Since the wide applicability of axisymmetric consolidation model, the axisymmetric consolidation problem of unsaturated soils has gradually become a hot issue. However, the mixed boundary conditions of axisymmetric free strain consolidation of unsaturated soils have not been fully considered. The boundary condition is the main factor affecting the consolidation process with the determined consolidation model and related parameters. In this paper, the governing equations of water and air in the polar coordinate were given according to two stress state variables theory of unsaturated soils, Darcy’s law, and Fick’s law under the axisymmetric condition. Based on the free strain hypothesis, a series of semianalytical solutions of the axisymmetric consolidation for unsaturated soil grounds under four different boundary conditions are proposed by using the Laplace transform and the finite Hankel transform. After the correctness of the proposed governing equations and semianalytical solutions is verified by degeneration verification, the parametric consolidation characteristics of unsaturated soils under different parameters through numerical examples and parametric studies are analyzed. Combining the four boundary conditions, the entire consolidation process under homogeneous boundary will be overestimated compared to that under the mixed boundary. In other words, the time required to complete consolidation will be extended accordingly if the boundary condition is not homogeneous. It is clear that the study on the axisymmetric consolidation of unsaturated soils considering multiple boundary conditions is conducive to a more comprehensive understanding of unsaturated soils and provides strong theoretical support for engineering practice.
The backfill construction of a utility tunnel is as important as its main structure construction. While the existing research on utility tunnels focuses on the construction of the main structure, rare attention has been paid to the backfill construction. In this paper, with a practical comprehensive utility tunnel project as the background, a variety of different backfill construction schemes were designed, and the corresponding numerical simulations were performed with the finite element analysis software Midas. The influence of different backfill construction schemes on the side wall, roof, and floor of the utility tunnel was systematically studied and analyzed, and the displacement and stress variation curves in the process of utility tunnel backfill were obtained. Based on the simulation results and the actual engineering situation, the optimal schemes for utility tunnel backfill construction were determined. The results show that the displacement of the side wall of the utility tunnel increased first and then decreased with increasing backfill soil in the unilateral backfill mode, and there was little displacement in the bilateral backfill mode. The shear stress of the side wall of the utility tunnel in both the unilateral and bilateral backfill modes gradually increased with the backfill process. Within the region 1 m above the roof of the utility tunnel, backfill modes had no effect on the final stress and displacement values, but the layering method made a difference. Accordingly, bilateral backfill mode is suggested for the region below the roof of the utility tunnel, while in the case of region 1 m above the roof, backfilling is recommended to be layered according to height rather than position.
This paper studies the one-dimensional (1D) consolidation behavior for unsaturated stratum subjected to piecewise cyclic loading. Combined with the widely accepted consolidation theory of unsaturated soils, a semianalytical method was employed to investigate the consolidation of unsaturated foundation considering piecewise cyclic loading in the Laplace domain. Furthermore, the reduced solutions were produced to perform the verification work accompanied by the results in the existing literature. Finally, a case study was conducted to explore the consolidation characteristics under piecewise cyclic loading (i.e., triangular and trapezoidal cyclic loadings). Parametric studies were carried out by variations of excess pore pressures and settlement against the ratio of air-water permeability coefficients, depth, and loading parameters. The research proposed in this paper can provide theoretical basis for the ground treatment of unsaturated soils, especially for rationally accelerating consolidation or avoiding sudden settlement.
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