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Abstract. Progressive fracturing contributes to structural degradation of 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, where non-invasive approaches are essential. This study aims to determine how fractures affect the dynamic properties of rock arches, focusing on resonance modes as indicators of structural health conditions. We hypothesize that damage resulting from fracture propagation may influence specific resonance modes that can be identified through ambient vibration modal analysis. We characterized the dynamic properties (i.e., resonance frequencies, damping ratios, and mode shapes) of Hunter Canyon Arch, Utah (USA), 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. Experimental data were then compared to numerical models with homogeneous and heterogeneous compositions, the latter implementing weak mechanical zones in areas of mapped fractures. All numerical solutions replicated the first two resonance modes of the arch, indicating these modes are insensitive to structural complexity derived from fractures. Meanwhile, heterogenous models with discrete fracture zones succeeded in matching the frequency and shape of one additional higher mode, indicating this mode is sensitive to the presence of fractures and thus most likely to respond to structural change from fracture propagation. An evolutionary crack damage model was then applied to simulate fracture propagation, confirming that only this higher mode is sensitive to structural damage resulting from fracture growth. While examination of fundamental modes is common practice in structural health monitoring studies, our results suggest that analysis of higher-order resonance modes can be more informative for characterizing fracture-driven structural damage.
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Variable-order fracture mechanics and its application to dynamic fracture
Abstract This study presents the formulation, the numerical solution, and the validation of a theoretical framework based on the concept of variable-order mechanics and capable of modeling dynamic fracture in brittle and quasi-brittle solids. More specifically, the reformulation of the elastodynamic problem via variable and fractional-order operators enables a unique and extremely powerful approach to model nucleation and propagation of cracks in solids under dynamic loading. The resulting dynamic fracture formulation is fully evolutionary, hence enabling the analysis of complex crack patterns without requiring any a priori assumption on the damage location and the growth path, and without using any algorithm to numerically track the evolving crack surface. The evolutionary nature of the variable-order formalism also prevents the need for additional partial differential equations to predict the evolution of the damage field, hence suggesting a conspicuous reduction in complexity and computational cost. Remarkably, the variable-order formulation is naturally capable of capturing extremely detailed features characteristic of dynamic crack propagation such as crack surface roughening as well as single and multiple branching. The accuracy and robustness of the proposed variable-order formulation are validated by comparing the results of direct numerical simulations with experimental data of typical benchmark problems available in the literature.
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- PAR ID:
- 10212806
- Publisher / Repository:
- Nature Publishing Group
- Date Published:
- Journal Name:
- npj Computational Materials
- Volume:
- 7
- Issue:
- 1
- ISSN:
- 2057-3960
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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