Research On Analytical Solution Of The Control Equation Of One-dimensional Finite Strain Consolidation

Since one-dimensional finite strain consolidation theory was proposed by Gibson in 1967, the study of it has never stopped, whether from the form of equations or the solution of equations. On the form of the control equations: there are equations based on the description of the different coordinates, and equations based on solid mechanics or continuum mechanics, as well as the equations that use different control parameters. On solving the equations, the finite element method based on the numerical solution develops much faster than the complete analytical solution. Besides, the semi-analytical and semi-numerical method is also adopted in this field, but it is scarcely applied in practical engineering.Under the description of material coordinates, the equation controlled by pore-solids ratio variables e is the simplest form; and under the description of space coordinates,the equation controlled by porosity ratio variable n is the simplest form. Because the equation of one-dimensional finite strain consolidation is a strongly nonlinear partial differential equation, it is very difficult to obtain its analytical solution in the absence of any reasonable assumptions. To solve this problem, the actual physical phenomena is observed and analyzed, the reasonable and consistent with the physical phenomena assumptions are introduced, the relation of void ratio and effective stress and the relation of porosity and permeability coefficient are fitted, the equations of one-dimensional finite deformation consolidation are transferred into a nonlinear partial differential equations in the classical form (the KdV equation and the Fisher equation), and the analytical solution of equations are obtained by using classical non-linear analytical solution of nonlinear wave equations in the mathematical theory in this thesis. By applying some experimental data, the comparison of the solutions of linear and nonlinear finite strain theory, as well as the numerical solution from finite element method is presented. It is shown that the model applied in this thesis is reasonable. The analytical solution in this thesis can provide wealthy content and meaningful research ideas for further understanding and exploring one-dimensional finite strain consolidation theory. Thereby, new ways are created for broadening the research areas of one-dimensional consolidation theory and extending multi-dimensional finite-dimensional consolidation theory. In addition, the analytical solution provides the physical meaning of the problem and control parameters, and its guiding significance of understanding the nature of phenomena and laws is self-evident. It is also a reliable judgment of numerical method.