Scattering around a circular lining in saturated poroelastic half-space under dilatational waves

In terms of Biot's dynamic theory and elastic wave theory, the method of functions of complex variable and multi-polar coordinate is used to solve the problem of scattering around a circular lining in saturated poroelastic half-space under harmonic plane dilatational waves. Here, a circular cavity with large radius is used to replace the straight boundary of the saturated poroelastic half space. The equations of the Biot wave motion for poroelastic and the equations of the isotropic elastic wave motion for lining are decoupled to Helmholtz equations by introducing potential functions. The general solution of Helmholtz equations is given by means of the complex series expansion technology. Utilizing the general solution of the potential functions, the expressions of the displacements, stresses and pore pressures of saturated soil and those of the displacements and stresses of lining structure can be obtained by using the boundary conditions and continuous conditons. Then the variations of the coefficients of dynamic stress concentration and the pore water pressures concentration on boundaries of the lining structure are discussed for different parameter conditions. The results of the given numerical example indicate that the method is useful and efficient to the scattering of lining in poroelastic half-space.