Changes in resonance frequency of rock columns due to thermoelastic effects on a daily scale: observations, modelling and insights to improve monitoring systems

Abstract

Summary Slope instabilities, including prone-to-fall rock columns, are known to exhibit clear vibrational modes. The resonance frequencies of these modes can be tracked by seismic instrumentation, allowing the rock column's mechanical and structural properties to be monitored, as well as providing precursors of imminent irreversible failures. In previous studies, superficial thermoelastic effects were assumed to drive daily fluctuations in resonance frequencies, but no qualitative or quantitative evidence was provided. The results presented here corroborate this hypothesis and quantify the physical processes involved. We interpreted daily variations of resonance frequencies in the Les Arches study site (Vercors, French Prealps) using a thermo-mechanical finite-element model. Modelled fluctuations of the resonance frequencies over a day closely matched experimental observations, reproducing the daytime frequency increase of around 2%. In addition, our model provides explanation of the various behaviors observed across study sites: the frequency response strongly depends on solar exposure, as well as the timing and intensity of both radiative and convective heat fluxes. We highlight acousto-elastic constants as key parameters of our semi-quantitative model, although they remain poorly constrained here. For future instrumentation, we therefore recommend the deployment of pyranometers on rocky sites to accurately invert these parameters over time, thus allowing rock fracturing to be quantitatively tracked by acousto-elastic monitoring.

A Comprehensive Seismic Monitoring of the Pillar Threatening the World Cultural Heritage Site Chauvet‐Pont d'Arc Cave, Toward Rock Damage Assessment

“…This observation suggests a thermally-dependent mechanism of the frequency drifts. A similar strong positive correlation between frequency and temperature has also been observed in other sites, where it was interpreted as an effect of stress stiffening of the external part of the rock mass (Colombero, Godio, & Jongmans, 2021;Geimer et al, 2022;Guillemot et al, 2022).…”

Meteorological Controls on Reversible Resonance Changes in Natural Rock Arches

“…Similar mechanisms have been cited to explain reversible frequency drifts in slope stability monitoring (reviews by Colombero et al, 2021;Larose et al, 2015;Le Breton et al, 2021), often supported by results from careful finite element modeling to incorporate the unique geometric complexities of each site Guillemot et al, 2022). Observations of positive temperature-frequency correlations at daily scale are widespread and have been interpreted as stress-stiffening effects (e.g., Burjánek et al, 2018;Starr et al, 2015;Valentin et al, 2017).…”

“…These features were: (a) the positive and steepening correlation of frequency to temperature over multiple months, (b) delayed frequency response to temperature on daily scales, and (c) a reversed and steepened correlation below 0° during freeze‐thaw cycles. In comparison to recent multiflux thermo‐acoustic‐elastic modeling of similar phenomena (Guillemot et al., 2022), we used simple harmonic temperature inputs and empirical stress‐ and temperature‐dependent elastic modulus to qualitatively replicate observed features, employing COMSOL Multiphysics to generate the coupled thermomechanical‐eigenfrequency solutions.…”

“…Infrared heat flux thus represents a potential modeling improvement, as Guillemot et al. (2022) combined it with acousto‐elastic theory to replicate daily resonance frequency variations of an unstable rock column. Last, we discuss the potential of an amplitude‐dependent explanation.…”

Coevolution of Rock Slope Instability Damage and Resonance Frequencies From Distinct‐Element Modeling

“…Demonstrated decreases in resonance frequencies before the failure of a rock column (Lévy et al., 2010) and a rock block collapse test (Taruselli et al., 2020), in addition to results of a study showing an increase in resonance frequencies of an unstable rock compartment after bolting reinforcement (Bottelin et al., 2017), highlight ambient vibration measurements as a valuable slope stability monitoring technique. Although numerous additional field‐based studies have attempted to capture frequency changes associated with landslide destabilization, often only environmentally driven recoverable changes are recorded (Bottelin, Lévy, et al., 2013; Burjánek et al., 2018; Colombero et al., 2018, 2021; Dietze et al., 2021; Guillemot et al., 2022; Häusler et al., 2021, 2022; Weber et al., 2018). In addition to resonance frequency values, seismic parameters including frequency‐dependent polarization azimuth and damping (e.g., Geimer et al., 2022) can be used to detect internal structural or material changes during stability monitoring (e.g., Häusler et al., 2022).…”