Micro and macroscopic models of rock fracture

Turcotte, Donald L.; Newman, William I.; Shcherbakov, R.

doi:10.1046/j.1365-246x.2003.01884.x

Cited by 209 publications

(161 citation statements)

References 57 publications

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“…For creep-relaxation experiments on rock, Hao et al (2014) found that the exponent β is about 2/3 (α = 2.5). Finally, in the analysis of viscoelastic fiber bundle models (Kun et al, 2003;Turcotte et al, 2003;Hao et al, 2012) β = 0.5 (α = 3). It should also be noted that, whereas Voight (1988Voight ( , 1989 originally proposed that precursory signals follow a single trend, an alternative view is that the trend evolves with time from conditions for α ≈ 1 to conditions for α ≈ 2 (Kilburn and Voight, 1998;Kilburn and Petley, 2003;Kilburn, 2012).…”

Section: Introductionmentioning

confidence: 99%

An accelerating precursor to predict “time-to-failure” in creep and volcanic eruptions

Hao

Yang

Elsworth³

2017

Journal of Volcanology and Geothermal Research

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Section: Introductionmentioning

confidence: 99%

An accelerating precursor to predict “time-to-failure” in creep and volcanic eruptions

Hao

Yang

Elsworth³

2017

Journal of Volcanology and Geothermal Research

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“…4, was previously analyzed by Lyakhovsky et al (1997a) to describe a stickslip motion under a constant rate of applied deformation. The solution of equations (5, 6) without irreversible strain accumulation prior to the final brittle failure gives a power-law time-to-failure relation consistent with the power-law seismic activation prior to some large earthquakes (Ben-Zion and Lyakhovsky, 2002;Turcotte et al, 2003). The analytical power-law scaling was obtained for a constant applied stress that mimics natural boundary conditions for a system at the stage of accelerating seismic release.…”

Section: Decay Of Activity (Analytical Solution)mentioning

confidence: 58%

“…Rabotnov (1988) related the damage variable to a reduction of the effective cross-section area that supports the load. Fiber-bundle models of damage (Newman & Phoenix, 2001;Turcotte et al, 2003) share the same idea, where cracks are equivalent to torn fibers.…”

Section: Theorymentioning

confidence: 99%

Damage Rheology Model and Decay Law of Aftershock Activity

Lyakhovsky¹,

Ben‐Zion²,

Caraballo³

et al. 2007

Earthquakes and Acoustic Emission

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Aftershocks are the response of a damaged rock surrounding large earthquake ruptures to the stress perturbations produced by the large events. Lyakhovsky et al. (1997a) developed a damage rheology model that provides a quantitative treatment for macroscopic effects of evolving distributed fracturing with local crack density represented by a damage state variable. A thermodynamically-based equation for damage evolution accounts for both degradation and healing of rock as a function of on-going deformation. The governing material properties are constrained by analyses of stress-strain and acoustic emission laboratory data during deformation leading to brittle failure of rocks. For analysis of aftershocks, we consider the relaxation process of a material following the application of a strain step associated with the occurrence of a main shock. The coupled differential equations governing the damage evolution and stress relaxation processes are written in non-dimensional form by scaling the elastic stress to its initial value and the time to characteristic time of damage evolution τ d . With this, the system behavior is controlled by the single non-dimensional ratio R representing the ratio between damage time scale to the Maxwell relaxation time (R = τ d /τ M ). For very small R there is no relaxation and the response consists of constant elastic strain leading to constant rate of damage increase until failure. For very large R there is rapid relaxation without significant change to the level of damage. For intermediate cases the equations are strongly coupled and nonlinear. The analytical solution for the damage evolution can be fitted well for various values of R with a power law similar to the modified Omori law for aftershocks. This also holds for 3-D numerical simulations of aftershock sequences in a multi-layered lithosphere model. Analytical and numerical results suggest that high values of R, corresponding to low viscosity material, produce diffuse aftershock sequences, while low values of R, corresponding to more brittle material, produce clear aftershock sequences. INTRODUCTIONRocks exhibit a wide variety of rheological behaviors ranging from ductile plastic flow and viscoelastic deformation in the earth mantle and lower crust, to fracture processes controlling the mechanical response and stability of rock mass in the seismogenic zone. A great challenge of theoretical geodynamic studies is to incorporate the interaction between mantle and lower crust into models that simulate deformational processes in the upper crust. Fundamental nonlinear aspects of rock deformation, such as microcrack and flaw nucleation and development of process zones at rupture tips do not have at present accepted quantitative theoretical framework. These aspects are of crucial importance for evolutionary self-organization of faults at various spatio-temporal domains. Lyakhovsky et al. (1997a) developed a thermodynamically-based version of damage rheology, which holds a potential for providing a framework for understanding r...

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“…In order to suppress possible voltage spikes, acquired AE signals with duration < 3 µs and count number < 3 were filtered out. Spatial identification of the arch's damaged zones was performed by applying triangulation equations to the received AE signals in order to localize the AE sources as active and propagating crack tips (Shah and Li, 1994;Shiotani et al, 1994;Grosse et al, 1997;Guarino et al, 1998;Ohtsu et al, 1998;Colombo et al 2003;Turcotte et al, 2003;Aggelis et al, 2013).…”

Section: Resultsmentioning

confidence: 99%

Signal frequency distribution and natural-time analyses from acoustic emission monitoring of an arched structure in the Castle of Racconigi

Niccolini

Manuello

Marchis

et al. 2017

Nat. Hazards Earth Syst. Sci.

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Abstract. The stability of an arch as a structural element in the thermal bath of King Charles Albert (Carlo Alberto) in the Royal Castle of Racconigi (on the UNESCO World Heritage List since 1997) was assessed by the acoustic emission (AE) monitoring technique with application of classical inversion methods to recorded AE data. First, damage source location by means of triangulation techniques and signal frequency analysis were carried out. Then, the recently introduced method of natural-time analysis was preliminarily applied to the AE time series in order to reveal a possible entrance point to a critical state of the monitored structural element. Finally, possible influence of the local seismic and microseismic activity on the stability of the monitored structure was investigated. The criterion for selecting relevant earthquakes was based on the estimation of the size of earthquake preparation zones. The presented results suggest the use of the AE technique as a tool for detecting both ongoing structural damage processes and microseismic activity during preparation stages of seismic events.

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Micro and macroscopic models of rock fracture

Cited by 209 publications

References 57 publications

An accelerating precursor to predict “time-to-failure” in creep and volcanic eruptions

An accelerating precursor to predict “time-to-failure” in creep and volcanic eruptions

Damage Rheology Model and Decay Law of Aftershock Activity

Signal frequency distribution and natural-time analyses from acoustic emission monitoring of an arched structure in the Castle of Racconigi

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