| | | 8.2.1 Effective Normal Tractions |
We will consider gravity and plate tectonics as sources of normal stresses acting on the fault surface. In a self-gravitating, spherical earth with only radial variations in material properties, the weight of the material generates lithostatic stresses (total stress due to gravity) with no shear stresses and equal axial stresses (Mohr's circle degenerates into a point). For homogeneous material properties, the lithostatic stresses increase linearly with depth. In addition to shear stresses, plate tectonics also creates normal stresses on the fault surface, especially in the case of inclined faults. The presence of water in the interstices of the grains generates pore pressures that decrease the effective normal stresses. The three definitive cases include: when the interstices contain no water, when the interstices are saturated with water at hydrostatic pressure, and when the interstices contain water at pressures greater than hydrostatic pressure.
If little or no water sits in the interstices, the pore pressures are negligible and the effective normal stresses equal the normal stresses. For homogeneous material properties and much larger lithostatic stresses than tectonic normal stresses, the effective normal stresses increase approximately linearly with depth. If the interstices are saturated with water, then the pore pressures equal the hydrostatic pressures, and the effective normal stresses are the difference between the normal stresses and the hydrostatic pressures. Under the assumptions of homogeneous material properties and greater lithostatic normal stresses than tectonic normal stresses, the effective normal stresses again increase approximately linearly with depth, but at a slower rate due to the presence of hydrostatic pore pressures. Finally, if the confining pressures reach high enough levels, the pore pressures may approach the normal stresses causing the effective normal stresses to become negligible. In this third case the material essentially "floats." The existence of topography and density variations implies large shear stresses at depth that require large normal stresses to prevent failure. Consequently, except in localized areas, we expect the pore pressures to be no greater than the hydrostatic pressures. We also expect the normal stresses on the fault from gravity to be much greater than the stresses from plate tectonics, so that the effective normal stresses closely resemble the normal stresses from gravity. Researchers often use uniform effective normal stresses for simplicity (Olsen et al. 1997)(Ben-Zion and Andrews 1998)(Madariaga et al. 1998) without acknowledging that assuming uniform effective normal stresses with depth implies very large confining pressures. We will examine the rupture behavior for all three cases of pore pressure in chapter 9.
| | | 8.2.1 Effective Normal Tractions |