This dissertation focuses on the development of a mechanics based soil-roller interaction model intended to determine the degree of compaction of the top soil layer. The model was calibrated with, and compared to, soils data obtained from field and laboratory tests. The model contained 2 soil layers, but can be expanded to include additional layers. This study concludes that the developed soil-roller interaction model is capable of accurately determining the degree of compaction of the upper soil layer through back calculation of the soil modulus values. The model was able to reach convergence between the calculated and measured values of roller drum deflection through a regression analysis of soil stiffness and damping characteristics. The final values of the stiffness and damping characteristics needed to achieve a 1 percent difference between the calculated and measured values of roller drum deflection fell within expected ranges for the type of material tested. Part of this study included a sensitivity analysis of the input characteristics. The results of the sensitivity analysis revealed that the output of the model was highly sensitive to the mass of the second soil layer and to the elastic and plastic stiffness characteristics within both soil layers, but relatively insensitive to the mass of the first soil layer. The lack of sensitivity to the mass of the first soil layer means that large changes in the layer mass, and by extension the density, will have little effect on the output of the model. This characteristic is a drawback for conventional, density based specifications. However, specifications based on installing fill to the designed values of stiffness or modulus could benefit from the model. Much of the initial difference between calculated and measured roller drum deflection was probably caused by the difficulty in determining accurate starting values for the soil stiffness, damping and mass model characteristics. Future research should focus on ways to determine accurate values of the required input characteristics.

"We focus attention on single-punch compaction of metal powders in cylindrical dies. In one case, we consider solid cylindrical compacts, and take the die walls to be frictionless in order to isolate the effects of initial nonuniformities in powder fill on the final green density distribution of the compact. First, a model is introduced in which the die is filled with n distinct powders that occupy concentric annular regions within the die. The model requires that the balance of mass, the balance of momentum, and a realistic equation of state be satisfied in each region, and includes a plausible constitutive relation that relates the induced radial pressure in each powder region to the corresponding axial pressure and the relative movements of the interfaces that confine the region. For specified powder properties, the model predicts the movements of the interface between the powders, the final density in each region, the pressure maintained in each region, and the total compaction load required. In the special case of two powders (n=2), we predict how the radial movement of the single interface depends on the mismatch between the properties of the two powders. For large values of n, and for powder properties that change gradually from one powder to the next, the model approximates a single powder filled nonuniformly in the die. Finally, a model is developed for a single powder with continuously varying powder properties. Formally, the model may be obtained by taking the limit of the n-powder model as n becomes unbounded. Employing the continuous model, we determine how nonuniformities in initial fill density can be offset by nonuniformities in other powder properties to yield perfectly uniform green densities. In a second case, we consider axisymmetric, hollow, cylindrical compacts, and include the effects of friction at the die wall and the core rod. The ratio of the induced radial pressure to the applied axial pressure is assumed to be constant throughout the compaction, and Coulomb friction acts between the powder and the die wall as well as between the powder and the core rod. We derive a closed form solution for the axial and radial variation of the axial pressure, radial pressure, and shear stress throughout the compact. This solution is combined with a plausible equation of state to predict the final green density distribution and the variation of applied load throughout the compact."