The report documents studies refining the procedures for calculation of one-dimensional consolidation behavior of very soft fine-grained dredged material. Both the conventional small strain theory of consolidation, which requires linear or constant soil properties, and the more general finite strain theory, which provides for nonlinear soil properties, are presented. Implications of the simplifying assumptions necessary in practical application of the theories are discussed and the general finite strain theory is shown to be superior for the treatment of dredged material. The governing equations for both theories are written in nondimensional terms and appropriate boundary and initial conditions are specified. Solutions in terms of figures relating the percent consolidation to the nondimensional time factor for small strain theory have been previously published. However, similar solutions based on the finite strain theory were not available and thus had to be developed. Using a computer program, a linearized nondimensional form of the general finite strain governing equation was solved for the cases of singly/doubly drained normally consolidated clays, and singly/doubly drained dredged fill. The figures given represent a significant advancement in the ability to accurately predict the consolidation behavior of thick deposits of very soft fine-grained materials having nonlinear soil properties. A method of obtaining soil parameters necessary for use of the new solution charts is proposed. (Author).