Sandbox tectonics &acirc;€“ Simple theory11

# Sandbox tectonics &acirc;€“ Simple theory11 -...

This preview shows pages 1–6. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
“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
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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 10/25/2010 for the course MIT Geodynamic taught by Professor Ywn during the Fall '10 term at MIT.

### Page1 / 9

Sandbox tectonics &acirc;€“ Simple theory11 -...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online