Stability analysis of circular tunnels using spatiotemporal accelerations formulated considering heterogeneity of seismic wave propagation velocities

Abstract

The space–time dependent horizontal and vertical seismic accelerations in a soil medium owing to the inhomogeneity in the shear and primary wave propagation velocities were analytically derived satisfying the boundary conditions on the ground surface and the base. The developed analytical formulations were applied to study the influence of wave velocity heterogeneity on the support pressure required for the circular tunnel stability placed in granular soils using the stress-based limit analysis in conjunction with finite elements. The support pressure was determined as the maximum normal stress exerted by the surrounding earth at its ultimate failure on the tunnel boundary. Further, the effect of frequency of seismic waves on the seismic accelerations, magnitude of tunnel support pressure and the variation of normal stress around the tunnel periphery has been presented in detail. The support pressure was found to be higher considering the heterogeneous wave velocity than the uniform one. A lower dimensionless frequency resulted in higher support pressures for a lower wave velocity ratio and higher power parameter of the power law used to model the wave velocity profile. Otherwise, for higher wave velocity ratio, the effect of power parameter diminishes, and the support pressure is higher for higher dimensionless frequency.