the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 04 Sep 2024
Array-based ambient vibration modal analysis describes fracture-controlled mode shapes at a natural rock arch (Utah, USA)
Abstract. Fracture generation and propagation are primary mechanisms of structural degradation in natural rock arches and other freestanding rock landforms. However, methods to detect structural changes arising from fracturing are limited, particularly at sites with difficult access and high cultural value. Here we show how ambient vibration modal analysis can be used to identify fracture-controlled resonance modes at a sandstone arch in Utah (USA) aiding the selection of relevant modes for structural health monitoring. We characterized modal properties of Hunter Canyon Arch (i.e., resonance frequencies, damping ratios, and mode shapes) using spectral and cross-correlation analyses of data generated from an array of nodal geophones. Results revealed properties of nine resonance modes with frequencies between 1 and 12 Hz, damping ratios between 0.6 and 4.3 %, and an assortment of 3D mode shapes. Experimental data were then compared to numerical models implementing both homogeneous media and heterogeneous configurations generated through discretization of compliant zones in areas of mapped fractures. Results showed that all numerical solutions replicated the first two resonance modes of the arch, indicating these are insensitive to structural complexity derived from fractures and thus may be poor targets for monitoring. Meanwhile, heterogenous models with implemented fracture zones succeeded in matching the frequency and shape of one additional higher mode, indicating this mode is sensitive to fracture properties and thus most likely to respond to structural change from fracture propagation. Evolutionary crack damage modelling confirmed the sensitivity of this mode, and conversely the relative insensitivity of other modes, to simulated fracture propagation. While examination of fundamental modes is common in structural health monitoring studies, our results suggest that identifying changes in higher-order modes, i.e., those determined to be affected by fractured areas, may be more informative for characterizing structural damage in monitoring applications.
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RC1: 'Comment on egusphere-2024-1894', Anonymous Referee #1, 07 Oct 2024
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This paper presents a seismic response analysis of the Hunter Canyon Arch (Utah, US). Both field observations and numerical modeling are adopted in the study. An array measurement of the arch’s ambient vibrations was performed with nine simultaneously recording seismic stations. A polarization analysis was performed on the recorded data, as well as a modal analysis using the cross-correlation technique. Modal frequencies, shapes, and corresponding damping ratios were estimated. Based on photogrammetry, a 3D geometrical arch model was developed, and present joint sets were characterized. This model was implemented into a finite element solver. The numerical model analysis was focused on the effects of fractures and their propagation on the modal frequencies and shapes. The numerical results were compared with the observations (modal frequencies, shapes). The authors demonstrate that the fundamental and the first higher modes are sensitive only to the overall shape and bulk modulus of the arch, while the third higher mode is sensitive to the presence of fracture and its extent. They conclude that the higher modes of the slender structures are more sensitive to the fractures (if present). Therefore, higher modes could be better suited for the monitoring of the localized damage compared to fundamental modes. The manuscript's topic is original, interesting, and suitable for the Earth Surface Dynamics journal. The presented analysis is in-depth, and the discussions are focused. The manuscript is well-written and comprehensible. In conclusion, I recommend only minor revisions.Specific comments:The addressing of the observed modes as presented in the text is not very convincing in some cases. This might be due to poor visibility of the weak modal motions in Fig. 4 (that is, the small vectors are too small):• Mode 2 (Fig. 4b) is addressed as a second-order transverse bending mode, but no node is visible in the observed shape, all points seem to be in phase. This, in my opinion, contradicts the simulation’s result (Fig 5c).• Mode 3 (Fig. 4c) looks very similar to Mode 1. The comparison with the simulation is also not very clear. The direct comparison of the motions at the observation points might be helpful.The cross-correlation technique is not very well introduced. A brief introduction would be helpful, outlining the suitability compared to other methods (frequency-domain decomposition, stochastic subspace identification)The relative modal mass (RMM) parameter is not well introduced in the text, although it is used as a criterion for the mode selection presented in Fig 5. A brief description should be included in the text, or RMM can be omitted in the text and the figure.The damping was not considered in the numerical simulations, although the observed values are discussed in the text. The possible implementation of damping in the simulations would give more insight. This could be stressed in the manuscript.The discussion of the damping ratios of different modes is not very clear. The damping ratio of the fundamental mode is found to be small, and it is stated in the manuscript: “These low damping values indicate that seismic energy is trapped within the structure and unable to propagate to the surrounding rock mass (Häusler et al., 2021b).” In contrast, in the explanation of the stronger damping of the higher modes, it is stated: “We hypothesize this change could arise from increasing participation of the abutment fracture area, and corresponding fracture shear and normal compliance, in modal deflection of the arch. The hypothesis of increasing energy transmissivity at the fracture scale is also supported by our numerical modeling results.” This is not clear. In general, seismic energy could leave the structure through the base and side of the arch which are assumed transparent. Indeed, the compliant fractures should result in lower transparency and, thus, even lower damping. However, the energy dissipation in the fracture might increase the damping. Please reformulate this part of the discussion.The angle difference presented in Fig. 6 is not defined in the text. Is the difference for the observed modes rather in horizontal or vertical direction?The name of the arch should be mentioned in the manuscript's title. Other arches are not studied and not much discussed in the text in the context of the study (higher modes and fractures).Different symbols should be used for the simulated modal frequencies (for example, in Fig. 5). You can use caret or tilde.Citation: https://doi.org/
10.5194/egusphere-2024-1894-RC1
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