Dynamic Response of a Fractured Tunnel to Seismic Waves, 14-9116 Printer Friendly VersionPrincipal Investigators Chris L. Hackert Amitava Ghosh Pei-cheng Xu Inclusive Dates: 01/15/99 - 01/15/2000
The static analysis of the combined response of fractured tunnels has already been reported. However, the reduction of the stiffness and integrity of the excavation due to fractures is far more significant under dynamic loads than static loads. In particular, upon oblique incident waves, the cavity acts as a wave guide, longitudinally, circumferentially, or both. Studies by the Lawrence Berkeley National Laboratory have shown that fractures also serve as hosts for guided waves. Guided waves are known to be energy focused and less attenuated than bulk waves. The composite guide waves due to both the excavation and fracture are more pronounced and complicated then that due to the excavation or fracture alone. The dynamic response of cavities and fractures to incoming waves has been studied extensively but separately in seismic literature. To the author's best knowledge, no quality models prior to SwRI work currently exist to predict the dynamic response of an excavation in a fractured host medium to incoming waves.
In the BIE, the unknown displacement components on the excavation boundary are coupled in boundary integral equations. The coefficients of the unknown quantities are the stress tensors associated with the Green's functions of the unbounded host rock in the absence of the tunnel and fractures. The displacements along the free surface of the excavation are then solved by the linear equations resulting from discretization of the integral equation. Finally, displacement and stresses at any given field location can be determined through direct evaluation of the boundary integral using the previously obtained boundary displacements.
Numerical results were obtained for different excavation shapes such as circle, slot, loaf, and dome intercepted by a fracture or fractures. Hoop stress on the surface of the excavation, as well as displacement and stress fields around the excavation, were computed and plotted in various forms. These results involve typical values of slip stiffness, fracture location, and orientation, frequency, and incident angle. The team found that an intersecting fracture re-distributes and usually amplifies the stress along and around the surface of the cavity. For certain combinations of the above parameters, the stress amplification and complication can be significant. An example is given in the illustration below. A 0.25-kilohertz P-wave is impinging, at 45°, a dome cavity (5 meters in height and 3 meters in width) with a horizontally crossing fracture at a height of 3 meters. The parameters of the host medium include: P wave speed , 1.754 kilometers per second; S wave speed, 1.0 kilometer per second; and mass density, 1.0 gram per cubic centimeter. Hoop stress is plotted on the boundary. The normalized normal and shear slip stiffness values used were 0 (free fracture), 2, 16, 400, and infinity (nonslip). It can be seen that the strongest stress concentration occurs not when the fracture is free, but when the slip stiffness is moderate. For very high values of slip stiffness, the hoop stress profile is approaching back toward that of the nonslip case. ^{
2001 IR&D
Home SwRI
Home
} |