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Natural arches are culturally valued rock landforms common in sedimentary rocks of the Colorado Plateau and additionally occur broadly around the world. Recent notable collapses of some of these landforms have highlighted the need to better understand the mechanics of their failure. While environmentally driven weathering has been the focus of most previous studies of arch collapse, comparably little attention has been given to anthropogenic vibration sources and how these often slight- to moderate-magnitude shaking events might steadily weaken arches over time. We collected 12–15 months of continuous ambient vibration data from arches and nearby bedrock in both anthropogenically ‘noisy’ and ‘quiet’ locations and used these datasets to develop an annual model of arch peak ground velocity based on magnitude-cumulative frequency distributions. Working from these models, we added vibration events of varying magnitude or frequency of occurrence, informed by field data, imitating arch vibration in response to different anthropogenic activities such as helicopter flights or induced earthquakes. We then applied subcritical fracture mechanics principles to predict annual crack growth rates in an idealized arch under these different vibration conditions. Our results demonstrate that in a single year, cracks grow minimally longer (∼1%) in ‘noisy’ environments than in areas not experiencing anthropogenicmore »vibration energy. Few (1+) 30-s moderate-magnitude events (∼15 mm/s) or many (>37,000) 30-s low-magnitude events (∼2 mm/s) cause markedly increased crack growth. Our approach provides a valuable new framework for assessing the range and frequency of occurrence of vibrations experienced by an arch, and for predicting arch damage. Our results, in turn, yield important new outputs applicable in support of conservation management of these and similar landforms world-wide under exposure to a range of human-induced vibration activity.« less

Abstract Modal analysis of freestanding rock formations is crucial for evaluating their vibrational response to external stimuli, aiding accurate assessment of associated geohazards. Whereas conventional seismometers can be used to measure the translational components of normal modes, recent advances in rotational seismometer technology now allow direct measurement of the rotational components. We deployed a portable, three-component rotational seismometer for a short-duration experiment on a 36 m high sandstone tower located near Moab, Utah, in addition to conducting modal analysis using conventional seismic data and numerical modeling. Spectral analysis of rotation rate data resolved the first three natural frequencies of the tower (2.1, 3.1, and 5.9 Hz), and polarization analysis revealed the orientations of the rotation axes. Modal rotations were the strongest for the first two eigenmodes, which are mutually perpendicular, full-height bending modes with horizontal axes of rotation. The third mode is torsional with rotation about a subvertical axis. Measured natural frequencies and the orientations of displacements and rotation axes match our numerical models closely for these first three modes. In situ measurements of modal rotations are valuable at remote field sites with limited access, and contribute to an improved understanding of modal deformation, material properties, and landform response to vibration stimuli.

Abstract Thousands of rock arches are situated within the central Colorado Plateau—a region experiencing small- to moderate-magnitude contemporary seismicity. Recent anthropogenic activity has substantially increased the seismicity rate in some areas, raising questions about the potential for vibration damage of natural arches, many of which have high cultural value. However, predictions of the vibration response and potential for damage at a given site are limited by a lack of data describing spectral amplification of ground motion on these landforms. We analyzed 13 sandstone arches in Utah, computing site-to-reference spectral amplitude ratios from continuous ambient seismic data, and compared these to spectral ratios during earthquakes and teleseismic activity. We found peak ground velocities on arches at their dominant natural modes (in the range of 2–20 Hz) are ∼20–180 times the velocity on adjacent bedrock, due to amplification arising from slender geometry and low modal damping (0.8%–2.7%). Ambient spectral ratios are generally 1.2–2.0 times the coseismic spectral ratios. Because arches experience highly amplified ground motion, the range of earthquakes considered potentially damaging may need to be revised to include lower-magnitude events. Our results have implications for conservation management of these and other culturally valuable landforms.

Abstract The dynamic properties of freestanding rock towers are important inputs for seismic stability and vibration hazard assessments, however data describing the natural frequencies, mode shapes, and damping ratios of these landforms remain rare. We measured the ambient vibration of 14 sandstone and conglomerate rock towers and fins in Utah, United States, using broadband seismometers and nodal geophones. Fundamental frequencies vary between 0.8 and 15 Hz—inversely with tower height—and generally exhibit subhorizontal modal vectors oriented parallel to the minimum tower width. Modal damping ratios are low across all features, between 0.6% and 2.2%. We reproduced measured modal attributes in 3D numerical eigenfrequency models for 10 of the 14 landforms, showing that the fundamental mode of these features is full-height bending akin to a cantilever. Fin-like landforms commonly have a torsional second mode whereas tower-like features have a second full-height bending mode subperpendicular to the fundamental. In line with beam theory predictions, our data confirm that fundamental frequencies scale with the ratio of a tower’s width to its squared height. Compiled data from 18 other sites support our results, and taken together, provide guidance for estimating the modal properties of rock towers required for vibration risk assessment and paleoseismic shaking intensity analysismore »in different settings.« less

Abstract. Helicopters emit high-power infrasound in a frequency range thatcan coincide with the natural frequencies of rock landforms. While a singleprevious study demonstrated that close-proximity helicopter flight was ableto excite potentially damaging vibration of rock pinnacles, the effects on abroader range of landforms remain unknown. We performed a series ofcontrolled flights at seven sandstone arches and towers in Utah, USA,recording their vibration response to helicopter-sourced infrasound. Wefound that landform vibration velocities increased by a factor of up to 1000during close-proximity helicopter flight as compared to ambient conditionsimmediately prior and that precise spectral alignment between infrasoundand landform natural frequencies is required to excite resonance. We defineadmittance as the ratio of vibration velocity to infrasound pressure andrecorded values of up to 0.11 mm s−1 Pa−1. While our resultsdemonstrate a strong vibration response, the measured velocities are lowerthan likely instantaneously damaging values. Our results serve as a basisfor predicting unfavorable degradation of culturally significant rocklandforms due to regular helicopter overflights.

Abstract. Natural rock arches are rare and beautiful geologic landforms with important cultural value. As such, their management requires periodic assessment of structural integrity to understand environmental and anthropogenic influences on arch stability. Measurements of passive seismic vibrations represent a rapid and non-invasive technique to describe the dynamic properties of natural arches, including resonant frequencies, modal damping ratios, and mode shapes, which can be monitored over time for structural health assessment. However, commonly applied spectral analysis tools are often limited in their ability to resolve characteristics of closely spaced or complex higher-order modes. Therefore, we investigate two techniques well-established in the field of civil engineering through application to a set of natural arches previously characterized using polarization analysis and spectral peak-picking techniques. Results from enhanced frequency domain decomposition and parametric covariance-driven stochastic subspace identification modal analyses showed generally good agreement with spectral peak-picking and frequency-dependent polarizationanalyses. However, we show that these advanced techniques offer the capability to resolve closely spaced modes including their corresponding modal damping ratios. In addition, due to preservation of phase information, enhanced frequency domain decomposition allows for direct and convenient three-dimensional visualization of mode shapes. These techniques provide detailed characterization of dynamic parameters, which can bemore »monitored to detect structural changes indicating damage and failure, and in addition have the potential to improve numerical models used for arch stability assessment. Results of our study encourage broad adoption and application of these advanced modal analysis techniques for dynamic analysis of a wide range of geological features.« less

Abstract We acquired a unique ambient vibration dataset from Castleton Tower, a 120 m high bedrock monolith located near Moab, Utah, to resolve dynamic and material properties of the landform. We identified the first two resonant modes at 0.8 and 1.0 Hz, which consist of mutually perpendicular, linearly polarized horizontal ground motion at the top of the tower. Damping ratios for these modes were low at ∼1%. We successfully reproduced field data in 3D numerical eigenfrequency simulation implementing a Young’s modulus of 7 GPa, a value ∼30% lower than measured on core samples. Our analysis confirms that modal deformation at the first resonant frequencies closely resembles that of a cantilever beam. The outcome is that with basic estimates of geometry and material properties, the resonant frequencies of other freestanding rock monoliths can be estimated a priori. Such estimates are crucial to evaluate the response of rock towers to external vibration inputs.