Two different aspects of the behavior of soil as a two-phase medium are studied, namely, the consolidation of soil and scaling relations for soils in centrifuge testing.
PART A
First a consistent approach is presented that unifies all current theories of consolidation of soil. For one-dimensional finite strain consolidation, a Lagrangian finite element scheme is then given and tested against three different experiments and found to give consistent results. For a quick solution to a particular problem, the regular perturbation method applied to the formulation in which the dependent variable is the natural strain is shown to give the most consistent results. For the Eulerian formulation, the material derivative contains a convective term. This convective effect is then analytically studied and found not to be negligible for a final natural strain greater than 10%. A method is then introduced that can account for both the moving boundary and the convective effect. This method is tested in a finite difference scheme and found to give identical results with the Lagrangian finite element scheme for the one-dimensional case. Finally the method is used for the axisymmetric problem of consolidation by vertical drain. The solution to this case suggests that arching and subsequent load redistribution should be considered.
PART B
Conceptually, when a centrifuge is used to test models, the centrifuge is assumed to produce an equivalent ng gravitational field (as on another planet) and the behavior of the model in the ng field is then assumed to be similar to that of the prototype. For most static problems, the centrifuge does model the prototype well but for some dynamic problems, these assumptions can break down. To investigate this, the similarity requirements are examined for the case of a single particle moving in a fluid. It is found that for the post-liquefaction process and for seepage flow, unless the Reynolds number is much less than one in both model and prototype, the centrifuge is not a good simulation of the prototype situation. But, perhaps contrary to expectations, the breakdown is due to the fact that the behavior in the ng planet is not similar to the prototype ig planet, whereas the centrifuge does simulate the ng planet well. Further, it is shown that the concept of "modeling of models" can lead to misleading results. Lastly, for cratering experiments, it is concluded that the centrifuge will only model the crater shape just after an explosion and not the final crater shape.
