The last of the CIRCULAR GRAPHS which will HAUNT YOU ALL QUARTER January 13, 2005 [Many thanks to H. Bob]

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Presentation transcript:

The last of the CIRCULAR GRAPHS which will HAUNT YOU ALL QUARTER January 13, 2005 [Many thanks to H. Bob]

Stress - Real Time

Map of global seismicity

Definitions: FRICTION Same as sliding blocks from physics class (kinetic friction) Determines slope of Coulomb failure envelope For unconsolidated materials,  = angle of internal friction = angle of repose. For rocks,  = coefficient of friction of sliding surfaces

Definitions: COHESION For whole rocks: C = breaking strength. For broken surfaces: C = static friction. For unconsolidated sediment: C = ZERO. Like “static friction” from physics class

No shear stress on a FREE SURFACE

If stresses were everywhere aligned with the earth’s surface…

But if stresses are angled at depth… Then they rotate to alignment near the surface!

Andersonian Theory of Faulting: The optimum shear fracture plane is always oriented at 60° to  1, 30° to  3,  2 is in the plane. Simple idea but VERY USEFUL - Provides link between faults and stresses - present and past.

Rules of Thumb “Thinning Direction” parallel to  1 “Thickening Direction” parallel to  3 Simple model - no motion along  2 SIMPLIFICATION! For now anyway. Remember the sandbox model from last week’s lab…

 1 horizontal,  3 vertical

 1 horizontal,  3 horizontal

 1 vertical,  3 horizontal

The last of the CIRCULAR GRAPHS which will HAUNT YOU ALL QUARTER And Now, As Promised…

Plane intersects sphere = Arc!

Convention: use the “Southern” Hemisphere of an imaginary sphere

Let’s start with a vertical plane cutting the hemisphere. It intersects on an ARC.

Now let’s look down from the North Star…

Assign a coordinate system to get us oriented… N S W E

Reduce the clutter to a circle. N S W E Now let’s graph a plane onto it! Vertical plane - straight line through the pole Strike=45

How about a horizontal plane? N S W E Strike=?? It sits through the equator - all lines are horizontal so there’s no unique strike line

How about plane 0/25W? N S W E Strike=0 Or plane 0/55W?

How about plane 45/25NW? N S W E Strike=45 How about plane 330/25NE ? Strike=330 PLANES INTERSECT AT A POINT

stereonet Template on which we can draw our circles: stereonet