Thursday, July 2, 2015

Effective Stress - Part 3

All those points contacting the grain express the full vector surface forces including shear.  Since the grain is at rest, the forces sum to zero.  When the beaker is filled with water, there is a hydrostatic pressure gradient.  Within the water itself, these forces balance to zero, and there is no flow, but the grain is exposed to a gradient.

The pressure is greater on the bottom than on the top.  So if sum the forces, there is uplift, which is called buoyancy.  The skeleton stresses on the grains are reduced, that is, the effective stress is reduced.  Now, here's the thing that loses seismologists.  If we filled the beaker with more water, or we attach a big pressure hose, there is no difference.  The gradients remain the same.

If we attach a hose to the bottom, and start injecting water, we get an unbalanced pressure gradient in the water, and it begins to flow upward (if we allow it to).  If we sum the forces on the grain, we find the balance goes to zero if the gradient keeps increasing, until it becomes zero, and the grain has no effective stress.  That is quick sand.  (Let's ignore viscous drag.)

If we reverse the pressure gradient downwards, then the effective stress increases, and the sand becomes as hard as rock.

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