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Advanced Structural Geology


GEOL 542 (3 credits)

Fall 2013
2 lectures per week: TR 11.00-12.15pm
Mines 306


Simon Kattenhorn
Department of Geological Sciences
Office: McClure 303B
Phone: (208) 885-5063


Office Hours: Tuesdays (1.30-3.00 pm)



Course Description

Concepts of linear elastic fracture mechanics as applied to the classification, origin and evolution of all types of rock fractures; continuum theory in rock mechanics; rock strength and failure criteria; stress tensors; elastic theory.


Vein infill of a fracture in metamorphic rocks north of Lake Superior, Ontario, Canada.

Stress field (isochromatics) around a dilating crack as measured in photoelastic material.


Prescribed Course Materials:

Lecture:

Textbook: Fundamentals of Structural Geology (Pollard & Fletcher). Cambridge Press (available in the UI bookstore)



Additional Reading (not required):

Fundamentals of Rock Mechanics, 4th ed. (Jaeger, Cook, & Zimmerman)
Fracture Mechanics of Rock (Atkinson)
Theory of Elasticity, 3rd ed. (Timoshenko & Goodier)


Course Breakdown:

1. Introduction. Definition of geomechanics and rock fracture mechanics. Importance of geomechanics and rock fracture studies. Rock rheology. Types of fractures in the Earth and their importance. Terminologies for natural fracture systems. Fractures from a mechanical perspective. Methodologies for geomechanical analyses. One-day field trip.

2. Deformation criteria. Physical quantities and units. What is a continuum? Coordinate systems and reference frames. Force and pressure. Tractions on a surface.

3. Stress. Introduction to stress. Mohr circles. Stress measurements in the Earth. Introduction to displacements and strain.

4. Elasticity fundamentals. Definition of elastic behavior. Relationship between stress and strain. Elastic constants. Evidence of elastic response in the Earth.

5. Rock mechanics. Theoretical strength of rocks. Determination of elastic moduli. Laboratory measurements of rock strength. Uniaxial and triaxial tests. Stress-strain relationships. Testing machine behaviors. Comparison of laboratory experiments to behavior in the Earth.

6. Failure in a continuum. Continuum criteria for strength. Mathematical criteria for brittle failure. Physical criteria for brittle failure. Tensile/shear strength and related fractures. Coefficient of friction. Coulomb stress. Mohr-Coulomb failure criterion. Amonton's and Byerlee's Laws. Crustal strength profiles. Ductile failure and viscosity. Lithospheric strength profiles. Crustal failure.

7. Griffith criteria for failure. Griffith-Inglis criteria for elliptical cracks in tension and compression. Derivation of crack solutions. Griffith energy criterion. Application to geological engineering.

8. Stress tensors. Mathematical overview. Definition of a tensor. Stress tensor components. Tensor notation. Relationship between traction vectors and stress tensors. Determination of principal stresses.

9. Elasticity theory in two dimensions. Physical quantities and notations. Plane strain. Plane stress. Hooke's law. Stress equilibrium. Strain compatibility. Governing equations and boundary conditions. Airy stress function. Antiplane strain. Applications to bodies with holes. Geological and engineering applications.

10. Stress functions. Complex representation of plane elastostatic problem. Westergaard functions. Stress function for uniformly loaded crack.

11. Displacement fields around cracks. Definition of displacement. Displacement field due to crack motion. Applications to planar intrusions and faults. Boundary element method and numerical models of displacement fields.

12. Stress fields around cracks. Components of stress derived from the stress function. Stress trajectories. Mean normal stress. Maximum shear stress. Near-tip stress fields. Applications to geology and geological engineering.

13. Propagation of fractures. Driving mechanisms for fractures. Stress intensity factor criterion for propagation. Energy release rate criterion. Process zones. Inelastic aspects of crack growth. Fracture propagation paths.



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Mandatory Field Trip

There will be a mandatory 7-day field trip to the Canyonlands region of southern Utah during the week of 26 September to 2 October. This will be a hiking/camping based trip so be prepared. Trip expenses have already been charged to student accounts as a course fee - no additional costs will be charged to students (however, be prepared to cover personal food costs during travel days). Please speak to the instructor for more information.



UI Civility Clause

In any environment in which people gather to learn, it is essential that all members feel as free and safe as possible in their participation. To this end, it is expected that everyone in this course will be treated with mutual respect and civility, with an understanding that all of us (students, instructors, professors, guests, and teaching assistants) will be respectful and civil to one another in discussion, in action, in teaching, and in learning. Should you feel our classroom interactions do not reflect an environment of civility and respect, you are encouraged to meet with your instructor during office hours to discuss your concern. Additional resources for expression of concern or requesting support include the Dean of Students office and staff (5-6757), the UI Counseling & Testing Center's confidential services (5-6716), or the UI Office of Human Rights, Access, & Inclusion (5-4285).



Faults and related joints in sandstone, Arches National Park, Utah.





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