What's wrong with our understanding of Soil Liquefaction?
I submitted my paper Grain Settlement and Fluid Flow Cause the Earthquake Liquefaction of Sand to Proceedings of the Royal Society A and just received reviewer comments today. This preprint summarizes what I've found in my PhD studies with regards to how soil liquefaction works. (Also some more details on the derivation).
The key finding is that contrary to every textbook definition of liquefaction, fluid flow is not ignorable, in fact fluid flow dynamics is a key component of how liquefaction occurs. The standard description of liquefaction involves "undrained" contraction of soil grains during shaking causing an increase of fluid pressure, and a transfer of total stress from the grain-grain contacts to the water pressure. If the water pressure gets high enough, the grains carry no stress and hence can not transfer shear stresses. At this point the slurry flows like a liquid.
Although it's been known that "void rearrangement" could occur (in which grains move one way and water moves the other), it was treated as a special case of soil liquefaction behavior. However, centrifuge scale-experiments and specialized tabletop experiments performed in the last decade have called this in to question, and the standard triaxial tabletop experiments involving 10 to 20cm sized samples of soil require enormous deformations that are unrealizable in-situ before water pressure exceeds total vertical stress. Why is soil so hard to liquefy in a triaxial machine?
Tabletop triaxial experiments involve sand and water wrapped in a completely impermeable rubber membrane, so that the total mass of water inside the membrane remains constant. In the soil, water can conduct from one place to another through the inter-grain spaces. The standard description assumes that such conduction is slow compared to the duration of an earthquake, and this assumption is so strong that some researchers have actually tried to compensate for the bulging of the membrane in these tabletop experiments under the assumption that even the slightest conduction of water causing the membrane to bulge would be more than the actual conduction in-situ.
The truth may be hard for the Geotech community to swallow. My analysis shows that for typical loose sands, water pressure transmission via fluid flow occurs over tens of meters on timescales of substantially less than a single earthquake loading cycle. In the paper I derive a dimensionless equation that describes the phenomenon in the top ~ 10 meters of surface soil and I show that the equation can be solved for equilibrium conditions to determine approximately the water pressure field. We can use an equilibrium solution rather than a dynamic time-varying one because equilibriation occurs so quickly compared to the earthquake duration. I then solve the equation for a variety of special cases that are relevant to actual physical experiments and show how the equation predicts the qualitative results of those experiments.