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Oxygen isotope evolution of the Lake Owyhee volcanic field, Oregon, and implications for the low-δ 18 O magmatism of the Snake River Plain–Yellowstone hotspot and other low-δ 18 O large igneous provinces

The Snake River Plain–Yellowstone (SRP-Y) hotspot track represents the largest known low-δ 18 O igneous province; however, debate persists regarding the timing and distribution of meteoric hydrothermal alteration and subsequent melting/assimilation relative to hotspot magmatism. To further constrain alteration relations for SRP-Y low-δ 18 O magmatism, we present in situ δ 18 O and U–Pb analyses of zircon, and laser fluorination δ 18 O analyses of phenocrysts, from the Lake Owyhee volcanic field (LOVF) of east-central Oregon. U–Pb data place LOVF magmatism between 16.3 and 15.4 Ma, and contain no evidence for xenocrystic zircon. LOVF δ 18 O(Zrc) values demonstrate (1) both low-δ 18 O and high-δ 18 O caldera-forming and pre-/post-caldera magmas, (2) relative increases in δ 18 O between low-δ 18 O caldera-forming and post-caldera units, and (3) low-δ 18 O magmatism associated with extension of the Oregon-Idaho Graben. The new data, along with new compilations of (1) in situ zircon δ 18 O data for the SRP-Y, and (2) regional δ 18 O(WR) and δ 18 O(magma) patterns, further constrain the thermal and structural associations for hydrothermal alteration in the SRP-Y. Models for low-δ 18 O magmatism must be compatible with (1) δ 18 O(magma) trends within individual SRP-Y eruptive centers, (2) along axis trends in δ 18 O(magma), and (3) the high concentration of low-δ 18 O magmas relative to the surrounding regions. When considered with the structural and thermal evolution of the SRP-Y, these constraints support low-δ 18 O magma genesis originating from syn-hotspot meteoric hydrothermal alteration, driven by hotspot-derived thermal fluxes superimposed on extensional tectonics. Lastly, this model is not restricted to continental hotspot settings and may apply to several other low-δ 18 O igneous provinces with similar thermal and structural associations.

58 GEOSCIENCES↗

A geochemical approach to constraining the formation of glassy fallout debris from nuclear tests

Reprocessed earth material is a glassy nuclear fallout debris from near-surface nuclear tests. A geochemical approach to analysis of glassy fallout is uniquely suited to determine the means of reprocessing and shed light on the mechanisms of fallout formation. An improved understanding of fallout formation is of interest both for its potential to guide post-detonation nuclear forensic investigations and in the context of possible affinities between glassy debris and other glasses generated by high-energy natural events, such as meteorite impacts and lightning strikes. Our study presents a large major-element compositional dataset for glasses within aerodynamic fallout from the Trinity nuclear test (“trinitite”) and a geochemically based analysis of the glass compositional trends. Silica-rich and alkali-rich trinitite glasses show compositions and textures consistent with formation through melting of individual mineral grains—quartz and alkali feldspar, respectively—from the test-site sediment. Furthermore, the volumetrically dominant glass phase—called the CaMgFe glass—shows extreme major-element compositional variability. Compositional trends in the CaMgFe glass are most consistent with formation through volatility-controlled condensation from compositionally heterogeneous plasma. Radioactivity occurs only in CaMgFe glass, indicating that co-condensation of evaporated bulk ground material and trace device material was the main mechanism of radioisotope incorporation into trinitite. CaMgFe trinitite glasses overlap compositionally with basalts, rhyolites, fulgurites, tektites, and microtektites but display greater compositional diversity than all of these naturally formed glasses. Indeed, the most refractory CaMgFe glasses compositionally resemble early solar system condensates—specifically, CAIs.

58 GEOSCIENCES↗

Microlite orientation in obsidian flow measured by synchrotron X-ray diffraction

Clinopyroxene and plagioclase (andesine) microlites in an obsidian flow from Glass Mountain (NE California, USA) display strong alignment. Synchrotron X-ray diffraction, coupled with Rietveld analysis, was used to quantify crystallographic-preferred orientation (CPO). Clinopyroxene, with a rod-shaped morphology, shows a strong alignment of [001] in the flow direction and (010) aligned parallel to the inferred flow plane. Andesine, with a platy morphology, displays an alignment of (010) platelets in the flow plane. Some pole densities exceed 90 multiples of random distribution. Applying a model of rigid ellipsoidal inclusions in a viscous matrix, the local pure shear strains are between 2 and 3.

58 GEOSCIENCES↗

High-pressure crystal structure and equation of state of ferromagnesian jeffbenite: implications for stability in the transition zone and uppermost lower mantle

Jeffbenite, ideally Mg 3 Al 2 Si 3 O 12 , has been identified as inclusions in super-deep diamonds originating from depths that exceed 300 km. Although Mg-end member jeffbenite has limited stability at upper-mantle conditions, iron-bearing jeffbenite may have broader P–T stability that extends to the transition zone or uppermost lower mantle, incorporating significant amounts of ferric iron. Using synchrotron-based, single-crystal X-ray diffraction (XRD) and synchrotron Mössbauer spectroscopy (SMS) at pressures up to 29 GPa, we report the crystal structure, compressibility, and likely spin transition of iron in ferromagnesian jeffbenite (Mg 2.32 Al 0.03 Fe 2+ 1.28 Fe 3+ 1.77 Si 2.85 O 12 ). High-pressure structure refinements reveal that Fe 3+ substitution for Si in the T2 site, which shares edges with the M2 octahedron, likely stabilizes jeffbenite at high pressure, because it increases the cation-to-cation distance between these sites. Although ferromagnesian jeffbenite does not undergo a structural phase transition below 30 GPa, SMS hyperfine parameters suggest the onset of an electronic spin transition of iron from high-spin (HS) to low-spin (LS) at around 22 GPa, which may increase its stability at high pressures. Pressure–volume data were fit to a third order Birch–Murnaghan equation of state, resulting in V o = 816.54(9), K To = 181.54(1.39), and K' T0 = 2.76(14). These equation of state parameters are applicable to evaluating the encapsulation pressures of super-deep diamonds. The density and bulk modulus of ferromagnesian jeffbenite are similar to or higher than pyrope–almandine, pyrope–majorite, and skiagite–majorite solid solution garnets, further suggesting that jeffbenite may be an important ferric–iron silicate in the deeper parts of the mantle transition zone and uppermost lower mantle. Furthermore, future studies on the influence of temperature and oxidation state on the stability and equations of state of iron-bearing jeffbennite are still needed to determine what role, if any, jeffbenite plays in transition-zone mineralogy.

58 GEOSCIENCES↗

The solubility of titanite in silicate melt determined from growth and dissolution experiments

The solubility of titanite (CaTiSiO 5 ) in Si-rich melts was measured experimentally through growth experiments at 800–1000 °C, 0.5–1.0 GPa, log fO 2 ~ CCO–0.8, t = 72–168 h, and H 2 O = 0 to 4 wt.%, and in dissolution experiments at 925–1300 °C, 0.8 GPa, t = 18–118 h, and H 2 O = 1–10 wt.% in a piston-cylinder apparatus. Run product glasses in growth experiments were homogeneous, and iron loss suppressed ilmenite crystallization. Saturation concentrations in dissolution experiments were estimated by fitting measured diffusion profiles. Titanite solubility increases with increasing temperature and melt composition parameter \(M = {\text{ molar }}\left( {{\text{Na }} + {\text{ K }} + {\text{ 2Ca}}} \right)/\left( {{\text{Al }} \times {\text{ Si}}} \right)\) . Multiple linear regression of glass composition data from growth and dissolution experiments ( n = 29) plus 39 experiments from the LEPR database (Hirschmann et al. 2008 ) yielded the titanite solubility equation (adj. r 2 = 0.95): \(\left( {TiO_{2} } \right)^{melt} \left( {wt.\% } \right) = 0.978 \times M + 0.0048 \times T\left( K \right){-}5.90\) . This model correctly predicted undersaturation in 95% of 2344 experiments from the LEPR database that did not have titanite or rutile. Application to natural rocks yields saturation temperatures that are similar to independent temperature estimates. Finally, this equation should be useful for constraining the temperatures of titanite-saturated melts, for determining whether titanite saturation in magmatic source regions is likely, and for determining when titanite can crystallize and begin to exert an influence on melt geochemistry.

58 GEOSCIENCES↗

Elastic thermobarometry on metapelites across the crustal section of the Famatinian Arc, Argentina

We applied elastic thermobarometry on garnet-bearing migmatites along two transects through the crustal section at Sierra Valle Fértil-La Huerta, Argentina. We performed quartz-in-garnet barometry and zircon-in-garnet thermometry on metapelites from different paleo-depths across the crustal section. Our work recovers entrapment pressures ranging from 240 to 1330 MPa and entrapment temperatures between 691 and 1574 °C. The entrapment conditions are broadly consistent with anticipated pressures and temperatures along the crustal section derived previously using conventional, thermodynamic thermobarometers. The quartz-in-garnet barometer reproduces those conventionally established entrapment conditions when samples only experienced conditions within the alpha-quartz stability field. Raman-derived pressures for samples that experienced beta-quartz reference conditions are commonly much higher than those established by conventional barometry. Samples that preserve compressive (positive) residual pressures best reproduce reference entrapment pressures. Entrapment temperatures show high variability and overestimation of temperature conditions compared to conventional results. These results indicate elastic thermobarometry over- or under-estimates crystallization conditions in rocks crystallized at high temperatures, as is common in the Famatinian Arc deep-crust. We suggest that modeling quartz behavior across the alpha–beta transition may present challenges, as does shape maturation, viscous deformation, and radiation damage in zircon.

58 GEOSCIENCES↗

Stressful crystal histories recorded around melt inclusions in volcanic quartz

Abstract Magma ascent and eruption are driven by a set of internally and externally generated stresses that act upon the magma. We present microstructural maps around melt inclusions in quartz crystals from six large rhyolitic eruptions using synchrotron Laue X-ray microdiffraction to quantify elastic residual strain and stress. We measure plastic strain using average diffraction peak width and lattice misorientation, highlighting dislocations and subgrain boundaries. Quartz crystals across studied magma systems preserve similar and relatively small magnitudes of elastic residual stress (mean 53–135 MPa, median 46–116 MPa) in comparison to the strength of quartz (~ 10 GPa). However, the distribution of strain in the lattice around inclusions varies between samples. We hypothesize that dislocation and twin systems may be established during compaction of crystal-rich magma, which affects the magnitude and distribution of preserved elastic strains. Given the lack of stress-free haloes around faceted inclusions, we conclude that most residual strain and stress was imparted after inclusion faceting. Fragmentation may be one of the final strain events that superimposes stresses of ~ 100 MPa across all studied crystals. Overall, volcanic quartz crystals preserve complex, overprinted deformation textures indicating that quartz crystals have prolonged deformation histories throughout storage, fragmentation, and eruption.

58 GEOSCIENCES↗

Exploring microstructures and anisotropies of serpentinites

Serpentine minerals have received a lot of attention because of their unique crystal structures, their wide occurrence in orogenic belts and their potential role in contributing seismic anisotropy in subducting slabs. Several studies have investigated crystal preferred orientation (CPO) in high temperature antigorite serpentinites from Japan, the Alps, Spain, Cuba and Tibet, documenting significant crystal alignment. However, only a limited number of lower grade serpentines have been explored to date. Mainly because of submicroscopic microstructural heterogeneities CPO cannot be measured with conventional methods such as optical microscopy and EBSD. In this study 15 serpentinites from different tectonic settings in California, the Central Alps and Northern Spain have been investigated, mainly with high energy synchrotron X-ray diffraction, to quantify bulk crystal alignment. We find that CPO is strong on sheared surfaces of fractured blocks and secondary veins but the bulk of most serpentinite samples, except high-grade recrystallized antigorite serpentinite, show only weak crystal alignment. Correspondingly calculated seismic anisotropy based on CPO is not very significant. This is supported by very heterogeneous microstructures as documented with SEM and TEM analyses.

58 GEOSCIENCES↗

Ascent and emplacement dynamics of obsidian lavas inferred from microlite textures

Here, to assess the eruption and emplacement of volumetrically diverse rhyolite lavas, we measured microlite number densities and orientations from samples collected from nine lavas in Yellowstone Caldera and two from Mono Craters, USA. Microlite populations are composed of Fe-Ti oxides ± alkali feldspar ± clinopyroxene. Number densities range from 10 8.11 ± 0.03 to 10 9.45 ± 0.15 cm -3 and do not correlate with distance from the vent across individual flows and are remarkably similar between large- and small-volume lavas. Together, those observations suggest that number densities are unmodified during emplacement and that ascent rates in the conduit are similar between small domes and large lava flows. Microtextures produced by continuous decompression experiments best replicate natural textures at decompression rates of 1–2 MPa hr -1 . Acicular microlites have a preferred orientation in all natural samples. Because the standard deviation of microlite orientation does not become better aligned with distance travelled, we conclude that microlites exit the conduit aligned and that strain during subaerial flow was insufficient to further align microlites. The orientations of microlite trend and plunge in near-vent samples indicate that pure shear was the dominant style of deformation in the conduit. In conclusion, we speculate that collapsing permeable foam(s) provides a mechanism to concurrently allow microlite formation and alignment in response to the combination of degassing and flattening by pure shear.

58 GEOSCIENCES↗

Ash production and dispersal from sustained low-intensity Mono-Inyo eruptions

Recent rhyolitic volcanism has demonstrated that prolonged low-intensity ash venting may accompany effusive dome formation. In this work, we examine the possibility and some consequences of episodes of extended, weak ash venting at the rhyolitic Mono-Inyo chain in Eastern California. We describe ash-filled cracks within one of the youngest domes, Panum Crater, which provide a textural record of ash venting during dome effusion. We use synchrotron-based X-ray computed tomography to characterize the particles in these tuffisites. Particle sizes in well-sorted tuffisite layers agree well with grain size distributions observed during weak ash venting at Soufrière Hills Volcano, Montserrat, and yield approximate upper and lower bounds on gas velocity and mass flux during the formation of those layers. We simulate ash dispersal with Ash3d to assess the consequences of long-lived Mono-Inyo ash venting for ash deposition and the accompanying volcanic hazards. Finally, our results highlight the sensitivity of large-scale outcomes of volcanic eruptions to small-scale processes.

54 ENVIRONMENTAL SCIENCES↗

MeMoVolc report on classification and dynamics of volcanic explosive eruptions

Classifications of volcanic eruptions were first introduced in the early twentieth century mostly based on qualitative observations of eruptive activity, and over time, they have gradually been developed to incorporate more quantitative descriptions of the eruptive products from both deposits and observations of active volcanoes. Progress in physical volcanology, and increased capability in monitoring, measuring and modelling of explosive eruptions, has highlighted shortcomings in the way we classify eruptions and triggered a debate around the need for eruption classification and the advantages and disadvantages of existing classification schemes. Here, we (i) review and assess existing classification schemes, focussing on subaerial eruptions; (ii) summarize the fundamental processes that drive and parameters that characterize explosive volcanism; (iii) identify and prioritize the main research that will improve the understanding, characterization and classification of volcanic eruptions and (iv) provide a roadmap for producing a rational and comprehensive classification scheme. In particular, classification schemes need to be objective-driven and simple enough to permit scientific exchange and promote transfer of knowledge beyond the scientific community. Schemes should be comprehensive and encompass a variety of products, eruptive styles and processes, including for example, lava flows, pyroclastic density currents, gas emissions and cinder cone or caldera formation. Furthermore open questions, processes and parameters that need to be addressed and better characterized in order to develop more comprehensive classification schemes and to advance our understanding of volcanic eruptions include conduit processes and dynamics, abrupt transitions in eruption regime, unsteadiness, eruption energy and energy balance.

58 GEOSCIENCES↗

Groundwater drainage from fissures as a source for lahars

One mechanism for generating lahars at volcanoes experiencing unrest is the disruption of internal aquifers. These disruptions can trigger releases of large quantities of groundwater. An example of such aquifer disruption occurred at Nevado del Huila Volcano, Colombia, during February and April 2007 when large fractures formed across the summit area of the volcano and lahars were emitted from them. Previous work interpreted that lahar volumes could not be accounted for by melted glacial snow or precipitation, and by elimination suggested that the primary water source was groundwater. Conceptual models have been developed for perched, confined aquifers that have been heated and pressurized by magma intrusions, followed by sudden pressure release and water emission during fracture formation. In this paper, we consider an alternative end member wherein water release from large fissures at volcanoes is driven by simple gravity drainage. We apply numerical modeling to quantify water discharge from the porous medium surrounding a fissure with a low-elevation free exit. If a long fracture with high vertical extent (on the order of hundreds of meters) intersects a highly connected saturated porous medium, large volumes (on order 10 3 m 3 /m of crack length) of water may be released within tens of minutes. The drainage rates from the model may be adequate to account for the Nevado del Huila events if the medium surrounding the crack contains a large volume of water and has high horizontal permeability. Finally, this simple but poorly understood mechanism can present a hazard on its own or compound other processes releasing water from volcanoes.

58 GEOSCIENCES↗

Revisiting short-term earthquake triggered volcanism

It has been noted for centuries that earthquakes appear to trigger the eruption of volcanoes. For example, analyses of global volcanic and seismic records since 1500 AD have shown that explosive eruptions with Volcanic Explosivity Index (VEI) values ≥2 are preceded within days by nearby major earthquakes (magnitude M8 or larger) about 4 times more often than expected due to coincidence, suggesting that large earthquakes can trigger eruptions. Here we expand the definition of a triggered eruption to include the possibility of M6 or greater earthquakes within 5 days and 800 km of a VEI 2 or greater eruption. Removing pre-1964 records, to ensure complete and accurate catalogs, we find 30 volcanoes that at some point experienced a potentially triggered eruption and define these volcanoes as “sensitive” volcanoes. Within this group of sensitive volcanoes, normalized distributions of volcano-centric factors such as tectonic setting, dominant rock type, and type of volcano are practically indistinguishable from those of sensitive volcanoes in which the time of eruption is randomized. Comparisons of sensitive volcanoes and insensitive volcanoes (i.e., volcanoes that have never experienced a triggered eruption) reveal that sensitive volcanoes are simply more active than insensitive volcanoes: They erupt more frequently, are located solely in subduction zones, and erupt primarily andesites and basaltic-andesites. The potentially triggered eruptions do not show the magnitude-distance relationship expected for seismically induced responses (e.g., hydrologic responses), and eruptions that do occur within days of nearby earthquakes do so within rates expected by random chance. There is, however, a 5–12% increase in the number of explosive eruptions in the 2 months to 2 years following major earthquakes. Finally, we conclude that short-term seismically triggered explosive eruptions occur less frequently than previously inferred, an important conclusion when considering volcanic hazards and for understanding the nature of earthquake-volcano interactions.

58 GEOSCIENCES↗

Topographic controls on a phreatomagmatic maar-diatreme eruption: field and numerical results from the Holocene Dotsero volcano (Colorado, USA)

We analyzed the eruptive products of Holocene Dotsero volcano (Colorado, USA; ~4.15 ka), which recorded evidence of a progression from effusive magmatic activity through explosive phreatomagmatic maar-forming activity to a final explosive magmatic phase. The nature of the deposits suggests that the irregular and mountainous pre-eruptive topography strongly influenced the formation of directed pyroclastic density currents (PDCs) during the phreatomagmatic phase, where the topographically high northern crater rim acted as a barrier and promoted transport to the south. Furthermore, the crater shape strongly controlled the grain size of the final deposits, providing further evidence that deposit grain size can be a misleading proxy for fragmentation or explosion intensity. We test these hypotheses, as gleaned from fieldwork, by implementing a multiphase numerical model to simulate discrete explosions and their resulting PDCs at maar-diatreme volcanoes. We confirm that a crater shape where one rim is higher than the other promotes multiple pulses of particle transport in the direction of the lower rim. The initial PDCs contain both coarse and fine particles, whereas PDCs generated by later pulses contain, predominately, finer particles. This mechanism provides an alternative explanation to the formation of lapilli tuff/tuff couplets often found at maar-diatreme tephra rings (including Dotsero volcano). Additional modeling shows how the crater depth can control grain size of the resulting PDC deposits. In the case of a deep crater and a relatively weak explosion, it is possible that only the fine particles escape following collapse of the eruptive column, resulting in a fine-grained deposit. This work allows us to improve models developed to describe emplacement of PDCs for different crater geometries and informs on the dynamics of maar-diatreme eruptions, but also highlights the limitations of our knowledge of key parameters, especially those related to the processes of magma-water interaction and syn-eruptive hydrogeology, during such events.

58 GEOSCIENCES↗

Volcano infrasound: progress and future directions

Over the past two decades (2000–2020), volcano infrasound (acoustic waves with frequencies less than 20 Hz propagating in the atmosphere) has evolved from an area of academic research to a useful monitoring tool. As a result, infrasound is routinely used by volcano observatories around the world to detect, locate, and characterize volcanic activity. It is particularly useful in confirming subaerial activity and monitoring remote eruptions, and it has shown promise in forecasting paroxysmal activity at open-vent systems. Fundamental research on volcano infrasound is providing substantial new insights on eruption dynamics and volcanic processes and will continue to do so over the next decade. The increased availability of infrasound sensors will expand observations of varied eruption styles, and the associated increase in data volume will make machine learning workflows more feasible. More sophisticated modeling will be applied to examine infrasound source and propagation effects from local to global distances, leading to improved infrasound-derived estimates of eruption properties. Future work will use infrasound to detect, locate, and characterize moving flows, such as pyroclastic density currents, lahars, rockfalls, lava flows, and avalanches. Infrasound observations will be further integrated with other data streams, such as seismic, ground- and satellite-based thermal and visual imagery, geodetic, lightning, and gas data. The volcano infrasound community should continue efforts to make data and codes accessible and to improve diversity, equity, and inclusion in the field. In summary, the next decade of volcano infrasound research will continue to advance our understanding of complex volcano processes through increased data availability, sensor technologies, enhanced modeling capabilities, and novel data analysis methods that will improve hazard detection and mitigation.

58 GEOSCIENCES↗

Volcanic electrification: recent advances and future perspectives

Abstract The electrification of volcanic plumes has been described intermittently since at least the time of Pliny the Younger and the 79 AD eruption of Vesuvius. Although sometimes disregarded in the past as secondary effects, recent work suggests that the electrical properties of volcanic plumes reveal intrinsic and otherwise inaccessible parameters of explosive eruptions. An increasing number of volcanic lightning studies across the last decade have shown that electrification is ubiquitous in volcanic plumes. Technological advances in engineering and numerical modelling, paired with close observation of recent eruptions and dedicated laboratory studies (shock-tube and current impulse experiments), show that charge generation and electrical activity are related to the physical, chemical, and dynamic processes underpinning the eruption itself. Refining our understanding of volcanic plume electrification will continue advancing the fundamental understanding of eruptive processes to improve volcano monitoring. Realizing this goal, however, requires an interdisciplinary approach at the intersection of volcanology, atmospheric science, atmospheric electricity, and engineering. Our paper summarizes the rapid and steady progress achieved in recent volcanic lightning research and provides a vision for future developments in this growing field.

58 GEOSCIENCES↗

Controls on the frequency content of near-source infrasound at open-vent volcanoes: a case study from Volcán Villarrica, Chile

Infrasound signals from open-vent volcanoes can contain information related to that volcano’s eruption dynamics and future activity. Studying a specific volcano’s acoustic signature during periods of relative quiescence is thus important for understanding potential warning signs of impending eruptions. Volcán Villarrica, located in southern Chile, has a long-lived active lava lake that produces continuous infrasound with spectral peaks centered around 1 Hz that vary by + / - ~ 0.2 Hz over day-to-week-long time scales. The infrasound frequency content has been shown to illuminate key volcanic properties such as eruption style and crater shape. Leading up to Villarrica’s most recent paroxysm in 2015, for instance, infrasound spectral changes coincided with a rise in Villarrica’s lava lake level. Quantifying and understanding the regular fluctuation in recorded infrasonic frequencies from Villarrica and other open-vent volcanoes is thus imperative during periods of relative calm. Our experiment entailed a week-long period of crater rim infrasound observations associated with stable, open-vent activity and revealed two independent source processes: spatter bursting events (relatively broadband infrasound) and lava lake-induced tremor (sustained signals peaked at 1 Hz). A comparison of these acoustic signals with results from 3-D finite-difference time-domain wave propagation models shows that while sound speed variability can influence Villarrica’s spectrum, it cannot explain the full extent of the observed frequency excursions. We conclude that source spectrum variability is primarily responsible for the frequency excursions. In conclusion, our work highlights the utility of data collected from a dense distribution of twenty infrasound sensors operating at the summit coupled with numerical modeling of sound radiation.

58 GEOSCIENCES↗

A thermomechanical anisotropic model for shock loading of elastic-plastic and elastic-viscoplastic materials with application to jointed rock

Here, a large deformation thermomechanical model is developed for shock loading of a material that can exhibit elastic and inelastic anisotropy. Use is made of evolution equations for a triad of microstructural vectors m i (i=1,2,3) which model elastic deformations and directions of anisotropy. Specific constitutive equations are presented for a material with orthotropic elastic response. The rate of inelasticity depends on an orthotropic yield function that can be used to model weak fault planes with failure in shear and which exhibits a smooth transition to isotropic response at high compression. Moreover, a robust, strongly objective numerical algorithm is proposed for both rate-independent and rate-dependent response. The predictions of the continuum model are examined by comparison with exact steady-state solutions. Also, the constitutive equations are used to obtain a simplified continuum model of jointed rock which is compared with high fidelity numerical solutions that model a persistent system of joints explicitly in the rock medium.

36 MATERIALS SCIENCE↗

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