16 July 2015GLG510 Advanced Structural Geology Force, Traction, and Stress.

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Presentation transcript:

16 July 2015GLG510 Advanced Structural Geology Force, Traction, and Stress

16 July 2015GLG510 Advanced Structural Geology Physical quantities Force, F = m a; [=]kg m s -2 = N (newton) Stress, s[=](kg m s -2 )m -2 = N m -2 = Pa

16 July 2015GLG510 Advanced Structural Geology Force: Newton’s Laws of Motion Law I: Every body continues in its state of rest, or in uniform motion in a straight line, unless it is compelled to change its state by forces impressed upon it. Law II: The rate of change of momentum is proportional to the impressed force and is made in the direction in which the force is impressed.

16 July 2015GLG510 Advanced Structural Geology Force: Newton’s Laws of Motion m = mass v = velocity vector t = time a = acceleration vector

16 July 2015GLG510 Advanced Structural Geology Force: Newton’s Laws of Motion Dimensional analysis: fundamental units Mass = amount of material in a body Weight = Force due to gravity action on a body 1 liter of water has a mass of on earth it weighs on the moon it weighs

16 July 2015GLG510 Advanced Structural Geology What does a Newton feel like? -Davis and Reynolds, p. 101

16 July 2015GLG510 Advanced Structural Geology Force: Newton’s Laws of Motion Law III: To every action there is always opposed an equal reaction, or the mutual actions of two bodies on each other are always equal in magnitude and opposite in direction

16 July 2015GLG510 Advanced Structural Geology Stress simply Simple definition of stress (for the moment) = pressure -D+R, p. 105

16 July 2015GLG510 Advanced Structural Geology Stress and deformation Rheology: relationship between stress and deformation

16 July 2015GLG510 Advanced Structural Geology Stress and deformation Use your stress and deformation words correctly: StressDeformation (strain) TensionExtension CompressionContraction or shortening -watch out for Art Sylvester!

16 July 2015GLG510 Advanced Structural Geology

16 July 2015GLG510 Advanced Structural Geology Tractions and stress A more strict definition of stress Traction is stress relative to a surface through a point p. Stress tensor is the field of tractions acting over a point p. Stress field is the entire collection of stress tensors in a body.

16 July 2015GLG510 Advanced Structural Geology Tractions and stress Start with equilibrium (Newton’s 3 rd Law): Resolve each into its components in the coordinate directions

16 July 2015GLG510 Advanced Structural Geology Tractions and stress Total torque must vanish

16 July 2015GLG510 Advanced Structural Geology Tractions and stress Rock quarried from the earth

16 July 2015GLG510 Advanced Structural Geology Tractions and stress Sign Conventions: compression positive -Fundamentals of Rock Mechanics by Jaeger and Cook (3 rd ed., p. 10) In many engineering situations, we consider tension as positive and compression negative. This is not usually the case in structural geology.

16 July 2015GLG510 Advanced Structural Geology Tractions and stress

16 July 2015GLG510 Advanced Structural Geology Tractions and stress (a) “Traction” or “Stress vector” (b) Equilibrium “Cauchy’s relationship (c) Components of the Traction Vector

16 July 2015GLG510 Advanced Structural Geology Stress tensor

16 July 2015GLG510 Advanced Structural Geology Stress tensor

16 July 2015GLG510 Advanced Structural Geology

16 July 2015GLG510 Advanced Structural Geology 3D Stress tensor Note that the opposite sides have the stress components too!

16 July 2015GLG510 Advanced Structural Geology Stress tensor

16 July 2015GLG510 Advanced Structural Geology Andersonian Faulting Theory Key assumptions: –Earth’s surface is a free surface (so it has no shear tractions acting along it). Therefore,  1,  2,  3 must be either parallel or perpendicular to it. –A fault will slip in the direction of maximum resolved shear traction

16 July 2015GLG510 Advanced Structural Geology Andersonian Faulting Theory Davis and Reynolds, p. 306

16 July 2015GLG510 Advanced Structural Geology Andersonian Faulting Theory Davis and Reynolds, p. 306

16 July 2015GLG510 Advanced Structural Geology Andersonian Faulting Theory Rowland and Duebendorfer

16 July 2015GLG510 Advanced Structural Geology -Engelder, 1993, Stress regimes in the lithosphere, Princeton Univ. Press

16 July 2015GLG510 Advanced Structural Geology

16 July 2015GLG510 Advanced Structural Geology

16 July 2015GLG510 Advanced Structural Geology

16 July 2015GLG510 Advanced Structural Geology

16 July 2015GLG510 Advanced Structural Geology World Stress Map

16 July 2015GLG510 Advanced Structural Geology North America Stress Map