Stability of circular tunnels in soft ground

This paper considers the undrained stability of a circular tunnel in soft ground where the strength increases linearly with depth. Solutions are obtained which enable designers to compute the tunnel pressure that is needed to maintain stability of an unsupported heading during the construction process. These solutions take account of the ground surcharge, the tunnel geometry, the soil unit weight, a non-homogeneous undrained shear strength, and are expressed in dimensionless form. The numerical results have been obtained using finite element formulations of the upper and lower bound theorems of limit analysis. By obtaining upper and lower bound estimates on the tunnel pressure, the actual tunnel pressure required to maintain stability can be bracketed from above and below. This provides an inbuilt error indicator for the accuracy of the solutions. Some upper bounds are also presented from the use of simple rigid block mechanisms. These mechanisms are shown to give accurate upper bounds in some cases. Where possible, the theoretical predictions are compared against experimental data obtained from centrifuge and laboratory tests