Rainbow Bridge vibration risk assessment: Ambient vibration testing and computer modeling results for Rainbow Bridge

Moore, Jeffrey

Rainbow Bridge is an exceptionally rare natural arch with deep cultural significance. This study analyzed the potential for aircraft, specifically helicopters and fixed-wing propeller-driven airplanes, to generate noise (i.e. air pressure waves) that excites resonance of Rainbow Bridge. Helicopters in particular emit noise at frequencies between ~10-30 Hz, controlled by the blade-pass frequency of the main rotor, which is in the range of known resonant frequencies for many natural structures. This noise is maximized in the plane of the main rotor and increases with forward air speed. When a periodic air pressure pulse acts on a structure with similar natural frequency, resonance can be excited, generating large deformations, internal stresses, and potential damage. We measured the natural frequencies of Rainbow Bridge during a field test recording ambient vibration data (i.e. no forced excitation). Using data from two broadband seismometers placed on the bridge, compared to two nearby reference stations, we distinguished several modes of vibration for Rainbow Bridge: results show strong spectral peaks at resonant frequencies of 1.1, 2.2, 2.5, 4.2, 4.4, 5.2, 6.2, 7.9, and 9.6 Hz. Each spectral peak was then processed for polarization attributes in an attempt to clarify the modes of vibration from experimental data; e.g. the fundamental mode at 1.1 Hz represents out-of-plane flexural bending of the arch. These modes were further explored through numerical modal analysis, where we used a new 3D photogrammetric model of Rainbow Bridge to predict the complete vibrational response. Results compare well with measured data, and we are able to match seven out of the first eight modes within expected margins of error. Wind generated strong vibration of the bridge, exciting resonance, while large site-to-reference spectral ratios resolved from experimental data indicate high amplification on the bridge as compared to nearby bedrock. While the lowest modes of vibration of Rainbow Bridge appear to be insensitive to helicopter or fixed-wing propeller aircraft excitation (i.e. well below typical blade-pass frequencies), significant higher-order modes may be excited by helicopters with unknown consequences for global or local rock mass damage. Moreover, several partly detached slabs on each bridge abutment may have unique resonant frequencies capable of being excited by helicopter noise, with unknown effects. Due to the complex composition of Rainbow Bridge, combined with its exceptional cultural significance, I recommend adopting conservative guidelines for aircraft standoff distances. Specifically, I recommend prohibiting helicopter flight within a ¼ mile (1320 ft or 400 m) horizontal radius of Rainbow Bridge for elevations below 5000 ft a.s.l. (i.e. 1050 ft or 320 m above the top of the bridge). Future field testing would be required to determine if the selected avoidance distances are sufficient to limit induced vibrations below the proposed velocity threshold for damage avoidance of 2 mm/s. I further compiled and analyzed data from several past Bureau of Reclamation reports, and conducted preliminary structural and thermal deformation analyses of Rainbow Bridge using the 3D numerical model. The results help inform proposed future studies and long-term monitoring to capture cumulative effects of natural and anthropogenic vibration sources. Wind may be one of the most damaging natural vibration sources affecting Rainbow Bridge, while a search of the USGS earthquake catalog revealed no likely damaging events have occurred in the past 35 years.

Rainbow Bridge vibration risk assessment: Ambient vibration testing and computer modeling results for Rainbow Bridge

Series