Geomechanics - Gphy 5813
Outline

• Introduction -- Rheology of the Earth
• Mechanics of the Lithosphere
  • Tensors
  • Stress
    • coordinate transformation of stress, Mohr's circle
    • stress invariants
    • hydrostatic (isotropic) stress, pressure
  • Strain
    • coordinate transformation of strain
    • strain invariants, dilatation
  • Elasticity
    • Hooke's Law
    • elastic constants
    • uniaxial stress, strain
    • overburden stresses
    • plane stress, plane strain
    • thermoelasticity
  • Elastic plate theory
    • bending of a plate under applied moments or loads
    • deformation of strata overlying an igneous intrusion
    • buckling of a plate under a horizontal load
  • Bending of the lithosphere
    • elastic plate with hydrostatic restoring force
    • stability of the lithosphere under an end load
    • bending of the lithosphere under the load of island chains
    • bending of the lithosphere at oceanic trenches
    • flexure of the lithosphere in sedimentary basins
  • Isostasy and compensation of topography
    • Pratt, Airy, regional compensation
    • free-air, Bouguer gravity
    • periodic loading of the lithosphere
    • gravity field of a periodic load on an elastic plate
• Heat Transfer in the Lithosphere
  • Modes of heat transfer
  • Heat conduction
    • Fourier conduction law
    • Joule heating law
    • heat conduction (diffusion) equation
    • cooling of a bar; dimensionless parameters
    • measurement of heat flow
  • Periodic heating of a semi-infinite slab
  • The Stefan problem: cooling and solidification of magmas
  • Cooling of oceanic lithosphere
    • temperature distribution
    • heat flow
    • thickness of the lithosphere
    • subsidence of oceanic lithosphere
  • Thermal subsidence of sedimentary basins
  • Temperature effects of faulting
    • effects of overthrusting on geothermal gradients
    • mechanics of faulting
    • Anderson theory of faulting
    • frictional heating along faults
• Fractals and Geology [time permitting]