Existing solutions for analyzing one-dimensional (1-D) consolidation of unsaturated soil are only derived to cater to two extreme drainage conditions (fully drained and undrained). This study presents a new explicit solution for 1-D consolidation of unsaturated soil with semi-permeable drainage boundary. Based on the assumptions of two independent stress variables and the governing equations proposed by Fredlund, the eigenfunction expansion method is adopted to develop an explicit analytical solution to calculate excess pore-water and pore-air pressures in an unsaturated soil when it is subjected to external loads. The developed general solutions are expressed in terms of depth, z, and time, t. For the semi-permeable drainage boundary, eigenvalues and eigenfunctions in the space domain are developed. The technique of Laplace transform is used to solve the coupled ordinary differential equations in the time domain. The newly derived explicit solution is verified with the existing semi-analytical method in the literature, and an excellent agreement is obtained. Compared with the semi-analytical solution, the newly derived analytical solution is more straightforward and explicit so that this solution is relatively easier to be implemented into a computer program to carry out a preliminary assessment of 1-D consolidation of unsaturated soil.
In multiphase flow analyses, rheological behavior has a significant influence on not only the heat and mass transfer but also the dynamics of the solid and fluid during melting and solidification. Based on previous work, it is possible to consider rheological behavior by estimating the viscosity of the liquid phase with its compositional development. The present study investigates this rheological behavior through simulations of multiphase heat transfer problems using the moving finite volume particle (FVP) method, by introducing a viscosity model that takes into account viscosity changes due to phase changes. To validate the applicability of this viscosity model, a series of melting experiments using Wood's metal are conducted, and the observed melting characteristics form the basis for computer simulations and 3D numerical analysis using the FVP method. Good agreement between simulation and experiment indicates that the proposed viscosity model reproduces well the rheological behavior during melting.
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