Analytical solution for one‐dimensional thaw consolidation model with double moving boundaries

Abstract

AbstractA one‐dimensional thaw consolidation model considering the density change from pore ice to pore water is established, and the model describes a special type of moving boundary problem with double moving boundaries. An analytical solution for the model under a time‐varying external load is developed using certain form of superposition principle and the similarity type of general solution. Some known solutions in literature can be recovered as special cases of the analytical solution once the density change from pore ice to pore water is neglected. If the thawing front was to cease at certain time, consolidation of thawed soil in a fixed region is then encountered, and an analytical solution for the post‐thawing consolidation problem is developed using the Green's function method. Computational examples of the analytical solutions are presented. First, comparison between our model and classical model of Morgenstern and Nixon (MN model) is conducted, showing the error caused by neglecting the density change from pore ice to pore water. The MN model overestimates the excessive pore water pressure at locations near the soil surface, while underestimates it at locations near the thawing front; the error caused by neglecting the density change becomes more pronounced with increasing ice content of frozen soil. Second, comparison between the thaw consolidation process under an instant load and that under a corresponding exponential load is made. The difference in thaw consolidation behavior between the two situations mainly displays during the early stage, when there is obvious discrepancy between the two external loads; the degree of consolidation and thaw consolidation settlement are more sensitive to the discrepancy in external load than the excessive pore water pressure is.