Physics for Geologists, Second edition

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94 Stress and strain Terzaghi postulated that the total vertical load on sediment is borne partly by the solid framework, and partly by the pore fluid: where S(=ybwz) is the total vertical component of overburden pressure, yb, the mean bulk wet density of the overburden in the vertical thickness z; a is the effective stress transmitted through the solids, and p is the pore-fluid pressure (which Terzaghi called the neutral stress). If for any reason the pore fluids are confined and their pressure increases, then there is a corresponding decrease in the effective stress - the stress that compacts sediment and sedimentary rock. Alternatively, if the pore fluid cannot escape, the sedimentary rock cannot compact because the pore fluid takes most of the load. If (S -p) is substituted for a, in the Mohr-Coulomb criterion, Equation 9.10, it will be seen that simple sliding can take place on slopes much less that @ as the effective stress is reduced. Note that the coefficient of sliding (tan @) is not changed, but the total effect is. This was studied extensively by Terzaghi (1936, 1943: 235; 1950) in the context of soil mechanics and landslides, and by Hubbert and Rubey (1959) in the broader context of geology. To pursue this topic, it may help to read Chapman (1979) first. In any case try this. Place a cold empty can of drink, after chilling in the fridge, upside down on a glass-topped table - that is, with the opening downwards. As the warmer external air warms the air in the can, so it expands and tends to lift the can, and it will slide on a very gentle slope. But it only slides until it reaches the edge of the glass. As soon as the air pressure can be reduced to normal, it stops sliding. The same principle is used for rotating the large radio telescopes. If a can that has a perforation at both ends is put to the same test, it will not slide when the other does. Lubricated sliding Following Kehle (1970), suppose an extensive, relatively thin sheet of a single liquid is flowing in uniform laminar flow down a gentle slope on a planar surface (Figure 9.3) and can be regarded as being newtonian (see page 91), then Assume that where H is the total thickness of liquid flowing and H - h is the thickness contributing to the shear stress at the level of interest. Note that the shear Copyright 2002 by Richard E. Chapman
Stress and strain 95 Figure 9.3 Idealized velocity profile through 2 km mudrock on a slope of 5". The assumed properties of the mudrock are: mass density 2 000 kg m-3, viscosity 10 x lo1' Pas. Figure 9.4 Lubricated sliding (idealized). The mudrock has the same properties as Figure 9.3. stress is maximum at the base, where the velocity is zero; and zero at the top where the velocity is greatest. Equating Equations 9.12 and 9.13, dV q- = (pb - pa)g(H - h)sin0 (9.14) dh and integrating with respect to h (noting that V = 0 when h = O), v=[ 7, I (pb - pa) g(Hh - h2/2) sin 0. If we now consider half of the thickness H to be composed of rigid material of the same density (Figure 9.4), its sliding velocity will be the same as at half the thickness of original lubricant. 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
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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 and 108: Stress and strain 91 Figure 9.1 New
Page 109: Stress and strain 93 Figure 9.2 Com
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
Page 159 and 160: 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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