Physics for Geologists, Second edition

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92 Stress and strain Kinematic viscosity We find in many expressions in fluid mechanics the ratio of the dynamic viscosity of a fluid to its mass density, qlp. It has the dimensions L~T-', with the symbol v (the Greek letter nu). It is known as kinematic viscosity because it concerns motion without reference to force. The unit is m2 s-I in SI, or the stoke, which is cm2 s-l. The stoke is named after Sir George Stokes (1819-1903), British mathematician and physicist, whose work on the internal friction of fluids and the motion of pendulums led to what is now called Stokes' Law for the terminal velocity of a single small sphere falling through a fluid. Sliding Sliding takes place in several geological processes. When rocks are faulted, sliding takes place in the fault plane. When a layered sequence of rocks is folded, some adjustment of the beds is likely to take place by sliding along bedding surfaces. When mountain ranges are created, slopes may be generated that are steep enough for rock-sequences to slide down the slope. This is not just a small-scale phenomenon, or a new conception. More than a hundred years ago, Tornebohm postulated movement of blocks at least 130 km long on Caledonian thrusts in Scandinavia. Sliding on such a scale raised an interesting question: the strength of the rocks themselves limited to a few kilometres the length of block that could be pushed, but if sliding down a slope is required, then the 65 km difference of elevation of a block 130 km long down a slope of 30°, which seemed to be required, was unacceptable - and there was no geological evidence for such a slope. The resolution of this paradox lies in the nature of sliding. There are two sorts of sliding: lubricated and unlubricated. We shall take unlubricated sliding first, for a better understanding of the two. Unlubuicated sliding When a rectangular block of thickness h is placed on a plane surface that is not sloping steeply enough for the block to slide, its weight o, in the ambient fluid, per unit area of the base, is where the suffix 'a' refers to the ambient fluid. This can be resolved into a component normal to the surface (Figure 9.2), and a shear component parallel to the surface, T = (pb - pa) gh sin 0. Copyright 2002 by Richard E. Chapman
Stress and strain 93 Figure 9.2 Components of weight of a block. The vertical component is a,, that normal to the sliding surface is a,, and that parallel to the sliding surface is T. The frictional resistance to sliding is r. These may be regarded as active stresses. They give rise to reactive stresses, a normal reaction and frictional resistance (t) that tends to prevent sliding. As the angle of slope 0 increases, so the shear component of weight increases. There is some critical value of 0 at which the shear component of weight is equal to the frictional resistance and the block is just about to slide. The friction is due to adhesion or cohesion between bodies, or to the roughness of the surfaces that would be sliding surfaces. The roughness can only be overcome by deformation or fracture of the protuberances. The Coulomb or Mohr-Coulomb criterion for simple unlubricated sliding (see Hubbert 1951: 363) is where to is the cohesive strength or initial shear strength of the material at the surface that will become the sliding surface, when the normal stress on is zero; and tan 4 is the coefficient of sliding friction, 4 being the internal angle of friction. Sliding will therefore take place when (pb - pa) gh sin 0 = to + (pb - pa) gh cos 0 tan +. (from Equations 9.8b, 9 .8~ and 9.9) and tan 0 = This equation shows that unlubricated sliding will usually take place on a slope 0 that is rather greater than 4. The effect of pore-fluid pressure can be very important, reducing the effec- tive stress and greatly reducing the angle at which sliding can take place. We cannot go into this in detail, but the outline is this. Copyright 2002 by Richard E. Chapman
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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
Page 57 and 58: 40 Gravity Figure 3.8 The siphon at
Page 59 and 60: 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: Stress and strain 91 Figure 9.1 New
Page 111 and 112: Stress and strain 95 Figure 9.3 Ide
Page 113 and 114: Fracture Stress and strain 97 We fo
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
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References Allum, J. A. E. (1966) P
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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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