Analytical Solution and Consolidation Analysis of One-dimensional Large Strain Consolidation Differential Equation

Abstract

Abstract:: According to the universal one-dimensional consolidation equation introduced by Gibson, the governing equation with the excess pore water pressure as the control variable is derived, and the Fourier series solution under the boundary condition of single-sided drainage is deduced in detail by the standard mathematical physical method. It verifies the correspondence between the analytical solution and the numerical solution from a theoretical point of view. Using this analytical solution, the nonlinear distribution of the excess pore pressure along the depth direction is obtained, and the traditional small strain consolidation is compared in terms of the average consolidation degree and the final settlement. Soft soil foundation, large deformation foundation Derive a consolidation equation for soft soils with large deformations using the super-static pore pressure as the control variable Formula derivation, Example analysis Based on Gibson's general equation of consolidation and its theory, the detailed derivation process of differential equations with excess pore water pressure as the control variable is given. According to the example, the image shows the distribution of excess pore pressure with depth, and comparative analysis of large and small strains, If all other conditions are the same, When mv1=1 MPa-1, it can be calculated according to the large and small strains, but when mv1≥3MPa-1, the two errors are large, The calculation must be considered separately.