Stress analysis around a tunnel in a gravitating poroelastic half plane

The present work deals with the mechanical behaviour of a circular tunnel embedded in a semiinfinite poroelastic half plane under gravitational body forces. Owing to the geometric layout, reference is made to bipolar cylindrical coordinates (, ) and symmetry occurs with respect to  coordinate. The fluid flux is assumed stationary, thus making the fluid pressure p a harmonic field, being Cn, Dn unkonwn arbitrary constants. The problem is governed by the following Navier equation in terms of the displacement field the solid phase, where  denotes the elastic shear modulus of the solid phase, g is the ground acceleration, e1 denotes the unit vector of the vertical axis, n is the porosity and the (real and positive) parameters and sw characterize completely the mechanical response of the poroelastic soil according to the Bowen formalism [1]. A particular solution of eqn (2) is found in closed form by introducing a Helmholtz potential for the displacement. However such a solution does not accomplish the BCs at the ring of the tunnel and at the free surface of the half plane. Then, by following the Jeffery procedure [2], an auxiliary Airy stress function is introduced that, added to the fundamental solution, allows accomplish the BCs. Two limit situations are considered at the ring of the tunnel. In particular, a given radial pressure acting at the ring of the tunnel (Dirichlet BCs) and a given fluid flux across the contour of the tunnel (Neumann BCs) have been considered [3]. The latter situation allows investigating the effect of a tunnel having an impermeable surface embedded in a gravitating poroelastic soil. Results in terms of fluid pressure and stress near the rim of the hole as well as at the free surface of the half plane are analysed in detail varying both the geometric and constitutive parameters of the system.