Upper-bound stability analysis of a plane strain heading in non-homogeneous clay

•We study tunnel stability in non-homogeneous soil using the multi-rigid-block method.•The collapse pressure increases as soil gravity increases or strength decreases.•New mechanism intermix inhomogeneous deforming region and rigid blocks translation.•An upper bound analytical solution for the plane strain heading is obtained.

This paper investigates the undrained stability of a plane strain tunnel heading in cohesive soil, whose undrained shear strength is assumed to increase linearly with depth. Upper bound stability solutions for a practical range of parameters of geometries and soil conditions are found using the multi-rigid-block upper bound method. The upper bound solutions obtained from the multi-rigid-block mechanisms significantly improve the classical solutions and have good agreement with those of the finite element limit analysis when C/D is small. An improved simple collapse mechanism which intermix inhomogeneous deforming region and rigid blocks translation together is proposed based on the multi-rigid-block upper-bound analysis. An upper bound analytical solution is then obtained in view of the numerical results of both the multi-rigid-block collapse mechanism and the improved simple collapse mechanism. And it predicts the plane strain heading stability relatively accurate for shallow tunnels.