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Short Note Dynamic Analysis of a Large Freestanding Rock Tower (Castleton Tower, Utah) by Jeffrey R

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Short Note Dynamic Analysis of a Large Freestanding Rock Tower (Castleton Tower, Utah) by Jeffrey R Bulletin of the Seismological Society of America, Vol. 109, No. 5, pp. 2125–2131, October 2019, doi: 10.1785/0120190118 Ⓔ Short Note Dynamic Analysis of a Large Freestanding Rock Tower (Castleton Tower, Utah) by Jeffrey R. Moore, Paul R. Geimer, Riley Finnegan, and Clotaire Michel 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. Supplemental Content: Two animations of the modal displacement field for the first two resonant modes of Castleton Tower. Introduction Knowledge of the dynamic properties of slender, free- natural towers, for example, offer limited access to points at standing structures is crucial to predict their response to exter- which vibration measurements can be made. Therefore meth- nal forces, for example, earthquakes (Carder, 1936; Hall et al., ods to characterize the natural modes of vibration typically 1995; Goel and Chopra, 1997). Although more than a century must rely on data stemming from only a few measurement of past research focused on characterizing the vibration proper- points (as in Dowding et al., 1983; King and Demarco, ties of man-made civil structures (e.g., Omori, 1900; Crawford 2003). Furthermore for natural features of high cultural and Ward, 1964; Clinton et al.,2006; Michel and Guéguen, value, forced vibration modal analysis techniques are rarely 2010), comparably little attention has been paid to understand- permissible, so methods are restricted to those analyzing ing the dynamics of natural structures such as rock towers ambient vibrations (e.g., Prieto et al., 2010; Moore et al., (Lévy et al., 2010; Bottelin et al.,2013; Valentin et al., 2017; 2016; Kleinbrod et al., 2019). Nonetheless, experimental Kleinbrod et al., 2019). Natural rock towers are anticipated and analytical techniques developed for civil structures are to respond in a similar dynamic manner as civil structures applicable to natural landforms and can be used to generate when excited by external forces such as wind, earthquakes, or data describing dynamic properties such as resonant frequen- anthropogenic energy. Therefore any effort to describe the cies, mode shapes, and damping. resulting structural response, and possible damage induced by In this study, we describe a rare and unique data set of these forces, requires accurate characterization of the feature’s ambient vibration measurements from one of the largest free- vibrational properties. Nonetheless, field measurements of standing rock towers in the western United States, Castleton the dynamic properties of freestanding rock towers remain Tower located near Moab, Utah. We process a limited dura- relatively rare (Dowding et al., 1983; King, 2001; King and tion dataset of continuous ambient vibration measurements Demarco, 2003; Kleinbrod et al., 2019). from the top of the tower to distinguish key dynamic proper- Although methods to measure the dynamic properties of ties for the first two resonant modes and derive an estimate civil structures are increasingly well established (e.g., Farrar for the globally averaged Young’s modulus of the feature. and James, 1997; Brownjohn, 2003; Michel et al., 2010; Li Ultimately, our description is limited by physical access to et al., 2010), measuring the dynamic properties of natural measurement points on the tower. Nevertheless, we show that landforms presents unique challenges. Foremost is access; the first modes of vibration can be recreated with numerical 2125 Downloaded from https://pubs.geoscienceworld.org/ssa/bssa/article-pdf/109/5/2125/4834142/bssa-2019118.1.pdf by Univ Utah Marriott Library user on 01 July 2020 2126 Short Note Figure 1. Map of Castleton Tower and surrounding area (see Data and Resources); contour interval is 25 m, coordinates are in meters for Universal Transverse Mercator (UTM) zone 12S. (Upper inset) Location within Utah. (Lower inset) Oblique ground-based image (credit: Ronald Scott) shows Castleton Tower—a 120 m high Wingate sandstone monolith perched atop a steep ridge composed of Chinle and Moenkopi formations (Doelling, 2002). The color version of this figure is available only in the electronic edition. eigenfrequency simulations, and reveal valuable new infor- cross-bedded eolian sandstone, and red coloration reflecting mation on material and dynamic properties of the tower high-iron content; it sits upon a steep ridge composed of itself. Our measurements represent a rare dataset that can Triassic Chinle and Moenkopi formations featuring alternat- be used to help predict the vibrational properties for dynamic ing beds of sandstone and siltstone (Doelling, 2002). The analysis of other rock towers in Utah and worldwide. tower’s monolithic nature and solitary setting contribute to its exceptional character, drawing photographers and climb- Site Description ers from across the world (e.g., Roper and Steck, 1979). Castleton Tower (also known as Castle Rock) is an Methods and Results iconic landform of the Colorado Plateau’s red-rock desert. Located 18 km northeast of Moab, Utah, the tower is a We conducted a field test to measure the ambient reso- 120 m high sandstone monolith perched on the crest of a nance of Castleton Tower on 12 March 2018 using two steep ridge (Fig. 1). The tower is composed of Jurassic Nanometrics Trillium Compact three-component broad- Wingate sandstone, massive with thick beds of fine-grained, band seismometers with 24-bit Centaur data loggers. The Downloaded from https://pubs.geoscienceworld.org/ssa/bssa/article-pdf/109/5/2125/4834142/bssa-2019118.1.pdf by Univ Utah Marriott Library user on 01 July 2020 Short Note 2127 instruments recorded data continuously for nearly 3 hr at 100 Hz, with one seismometer located directly on top of Castleton Tower (CASTA), and the other instrument located ∼100 m north of the base of the tower on the bedrock ridge serving as a reference (CASTB). Each seismometer was leveled, aligned to magnetic north, and enclosed within an insulating cover. The deploying climbers stayed with the equipment throughout the length of the recording. Because Castleton Tower is a popular climbing destination, portions of the record featured anthropogenic noise caused by climb- ers on the summit. We process seismic data following methods outlined by Koper and Burlacu (2015) and Koper and Hawley (2010) to obtain frequency content and polarization attributes of ambi- ent noise. Figure 2 compares the power spectra from stations CASTA and CASTB. We observe strong spectral peaks at 0.8 and 1.0 Hz at CASTA that are only weakly present at CASTB, which we identify as the first two resonant modes of Castleton Tower. We further obtain polarization attributes for select natu- ral frequencies, providing azimuth and inclination of particle motion at the location of seismometer CASTA. The first two resonant frequencies of Castleton Tower show strongly polar- ized and mutually perpendicular, subhorizontal ground motion (Fig. 2), whereas higher order modes are observed but cannot be interpreted due to the limited spatial sampling (i.e., single sensor deployed on the tower). We further explored the experimental dataset by processing ambient seismic recordings using the enhanced Figure 2. Power spectral density plots for station CASTA on frequency domain decomposition method (see Brincker and Castleton Tower and reference station CASTB ∼100 m north on the – – Ventura, 2015). This method is popular in mechanical and ridge for the first hour of the test (20:30 21:30 UTC). (a) North south (N-S) horizontal, (b) east–west (E-W) horizontal, and (c) vertical civil engineering (e.g., Michel and Guéguen, 2018), and (vert.) component. All hours exhibit similar spectra from which we recently been applied to geological features such as sedi- identify the first two resonant frequencies of Castleton Tower as 0.8 ment-filled valleys (Poggi et al., 2015), glaciers (Preiswerk and 1.0 Hz. These frequencies are labeled along with other higher et al., 2018), and rock slopes (Häusler et al., 2019). The goal spectral peaks exhibiting weaker polarization. Power is measured in 10 2 4 for the present study, which included only two sensors (six decibel (dB) units of ground acceleration, log10 m =s =Hz .The color version of this figure is available only in the electronic edition. recordings), was to retrieve damping ratios. For that purpose, the selected mode bells were transformed from the frequency to the time domain, and their decay fitted by a logarithmic and Resources), outputting eigenfrequencies and correspond- decrement. The first two modes were thus determined to ing modal displacement and strain fields. In addition to geom- have damping ratios of 1:1% 0:2%. Rare past measure- etry, COMSOL requires user-defined material properties and ments of damping ratios at other natural pinnacles have boundary conditions for eigenfrequency analysis. We assigned shown similarly low values (e.g., King and Demarco, 2003). a uniform density (ρ)of2200 kg=m3, based on measurements 3D numerical modal analysis was used to verify our from a cored block we collected in the area, and Poisson’sratio results and provide further detail of the displacement and strain of 0.25. Because Castleton Tower is a freestanding landform, fields for first resonant modes of Castleton Tower.
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