Stability of a single tunnel in cohesive–frictional soil subjected to surcharge loading

This paper focuses mainly on the stability of a square tunnel in cohesive–frictional soils subjected to surcharge loading. Large-size noncircular tunnels are quickly becoming a widespread building technology by virtue of the development of advanced tunneling machines. The stability of square tunnels in cohesive–frictional soils subjected to surcharge loading has been investigated theoretically and numerically, assuming plane strain conditions. Despite the importance of this problem, previous research on the subject is very limited. At present, no generally accepted design or analysis method is available to evaluate the stability of tunnels or openings in cohesive–frictional soils. In this study, a continuous loading is applied to the ground surface, and both smooth and rough interface conditions between the loading and soil are modelled. For a series of tunnel geometries and material properties, rigorous lower and upper bound solutions for the ultimate surcharge loading of the considered soil mass are obtained by applying recently developed numerical limit analysis techniques. The results obtained are presented in the form of dimensionless stability charts for practical convenience, with the actual surcharge loads being closely bracketed from above and below. As a handy practical means, upper bound rigid-block mechanisms for square tunnels have also been developed, and the obtained values of collapse loads were compared with the results from numerical limit analysis to verify the accuracy of both approaches. Finally, an expression that approximates the ultimate surcharge load of cohesive–frictional soils with the inclusion of shallow square tunnels has been devised for use by practicing engineers.