Use of Seismic Resonance Measurements to Determine the Elastic Modulus of Freestanding Rock Masses

Moore, Jeffrey R.; Geimer, Paul R.; Finnegan, Riley; Thorne, M. S.

doi:10.1007/s00603-018-1554-6

Cited by 27 publications

(32 citation statements)

References 24 publications

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“…Alternatively, the resonance frequencies and normal modes could be also estimated by modal analysis modules available in commercial/noncommercial finite element method codes (COMSOL Multiphysics, ANSYS, Elmer, etc.). These methods are particularly useful for free standing structures (Moore et al, 2018(Moore et al, , 2019 or soft enclosed sedimentary basins (Ermert et al, 2014). Such structures efficiently trap seismic energy and do not radiate much into the embedding bedrock; thus, the bedrock boundary does not play an important role and can be even fixed.…”

Section: Ambient Vibration Simulationsmentioning

confidence: 99%

Modeling the Seismic Response of Unstable Rock Mass With Deep Compliant Fractures

2019

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An experimental quantification of the strength and volume of real, heterogeneous, fractured rock masses is crucial when assessing rock slope stability. In order to quantitatively characterize the internal structure of fractured rock slopes, we present three‐dimensional numerical simulations of seismic wave propagation and compare with observations. We introduce a simple, effective model for fractured rock mass, which can easily be applied to simulate weak‐motion seismic wave propagation. The macroscopic compliant fractures cutting the rock mass are modeled as finite‐width zones of reduced elastic parameters characterized by shear and normal stiffness. The widths of such zones are not fixed and can be adjusted to fit the grid step in the numerical method. The proposed rock mass model is applied and tested for the Walkerschmatt site in southwest Switzerland. Synthetic ambient vibrations are generated using a finite‐difference method for the fractured rock mass, shaped by the real terrain geometry, and compared with the measurements. The observed seismic response is satisfactorily reproduced in a broad frequency range (0.5–10 Hz). The synthetized response is primarily controlled by the stiffness, depth, number of fractures, and inertial mass of the fractured rock. The simulated amplification and ground‐motion directionality correspond with the observed levels, unless (1) the simplified cracks reach depths of 200–300 m; and (2) the fracture network is larger with respect to the mapped network. This illustrates the potential of ambient vibration methods in combination with numerical simulations to infer depth, volume, and mechanical characteristics of slope instability.

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Section: Ambient Vibration Simulationsmentioning

confidence: 99%

Modeling the Seismic Response of Unstable Rock Mass With Deep Compliant Fractures

2019

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“…Ambient seismic vibration measurements have been increasingly used to characterize unstable slopes (Del Gaudio et al, 2014;Del Gaudio & Wasowski, 2011;Galea et al, 2014;Iannucci et al, 2018;Jongmans et al, 2002;Kleinbrod et al, 2017), prone-to-fall rock columns Colombero et al, 2018;Lévy et al, 2010;Valentin et al, 2017), and rock arches (Moore et al, 2016;Moore et al, 2018;Starr et al, 2015). Of particular interest is such seismic mapping in case of brittle rock failure, where only little prefailure displacements can be registered.…”

Section: Introductionmentioning

confidence: 99%

Fracture Network Imaging on Rock Slope Instabilities Using Resonance Mode Analysis

Häusler

Michel²,

Burjánek

et al. 2019

Geophysical Research Letters

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We performed modal analysis using frequency domain decomposition of ambient seismic vibration data collected on large rock slope instabilities. This technique enables a robust detection of resonance frequencies and provides the corresponding mode shape vectors. We applied the technique to synthetic and field data sets acquired by seismometer arrays on two rock instabilities in Switzerland. We found that, at the fundamental mode, the entire instability vibrates in‐phase with the dominant mode shape vector oriented perpendicular to dominant fracture systems. At higher frequencies, different compartments of the instability resonate antiphase. Therefore, delineating the zero crossings between the phases allows dominant fractures to be efficiently mapped. Approximately 1 hr of ambient vibration data suffices to apply the method successfully. The method also potentially detects hidden fractures that cannot be observed by geological field mapping. In addition, this approach combines classic amplification and polarization analysis into one technique, simplifying data processing efforts.

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“…Conversely, arches with low elastic moduli may reflect diagenetic effects related to stratigraphic position (Moore et al, 2018). Aqueduct Arch, in the iron‐depleted upper Wingate, has an elastic modulus lower than the average of the similar eolian Navajo sandstone.…”

Section: Discussionmentioning

confidence: 99%

“…Under assumptions of linear elasticity, small deflections, and consistent boundary conditions, the resonant frequencies ( f i ) of a beam vary as

f_{i} \propto \sqrt{\frac{E}{ρ}}

where E is Young's modulus and ρ density (Chopra, 2011). Following data collected from representative Navajo and Wingate sandstone samples in southern Utah, we held density constant at 2,000 kg/m 3 for all materials and allowed E to vary to reproduce observed resonant frequencies (Moore et al, 2018).…”

Section: Methodsmentioning

confidence: 99%

“…SHM of natural rock arches is in turn motivated by rockfall events at Landscape Arch in 1991 and 1995 and the collapse of nearby Wall Arch (both in Arches National Park) in 2008. Studies to date, however, have been narrow in scope, with single‐site evaluations of dynamic properties (Moore et al, 2016; Starr et al, 2015) and assessment of stiffness variations within a single geologic unit (Moore et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

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Sparse Ambient Resonance Measurements Reveal Dynamic Properties of Freestanding Rock Arches

Geimer

Finnegan

Moore

2020

Geophysical Research Letters

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The dynamic properties of freestanding rock landforms are a function of fundamental material and mechanical parameters, facilitating noninvasive vibration-based structural assessment. Characterization of resonant frequencies, mode shapes, and damping ratios, however, can be challenging at culturally sensitive geologic features, such as rock arches, where physical access is limited. Using sparse ambient vibration measurements, we describe three resonant modes between 1 and 40 Hz for 17 natural arches in Utah spanning a range of lengths from 3-88 m. Modal polarization data are evaluated to combine field observations with 3-D numerical models. We find outcrop-scale elastic moduli vary from 0.8 to 8.0 GPa, correlated with diagenetic processes and identify low damping at all sites. Correlation of dense-array measurements from one arch validates predictions of simple bending modes and fixed boundary conditions. Our results establish use of sparse ambient resonance measurements for structural assessment and monitoring of arches and similar freestanding geologic features worldwide.Plain Language Summary Natural rock arches vibrate under ambient conditions with a unique set of frequencies controlled by geometry, host material, and interactions with nearby bedrock. Recent rockfall events at well-known arches in Utah have highlighted the need to develop noninvasive assessment methods to better understand how these sensitive landforms evolve. To reduce site impacts, we employed limited instrumentation to measure ambient vibrations of 17 arches across Utah for identification of resonant frequencies. We combine direct observations with predictive numerical models to visualize resonant mode shapes and describe the controlling material properties and structural boundaries. In defining the first three modes of each site, we are able to characterize dynamic properties at arches encompassing several geologic formations and a range of length scales. These results establish a versatile method for structural evaluations of arches and other significant freestanding geologic features.

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Use of Seismic Resonance Measurements to Determine the Elastic Modulus of Freestanding Rock Masses

Cited by 27 publications

References 24 publications

Modeling the Seismic Response of Unstable Rock Mass With Deep Compliant Fractures

Modeling the Seismic Response of Unstable Rock Mass With Deep Compliant Fractures

Fracture Network Imaging on Rock Slope Instabilities Using Resonance Mode Analysis

Sparse Ambient Resonance Measurements Reveal Dynamic Properties of Freestanding Rock Arches

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