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.