Semi-analytical solutions to two-dimensional plane strain consolidation for unsaturated soil

• Published in: Computers and geotechnics 2018-09, Vol.101, p.100-113
• Main Authors: Wang, Lei, Xu, Yongfu, Xia, Xiaohe, Sun, De'an
• Format: Article
• Language: English
• Subjects: Boundary conditions; Consolidation; Differential equations; Finite element analysis; Finite sine transform; Homogeneous and mixed boundaries; Laplace transform; Laplace transforms; Mathematical analysis; Mathematical models; Partial differential equations; Plane strain; Semi-analytical solution; Soil; Soil investigations; Soils; Strain analysis; Time domain analysis; Two dimensional analysis; Two-dimensional plane strain consolidation; Unsaturated soil; Unsaturated soils
• ISSN: 0266-352X; 1873-7633
• DOI: 10.1016/j.compgeo.2018.04.015

This paper presents semi-analytical solutions to two-dimensional plane strain consolidation of unsaturated soils under different initial and boundary conditions. By applying the finite sine and Laplace transforms, the partial differential equations are converted to the ordinary differential equations. The semi-analytical solutions are obtained by using the finite sine inversion transform. Crump’s method is adopted to perform the inverse Laplace transform to obtain analytical solutions in time domain. The present solutions are more general and can be degenerated into conventional solutions to one-dimensional consolidation of unsaturated soils. Several examples are provided to investigate two-dimensional plane strain consolidation behavior of unsaturated soils.