Homework: 1. Turn them in whether you are done or not. I will go over all the questions with you in the next lecture. 2. Class presentations: You must give me the paper title, year, author name, journal name, and page numbers by the end of the week. 3. Format of the presentations: (a) Ten minutes per person, allowing 12 minutes questioning session after each talk. (b) You should have no more than 10 slides. (c) Your talk must consists of the following components: (1) the main problem to be addressed, (2) methods used for data collection, (3) authors interpretations, and (4) your critics of the strength and weakness of the paper. 4. You should dress up as a professional for the presentation, a chance to practice interviews or professional presentations in future. 5. The contents of student presentations will appear in your test.
Structural Geology
1. Discontinuous Deformation (Faulting and Joint Formation)
(a) Non-coaxial strain => Riedel shears (b) Coaxial strain => Coulomb fractures
Study of Rock Deformation
2. Continuous Deformation (Flow expressed by folding and fabric development)
We need to relate deformation to strain state and then stress state.
Structural Geology: Strain
1. What is strain? A quantitative measure of deformation. 2. How is strain quantified? a. Linear strain: extension (e) = (Lf-Lo)/Lo stretching (S) = Lf/L0 quadratic elongation ( ) = S2 b. angular strain and shear strain: Angular (1) strain ( ) is measured by the angle departing from the original orthogonal relationship due to deformation. (2) Shear strain = tan() c. volume strain: = V/V
Terminology in strain analysis: a. Infinitesimal stain b. Finite strain c. Strain paths d. Incremental strain e. Homogeneous strain f. Coaxial and non-coaxial strain
1. Relationship between displacement field and strain: A strain tensor can be expressed by gradient. components of displacement. 2. Relationship between velocity field and strain rate: A strain-rate tensor can be expressed by gradient components of displacement.
For a velocity field V = (ux, uy, uz), the velocity gradient matrix is
ui,j = () (ui,j + uj,i) + () (ui,j uj,i), in which deij/dt = () (ui,j + uj,i) is the strain rate tensor, and W = () (ui,j uj,i) = (w1, w2, w3) represent three local rotation rates about x, y, and z axis and together known as vorticity. When vorticity is zero deformation is coaxial. When vocticity is not zero, deformation is coaxial.
Rheology = constitutive equations: relationship between stress and strain at a given pressure and temperature condition: 1.Elastic materials: stress is proportional to strain. 2.Newtonian viscous materials: stress is proportional to strain rate. 3.Power-law materials: stress is proportional to a power of strain rate. 4.Plastic deformation: Material breaks/fails when shear stress reaches a critical value.