Cavity expansion theory has been well-developed in the past few decades, but little progress has been made to cavity expansion theory regarding biaxial in-situ stresses. Owing to the two-dimensional nature of cavity expansion under anisotropic in-situ stresses, a rigorous analytical or semi-analytical solution is no longer available for such cavity expansion problems. In this paper, a numerical study is performed to investigate the drained expansion responses of a cylindrical cavity under biaxial in-situ stresses. The advanced anisotropic S-CLAY model integrated by the fully implicit backward Euler algorithm is implemented as a user defined materials (UMAT) subroutine in the finite element model (FEM) to represent the elastoplastic behaviours of the anisotropic soils during cavity expansion. The FEM is validated by comparing with a benchmark semi-analytical solution under the uniform in-situ stress. The expansion responses under biaxial in-situ stresses, including the distributions of stress components, the evolutions of expansion pressures, stress paths and yield surfaces, are subsequently investigated on leverage of the FEM and compared with those from approximate solutions. The present FEM in conjunction with the UMAT subroutine provides a benchmark for validation of approximate solutions and the outcomes give significant insights into practical geotechnical problems pertaining to cavity expansion under biaxial in-situ stresses.
Geosynthetic materials are widely adopted as part of barrier liners in landfills, while the existence of defects in geomembrane (GM) will significantly reduce the barrier efficiency and lead to unexpected pollution in the surrounding environment. In this study, a novel semi-analytical model was proposed to investigate the two-dimensional (2D) migration of organic contaminant through the GM with strip defects to the underlying soil liner (SL). This model has the superiority to consider the concentration condition in the defects, and describe more accurate concentration profiles in the SL. The combination of discretization method and integral transforms were applied to obtain semi-analytical solutions, which were then verified by numerical solutions. Results show that the existence of defects can substantially accelerate the migration process of contaminant through flawed GM to the underlying SL. Specifically, the time interval between migration curves in the model with defects can be 2 or 3 orders of magnitude shorter than that without defects under the same condition.
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