. Folding requires compensation in space, either by sliding on surfaces, or flowing of the less viscous material, or both. Bending a beam puts the con- cave side in compression and the convex side in extension. Under some circumstances this can cause fracture, but in some cases natural rocks can- not sustain such stresses over long periods of time, and behave more like liquids. Copyright 2002 by Richard E. Chapman Figure 9.5 Folding can be by bending or buckling.
Fracture Stress and strain 97 We follow Otto Mohr, and Hubbert (1951). Consider a rectangular solid in which the principal stresses are approximately equal. If a compressive force is applied between two parallel faces, the principal stress normal to those faces will increase; there will then be a maximum principal stress, a minimum principal stress and an intermediate principal stress, which we shall denote 01,03 and 02 respectively. Consider a small prism of unit width on an arbitrary plane (Figure 9.6), the prism being small enough for its weight to be negligible in the whole, but not so small that it is no longer mechanically representative of the whole. We shall assume that only ol and a3 are significant in the analysis, 02 being parallel to the arbitrary plane. Let an be the normal stress on the surface, and t the shear component along the surface. Let the side AB have unit length, then the sum of the vertical and horizontal components of the forces acting on the prism are, respectively, Solving these for on and t, 2 2 On = 01 COS C1-k a3 sin a; t = (al - a3) sin a cos a. These can be reduced to the more useful form Mohr represented these relationships in a simple geometrical construction that has become known as Mohr's circle (Figure 9.7). From this we see Copyright 2002 by Richard E. Chapman Figure 9.6 Stresses on a small prism of rock. The stresses are across a surface that lies at an angle a with the least principal stress, a3.
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Physics for Geologists Second editi
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Copyright 2002 by Richard E. Chapma
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... vlii Contents Polarization 47 L
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Figures Copyright 2002 by Richard E
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Tables Copyright 2002 by Richard E.
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xiv Preface waves diminishes with d
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xvi Preface provides. This book is
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xviii Acknowledgements to K. Whaler
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xx Symbols mass refractive index bu
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2 Basic concepts Table 1.1 Dimensio
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4 Basic concepts Table 1.2 Basic SI
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6 Basic concepts pascal (Pa) and si
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8 Basic concepts all the relevant d
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10 Basic concepts relating them by
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2 Force The dimensions of force are
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14 Force The ratio of the Moon's ac
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16 Force Figure 2.1 The sum of the
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18 Force When a motorcycle takes a
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20 Force Figure 2.3 Torque is the p
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22 Force How does momentum differ f
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24 Force the weights - that is, the
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26 Force Figure 2.6 Wall-sticking i
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3 Gravity Universal gravity When di
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30 Gravity are significant to geolo
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32 Gravity Figure 3.2 The tractive,
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34 Gravity Mean sea level It might
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36 Gravity The benefits of space fl
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38 Gravity Figure 3.6 Profile of th
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40 Gravity Figure 3.8 The siphon at
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4 Optics Light is an electromagneti
Page 61 and 62: 44 Optics Figure 4.2 Refraction. (a
Page 63 and 64: 46 Optics The coeficient of reflect
Page 65 and 66: 48 Optics only the light oscillatin
Page 67 and 68: 50 Optics called Iceland Spar. Two
Page 69 and 70: 52 Optics Diffraction If you shine
Page 71 and 72: 54 Optics Figure 4.7 Geometrical op
Page 73 and 74: 56 Optics Figure 4.9 The mirrors in
Page 75 and 76: 5 Atomic structure and age-dating P
Page 77 and 78: 60 Atomic structure and age-dating
Page 83 and 84: 66 Electromagnetic radiation radiat
Page 85 and 86: 68 Electromagnetic radiation Source
Page 87 and 88: Heat and heat flow The noun heat ha
Page 89 and 90: 72 Heat and heat flow Second Law: A
Page 91 and 92: 8 Electricity and magnetism Electri
Page 93 and 94: Electricity and magnetism 77 Figure
Page 95 and 96: Electricity and magnetism 79 rivett
Page 97 and 98: Electricity and magnetism 8 1 defin
Page 99 and 100: Electricity and magnetism 83 is kno
Page 101 and 102: 9 Stress and strain Pressure, p, is
Page 103 and 104: Stress and strain 87 than some natu
Page 105 and 106: These three elastic constants are r
Page 107 and 108: Stress and strain 91 Figure 9.1 New
Page 109 and 110: Stress and strain 93 Figure 9.2 Com
Page 111: Stress and strain 95 Figure 9.3 Ide
Page 115 and 116: Stress and strain 99 from which we
Page 117 and 118: 10 Sea waves The nature of water wa
Page 119 and 120: Sea waves 103 Figure 10.1 Wave moti
Page 121 and 122: Sea waves 105 refraction by islands
Page 123 and 124: Acoustics: sound and other waves 10
Page 125 and 126: Acoustics: sound and other waves 10
Page 127 and 128: 12 Fluids and fluid flow Introducti
Page 129 and 130: Fluids and fluid flow 1 13 Figure 1
Page 131 and 132: Fluids and fluid flow 115 Figure 22
Page 133 and 134: Fluids and fluid flow 117 and the f
Page 135 and 136: water above a vertical thickness h
Page 137 and 138: Fluids and fluid flow 121 where V i
Page 139 and 140: Fluids and fluid flow 123 ardentes,
Page 141 and 142: Fluids and fluid flow 125 Figure 12
Page 143 and 144: - 14 $ 12 E 10 K .- 3 8 r cll + 6 0
Page 145 and 146: Fluids and fluid flow 129 the liqui
Page 147 and 148: Some dangers of mathematical statis
Page 155 and 156: Appendix 139 What would happen if y
Page 157 and 158: Notes 141 and since x is very large
Page 159 and 160: References Allum, J. A. E. (1966) P
Page 161 and 162: References 145 -(1950) 'Mechanism o
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Further reading 147 Trigg, G. L. an
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Physics for Geologists, Second edition

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