Sandbox tectonics – Simple theory11

Sandbox tectonics – Simple theory11 -...

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12.005 Lecture Notes 11 Sandbox tectonics – Simple theory (after Dahlen ’84) Assumptions Coulomb failure τ =− µ (1 λ ) σ n Based decollement may have different (or ) ( b b ? ) fluids in count? Material is on the verge of failure everywhere Mohr circle construction Inertia negligible 0 Fm a ⇒= = ± ± 4 parameters ( , , b , b ? ), 2 variables Neglect complications of being under water (? ) Figure by MIT OCW. Figure 11.1
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α surface slope β basal slope ψ 0 angle between and surface (or more fundamentally, and z axis) σ III I b angle between and base I Figure by MIT OCW. Figure by MIT OCW. Figure 11.2 Figure 11.3
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Equilibrium equations: τ ij , j + f i = 0 σ xx x + xz z ρ g sin α = 0 xz x + zz z + g cos = At z = 0 xz = zz = For now, ignore effects of pore fluid pressure – will go back to this later. Dry sand “Physical” space Figure by MIT OCW. Figure 11.4
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“Mohr” space Argue: No strength: no scale length s 0 = 0 x = 0 σ Ι & III functions of z only ψ 0 is a constant Plug in to equilibrium equations: zz =− ρ gz cos α xz = gz sin satisfies equilibrium equations and boundary conditions How to relate and α ? 0 If stress is critical everywhere, can use Mohr circle. Say c = I + III 2 r = I III 2 Geometry of Mohr circle csc φ = c r Figure by MIT OCW. Figure 11.5
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tan2 ψ 0 = σ xz zz c sec2 0 = r zz c Equilibrium xz zz =− tan α Solving 4 equations tan = 0 csc φ sec2 0 1 The March of Science revisited (after S. V. Panasyuk) To introduce the notation, let's draw a sketch: We can use the well known Mohr's circle technique to describe the wedge behaviour.
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This note was uploaded on 10/25/2010 for the course MIT Geodynamic taught by Professor Ywn during the Fall '10 term at MIT.

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Sandbox tectonics – Simple theory11 -...

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