Supplementary lecture materials.
Stress field (isochromatics) around a dilating crack as measured in photoelastic material.
Course Syllabus:
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.
Prescribed Textbook:
Fundamentals of Structural Geology (Pollard & Fletcher) - Cambridge Press (available in the UI bookstore)
Electronic Materials:
Homework exercises, syllabus, and lecture outline.
Supplementary lecture materials.
Stress field (isochromatics) around a dilating crack as measured in photoelastic material.
Course Syllabus:
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.
