State space solution of non-axisymmetric Biot consolidation problem for multilayered porous media

摘要: Abstract In this paper, the non-axisymmetric Biot consolidation problem for multilayered porous media is studied. Taking stresses, pore pressure and displacements at layer interfaces as basic unknown functions, two sets of partial differential equations, which are independent each other, formulated. Using Fourier expansion, Laplace transforms Hankel with respect to circumferential, time radial coordinates, respectively, equations presented reduced ordinary equations. Transfer matrices describing transfer relation between state vectors a finite derived explicitly in transform space. presented, three cases studied lower surface: (1) permeable rough rigid base, (2) impermeable (3) poroelastic half The explicit solution space presented. Considering continuity condition interfaces, solutions problems semi-infinite integral form. histories displacements, stresses obtained by solving linear equation system discrete values Laplace–Hankel inversions.