This is taken largely from Mean, Stress and Strain, Basic Concepts of Continuum Mechanics For Geologists, Springer Verlag, p. 115-117.

As you descend in the crust the vertical traction on a horizontal plane will increase due to the increasing load of rock overhead. This is known as the lithostatic gradient. Given average continental crust densities this would be .027 MPa/m, .267 bar/m, or 1.2 psi/ft. If you want a more specific number of a case, then the density times the gravitational acceleration times the depth will yield the vertical load. In this way one can compute the vertical traction with depth. In flatland, with a surface as a principal plane (one that has no shear stresses on it), the vertical traction would also be one of the three principal stresses.

Elasticity theory indicates that if you push down vertically on an interior block with a certain load, it will try to respond by horizontal extension, but adjacent rock is in the way, and so a horizontal stress traction develops. With water, which is incompressible, the horizonal stress is the same as the vertical (i.e. a hydrostatic stress state). With rock is the horizontal stress traction (on a vertical plane) is some fraction of the vertical load. A material property called Poisson's ratio helps compute what fraction. The horizontal traction witll be equal to Pr/(1-Pr) times the vertical. A typical value for Poisson's ratio is .25. However, in some situations it increases with depth. While we won't include that in our model we could.

You can then add a horizontal tectonic stress in some direction. Earthquakes often indicate tectonic stresses of 10 Mpa, and so we will use that value. Means indicate that given a common coordinate axis system, the resulting stress state from the two tensors (lithostatic and tectonic) are the simple addition of the components of the tensors. In Mean's model he does not consider how the tectonic load will induce vertical and an orthogonal horizontal components of its own as was done for the lithostatic load.

Note that at a shallow level the horizontal tectonic stress is the largest and so is sigma one, but at some depth the lithostatic gradient overcomes it and sigma one becomes vertical. This implies that different levels of the crust can be in different dynamic states with different expected kinematics. We can compute that switchover depth of sigma one.

Below are results from an excel model with a 10 Mpa E-W traction added to a lithostatic gradient and a constant Poisson's ratio of .3. Note the switchover depth is about 400 meters. Increasing Poisson's ratio increases the switchover depth.

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