Granular Rocks Research Articles

Composition of the Lithospheric Mantle in the Siberian Craton: New Constraints from Fresh Peridotites in the Udachnaya-East Kimberlite

We present petrographic, major element and trace element data for bulk-rocks and minerals for a suite of 34 remarkably fresh peridotite xenoliths in the Udachnaya kimberlite recovered from deep horizons of the open pit mine. The xenoliths are spinel peridotites, granular and deformed garnet peridotites (as well as a megacrystalline dunite) in proportions similar to those reported by previous work on altered xenoliths from less deep levels in the mine. Equilibration temperatures (T) range from 760–965°C for the spinel peridotites to 1200–1320°C for sheared garnet peridotites; the latter yield pressures (P) of 5·4–6·6 GPa. The majority of the granular garnet peridotites equilibrated at 860–1000°C and 2·6–5·5 GPa, but two samples yield much higher T and P values (1176°C, 6·1 GPa; 1340°C, 6·8 GPa) indicating the presence of undeformed rocks near the base of the lithosphere. Strong enrichments in silica and opx relative to dry melting residues are not common in our granular peridotites (e.g. 11 samples out of 18 analyzed plot on Boyd’s ‘oceanic trend’); they have distinctly lower modal opx than low-T peridotites from the Kaapvaal craton and could be formed by ∼30–45% of melt extraction at 1–5 GPa. Minor to moderate enrichments in silica relative to experimental melting trends seen in some xenoliths may indicate that subduction-related settings were involved in their origin. Garnets are usually unzoned but some are enriched in Ti at the rims. Their contents of CaO (4–7 wt %) and Cr2O3 (2–12 wt %) show inverse power-law correlations with whole-rock CaO, Al2O3 and Al/Cr ratios; the latter can be estimated from garnet analyses. Garnets from the dominant cpx-free and cpx-bearing harzburgites and less common low-cpx (5–6%) lherzolites fall into the G9 ‘lherzolite’ field; garnets from three cpx-rich (9–15%) lherzolites are in the G5 ‘pyroxenite’ field. Rare earth element (REE) patterns in cpx and garnet range from sinusoidal to bell-shaped and light REE (LREE)-depleted; the latter are common in sheared rocks and may be close to equilibrium with metasomatic liquids. Garnets from some granular rocks show low heavy REE (HREE) and continuous depletion in LREE, as in melting residues. Trace element patterns and ratios in many bulk peridotites are distinct from those in the host kimberlites and may not be much affected by contamination. Bulk-rock abundances of moderately incompatible elements are lowest in spinel harzburgites (20–50 times lower than in primitive mantle for HREE) and highest in sheared rocks. Some bulk-rocks show depletion from Lu to Er attributed to 30–40% of melt extraction first in the presence of garnet, then in the spinel field. Overall, the observations on fresh Udachnaya peridotites show less evidence for silica and opx enrichments and smaller compositional effects of syn- and post-eruption alteration than earlier work. The abundances of cpx and garnet and bulk-rock Al2O3 do not vary systematically with depth except that rare sheared xenoliths anomalously enriched in cpx and garnet occur near the base of the lithosphere. The remarkable preservation of olivine and opx shows in detail the transformation of granular microstructures into different types of porphyroclastic fabrics and their relations to chemical compositions.

Development and genetic mechanism of complex carbonate reservoir fractures: A case from the Zanarol Oilfield, Kazakhstan

Abstract By core observation and slice analysis, two types of fractures can be identified in reservoirs of Zanarol Oilfield, including macro-fractures and micro-fractures. Macro-fractures refer to tectonic fractures and stylolites, and micro-fractures mainly refer to grain breakage fractures and micro-tectonic fractures. The development of the different scale fractures is controlled by lithology, formation texture and stress field. Macro-fractures are well developed in tight rocks such as micrite and micro-fractures are well developed in granular carbonate rocks of good porosity and permeability. The Zanarol Oilfield is a typical layered pool, with interbeds of granular carbonates and tight carbonates, and this texture controls the vertical distribution of macro-fractures and micro-fractures. Macro-fractures in the ? layer are well developed due to its tight reservoir, and micro-fractures are well developed in the ? layer because of its loose reservoir. The planar distribution of the fractures is controlled by principal stress, and fractures are well developed in zones with high principal stress.

Bed-parallel compaction bands in aeolian sandstone: Their identification, characterization and implications

This study combines field observations and laboratory analyses to identify and characterize predominantly bed-parallel compaction bands in the aeolian Aztec Sandstone exposed in the Valley of Fire State Park, Nevada. These bed-parallel compaction bands display morphological and geometrical characteristics of deformation bands of various modes previously described in the literature, such as positive relief, echelon geometry, “bridge” and “eye” structure, and zonal occurrence. Portions of some bands cross-cut sedimentary layers, thereby distinguishing themselves from depositional bedding. Laboratory image analyses of several samples collected from bed-parallel bands, using a computational rock physics algorithm, show that their porosities are less than half that of the host rock and their permeability is nearly one order of magnitude less. In addition, the study area includes compaction bands that have dip angles ranging from sub-horizontal to greater than 20°. Parts of these bands have even higher dip angles and show evidence for increasing intragranular fracturing and shearing as the band inclination increases. We attribute this variation to shear-enhanced compaction, a mechanism proposed earlier by experimental rock mechanists. One of the implications of the occurrence of localized compaction in the form of discrete bands parallel to flat-lying and low-angle bedding is that it provides an alternative or an additional mode to a vertically continuous compaction in loose or poorly cemented sediments. If pervasive, bed-parallel compaction bands with significantly lower porosity than that of the surrounding undeformed rock should result in a significant heterogeneity and vertical anisotropy in seismic velocities and hydraulic properties of granular rocks.

Ultrasonic moduli for fluid-saturated rocks: Mavko-Jizba relations rederived and generalized

Mavko and Jizba propose a quantitative model for squirt dispersion of elastic-wave velocities between seismic and ultrasonic frequencies in granular rocks. Their central results are the expressions for the so-called unrelaxed frame bulk and shear moduli computed under an assumption that the stiff pores are drained (or dry) but the soft pores are filled with fluid. Mavko-Jizba expressions are limited to liquid-saturated rocks but become inaccurate when the fluid-bulk modulus is small (e.g., for gas-saturated rocks). We have derived new expressions for unrelaxed moduli of fluid-saturated porous rocks using Sayers-Kachanov discontinuity formalism. The derived expressions generalize the established Mavko-Jizba relations to gas-saturated rocks, reduce to Mavko-Jizba results when the pore fluid is liquid, and yield dry moduli when fluid-bulk modulus tends to zero. We tested this by comparing our model and the model of Mavko and Jizba against laboratory measurements on a sample of Westerly granite.

Visual simulation for granular rocks crush in virtual environment based on fractal geometry

In this paper, a new method is proposed for the simulation of rock crushing in virtual environment. The method can be described as a combination of a physical behavioral model with a phenomenological rock generator. The main modules of the solution consist of a Virtual Reality system, fractal geometric modeling, and physical control models. Virtual Reality and geometric modeling compose the phenomenological rock generator, which simulates the process; while the physical behavioral model controls or affects the results of the simulation, We present the key algorithms of the visual simulation solution, such as the rapid modeling algorithm for rock with complex topology, distributed parallel rendering for large scale and complex rock objects. To evaluate the system, a virtual simulation for rocks crushed in cone crusher is introduced.

Effect of the volume of the drainage system on the measurement of undrained thermo-poro-elastic parameters

For evaluation of the undrained thermo-poro-elastic properties of saturated porous materials in conventional triaxial cells, it is important to take into account the effect of the dead volume of the drainage system. The compressibility and the thermal expansion of the drainage system, along with the dead volume of the fluid filling this system, influence the measured pore pressure and volumetric strain during an undrained thermal or mechanical loading in a triaxial cell. The correction methods previously presented by Wissa [Pore pressure measurement in saturated stiff soils. ASCE J Soil Mech Found Div 1969;95(SM 4):1063–73], Bishop [Influence of system compressibility on observed pore pressure response to an undrained change in stress in saturated rock. Geotechnique 1976;26(2):371–5] and Ghabezloo and Sulem [Stress dependent thermal pressurization of a fluid-saturated rock. Rock Mech Rock Eng 2009;42(1):1–24], only permit one to correct the measured pore pressures during an undrained isotropic compression test or an undrained heating test. An extension of these methods is presented in this paper to correct the measured volumetric strain, and consequently the measured undrained bulk compressibility and undrained thermal expansion coefficients, during these tests. Two examples of application of the proposed correction method are presented for an undrained isotropic compression test and an undrained heating test performed on a fluid-saturated granular rock. A parametric study has demonstrated that the porosity and the drained compressibility of the tested material, and the ratio of the volume of the drainage system to the one of the tested sample, are the key parameters that most influence the error induced by the drainage system.

Geomorphology of the Pohorje mountains

The Pohorje mountain range, young mountains with prevailing metamorphic rocks and dacite, continues to uplift above the igneous laccolith in the area of the rapid rising asthenosphere in the transition to the Pannonian basin also due to changes in temperature and, resultantly, of the density of uplifting dacite- and other intrusions which have not metamorphosed the surrounding sediments. On the Pohorje by the river Drava (hereinafter the Drava Pohorje), the drainage network does not match the orography, because, between the Vuzenica-Radlje basin and Fala, the Drava epigenetically deepened its gorge into the marginal range of Kobansko. Modest plateaus on the ridge of the Pohorje originate from the time when the base level maintained a cover of the so-called Eibiswald strata between the Karavanke and the Kobansko in the upper Miocene. The originally larger ridge plateau in the centre of the Pohorje was lowered by erosion and periglacial processes; it has been preserved as an inclined plateau on the Eastern Pohorje. Explained through the recent tectonic shifting, established by means of GPS in the years 1996–2002 at the peak Velika Kopa, is the southeastwards curving of the five valleys above the Legen terrace where, supposedly, original headwaters of the Spodnja Mislinja came from. Due to its geological, geomorphological and hydrological peculiarities the Legen Quaternary terrace deserves that it should be declaired the ‘geopark’, the first one in Slovenia. Even more explicit and extensive is the westwards curving of the valleys on the northern slope of the Pohorje, and their northeastward orientation in the Ribnica-Lovrenc-Selnica valley system. In the east section of the Lovrenc valley system above Fala the brook Rečnikov potok has not adjusted its course to the recent tectonic subsiding, so that its valleys run obliquely to the slope inclination. The up to 700 metres deep Mislinja rift lowered the central ridge of the Pohorje to 1299 metres. Blowing intensely across it, the northeastern Pleistocene cold winds made possible the origination of two smaller glaciers in the upper drainage basin of the Radoljna. The gently sloping Pohorje landforms are not the result of the old age but of the disintegration of granular rocks to permeable sand, above which the thick cover of continuous roots of grasses and prevailing spruce reduces the erosion.

An efficient method for packing polygonal domains with disks for 2D discrete element simulation

The discrete element method (DEM) is frequently used in numerical simulation of the behaviour of discontinuum often encountered in granular flow, soil or rock mechanics or powder compaction. The DEM requires an assemblage of elements that need to fill the domain geometry. Generation of such arrangement of elements, such as disks in 2D DEM simulation is not a trivial task. The available methods to create the arrangements of disks can either take considerable time, have limited control over the final outcome of the disk generation or exhibit difficulty in generating a tight arrangement of disk with varying radii. This paper presents an algorithm employing principles of computational geometry to efficiently generate a tight packing of disks while addressing the common problems of disk generation. The algorithm’s performance is linear with respect to time and scales well. As a demonstration of the algorithm’s capabilities, a DEM model of an ore pass is presented.

Stress dependent thermal pressurization of a fluid-saturated rock

Temperature increase in saturated porous materials under undrained conditions leads to thermal pressurization of the pore fluid due to the discrepancy between the thermal expansion coefficients of the pore fluid and of the solid matrix. This increase in the pore fluid pressure induces a reduction of the effective mean stress and can lead to shear failure or hydraulic fracturing. The equations governing the phenomenon of thermal pressurization are presented and this phenomenon is studied experimentally for a saturated granular rock in an undrained heating test under constant isotropic stress. Careful analysis of the effect of mechanical and thermal deformation of the drainage and pressure measurement system is performed and a correction of the measured pore pressure is introduced. The test results are modelled using a non-linear thermo-poro-elastic constitutive model of the granular rock with emphasis on the stress-dependent character of the rock compressibility. The effects of stress and temperature on thermal pressurization observed in the tests are correctly reproduced by the model.

Hydrothermal deformation of granular quartz sand

Isotropic and triaxial compression experiments were performed on porous aggregates of St Peter quartz sand to explore the influence of temperature (to 225°C). During isotropic stressing, samples loaded at elevated temperature exhibit the same sigmoidal stress‐strain curves and non‐linear acoustic emission rates as have previously been observed from room temperature studies on sands, sandstones, and soils. However, results from our hydrothermal experiments show that the critical effective pressure (P*) associated with the onset of significant pore collapse and pervasive cataclastic flow is lower at increased temperature. Samples subjected to triaxial loading at elevated temperature show yield behavior resembling that observed from room temperature studies on granular rocks and soils. When considered in terms of distortional and mean stresses, the yield strength data for a given temperature define an elliptical envelope consistent with critical state and CAP models from soil mechanics. For the conditions we tested, triaxial yield data at low effective pressure are essentially temperature‐insensitive whereas yield levels at high effective pressure are lowered as a function of elevated temperature. We interpret our yield data in a manner consistent with Arrhenius behavior expected for thermally assisted subcritical crack growth. Taken together, our results indicate that increased stresses and temperatures associated with subsurface burial will significantly alter the yield strength of deforming granular media in systematic and predictable ways.

A discrete element model for the development of compaction localization in granular rock

A discrete element model was developed to simulate the micromechanics of compaction localization in a granular rock. The rock was modeled as a bonded assembly of circular disks, and seven different distributions of radius were considered. To simulate grain crushing and pore collapse, an intragranular damage mechanism was introduced that allows for the shrinkage of a disk if one of its normal contact stresses attains a critical value. The model captures key attributes of failure mode and damage evolution associated with the brittle‐ductile transition in porous sandstones. Our simulations indicate that the development of discrete compaction bands is promoted in a relatively homogeneous granular aggregate, while diffuse band growth and distributed cataclastic flow are preferred modes of compaction in a more heterogeneous system. To interpret the former result an Eshelby inclusion model was proposed to estimate analytically the local stress perturbations due to pore collapse in a homogeneous aggregate.

Acoustic properties of carbonates: Effects of rock texture and implications for fluid substitution

More than 250 plugs from outcrops and three nearby boreholes in an undisturbed reef of Miocene (Tortonian) age were quantitatively analyzed for texture, mineralogy, and acoustic properties. We measured the P- and S-waves of carbonate rocks under dry (humidified) and brine-saturated conditions at [Formula: see text] effective pressure with an ultrasonic pulse transmission technique [Formula: see text]. The data set was compared with an extensive database of petrophysical measurements of a variety of rock types encountered in carbonate sedimentary sequences. Two major textural groups were distinguished on the basis of trends in plots of compressional-wave velocity versus Poisson’s ratio (a specific ratio of P-wave over S-wave velocity). In granular rocks, the framework of depositional grains is the main medium for acoustic-wave propagation; in crystalline rocks, this medium is provided by a framework of interlocking crystals formed during diagenesis. Rock textures are connected to primary depositionalparameters and a diagenetic overprint through the specific effects on Poisson’s ratio. Calculating acoustic velocities using Gassmann fluid substitution modeling approximates measured saturated velocities for 55% of the samples (3% error tolerance); however, it shows considerable errors because shear modulus changes with saturation. Introducing brine into the pore space may decrease the shear modulus of the rock by approximately [Formula: see text] or, alternatively, increase it by approximately [Formula: see text]. This change in shear modulus is coupled with the texture of the rock. In granular carbonates, the shear modulus decreases; in crystalline and cemented carbonates, it increases with saturation. The results demonstrate the intimate relationship between elastic behavior and the depositional and diagenetic properties of carbonate sedimentary rocks. The results potentially allow the direct extraction of granular and crystalline rock texture from acoustic data alone and may help predict rock types from seismic data and in wells.

Genesis of the channel iron deposits (CID) of the Pilbara region, Western Australia

Miocene fluvial goethite/hematite channel iron deposits (CID) are part of the Cenozoic Detritals 2 (CzD2), of the Western Australian Pilbara region. They range from gravelly mudstones through granular rocks to intraformational pebble, cobble and rare boulder conglomerates, as infill in numerous meandering palaeochannels in a mature surface that includes Precambrian granitoids, volcanics, metasediments, BIF and ferruginous Palaeogene valley fill. In the Hamersley Province of the Pilbara, the consolidated fine gravels and subordinate interbedded conglomerates, with their leached equivalents, are a major source of export iron ore. This granular ore typically comprises pedogenically derived pelletoids comprising hematite nuclei and goethite cortices (ooids and lesser pisoids), with abundant coarser goethitised wood/charcoal fragments and goethitic peloids, minor clay, and generally minimal porous goethitic matrix, with late-stage episodic solution and partial infill by secondary goethite, silica and siderite (now oxidised) in places. Clay horizons and non-ore polymictic basal and marginal conglomerates are also present. The accretionary pedogenic pelletoids were mostly derived from stripping of a mature ferruginous but apparently well-vegetated surface, developed in the Early to Middle Miocene on a wide variety of susceptible rock types including BIF, basic intrusives and sediments. This deep ferruginisation effectively destroyed most remnants of the original rock textures producing a unique surface, very different to those that produced the underlying CzD1 (Palaeogene) and the overlying CzD3 (Pliocene – Quaternary). The peloids were derived both intraformationally from fragmentation and reworking of desiccated goethite-rich muds, and from the regolith. Tiny wood/charcoal fragments replaced in soil by goethite, and dehydrated to hematite, formed nuclei for many pelletoids. Additionally, abundant small (≤10 mm) fragments of wood/charcoal, now goethite, were probably replaced in situ within the consolidating CID. This profusion of fossil wood, both as pelletoid nuclei and as discrete fragments, suggests major episodic wild fires in heavily vegetated catchments, a point supported by the abundance of kenomagnetite – maghemite developed from goethite in the pelletoids, but less commonly in the peloids. The matrix to the heterogeneous colluvial and intraformational components is essentially goethite, primarily derived from modified chemically precipitated iron hydroxyoxides, resulting from leaching of iron-rich soils in an organic environment, together with goethitic soil-derived alluvial material. Major variations in the granular ore CID after deposition have resulted from intermittent groundwater flow in the channels causing dissolution and reprecipitation of goethite and silica, particularly in the basal CID zones, with surface weathering of eroded exposures playing a role in masking some of these effects. However, significant variations in rock types in both the general CID and the granular ore CID have also resulted from the effects of varied provenance.

Acoustic response of cemented granular sedimentary rocks: Molecular dynamics modeling

The effect of cementation processes on the acoustical properties of sands is studied via molecular dynamics simulation methods. We propose numerical methods where the initial uncemented sand is built by simulating the settling process of sediments. Uncemented samples of different porosity are considered by emulating natural mechanical compaction of sediments due to overburden. Cementation is considered through a particle-based model that captures the underlying physics behind the process. In our simulations, we consider samples with different degrees of compaction and cementing materials with distinct elastic properties. The microstructure of cemented sands is taken into account while adding cement at specific locations within the pores, such as grain-to-grain contacts. Results show that the acoustical properties of cemented sands are strongly dependent on the amount of cement, its stiffness relative to the hosting medium, and its location within the pores. Simulation results are in good correspondence with available experimental data and compare favorably with some theoretical predictions for the sound velocity within a range of cement saturation, porosity, and confining pressure.

Ground vibrations produced by rock motions and debris flows

In this study we compare ground vibrations generated by various rocks and debris flows at the same channel to explore the origin of ground vibrations caused by debris flows. In field experiments we identified the ground vibrations caused by motions of individual rocks. Ground vibrations were detected by geophones and analyzed in the time‐frequency domains. We found that ground vibrations caused by individual rocks were 10–150 Hz and that larger stones generate ground vibrations with lower peak frequencies. A sphere‐packing model of granular rocks was used to estimate the propagation speed of ground vibrations. This was found to be underestimated when compared with our experimental data. The signal decay rate was obtained under the assumption that ground vibrations propagate as exponentially attenuating cylindrical waves. Ground vibrations produced by a debris flow at Ai‐Yu‐Zi Creek, Nan‐Tou, Taiwan, on 2 July 2004 revealed that the debris flow forefront produced vibrations lower than 50 Hz and ranged between 50 and 100 Hz after the front had passed. When the main front was closest to the sensor, the frequency spectrum covered a wide range, from 10 to 250 Hz. The mean velocity of the debris flow front was 13.3 m/s. Frequencies of ground vibrations caused by individual rocks are within the frequency range of ground vibrations captured during the debris flow, confirming that one of the main sources of ground vibration caused by debris flows is the interaction of rocks or boulders with the channel bed.

Modeling Granular Crushing in Ring Shear Tests: Experimental and Numerical Analyses

A fault consists of a zone of heavily fragmented granular rock (gouge), which is confined between two rough walls made of fractured rock. The granular gouge is the result of previous fracturing of the wall rock by the combined effect of compressive and shear stresses. Through time, the granular fault gouge will experience various episodes of further fragmentation (crushing) as a result of the mobilization by shear of the fault walls. The evolution of crushing in a simulated gouge material was studied using laboratory ring shear tests and DEM ring shear simulations. The laboratory ring shear tests were developed using sugar as a weak granular material. It was found that the residual friction coefficient of this material maintained a constant value regardless of the severe degradation of the particles. This degradation was induced by increasing the angular deformation or increasing the applied vertical stress. Moreover, it was found that the grain size distribution of the original uniform material evolved toward a fractal distribution of sizes. The results from the DEM simulations confirmed those from the laboratory tests and provided also a visualization of the evolution of crushing. Event though originally DEM does not consider particle breakage, this was allowed by replacing particles fulfilling a predefined tensile failure criterion with an equivalent group of smaller particles.

Near-tip stress rotation and the development of deformation band stepover geometries in mode II

Research Article| March 01, 2006 Near-tip stress rotation and the development of deformation band stepover geometries in mode II Chris. H. Okubo; Chris. H. Okubo 1Geomechanics–Rock Fracture Group, Department of Geological Sciences and Engineering/172, University of Nevada, Reno, Nevada 89557-0138, USA Search for other works by this author on: GSW Google Scholar Richard A. Schultz Richard A. Schultz 1Geomechanics–Rock Fracture Group, Department of Geological Sciences and Engineering/172, University of Nevada, Reno, Nevada 89557-0138, USA Search for other works by this author on: GSW Google Scholar GSA Bulletin (2006) 118 (3-4): 343–348. https://doi.org/10.1130/B25820.1 Article history received: 12 Mar 2005 rev-recd: 04 Aug 2005 accepted: 26 Aug 2005 first online: 08 Mar 2017 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn MailTo Tools Icon Tools Get Permissions Search Site Citation Chris. H. Okubo, Richard A. Schultz; Near-tip stress rotation and the development of deformation band stepover geometries in mode II. GSA Bulletin 2006;; 118 (3-4): 343–348. doi: https://doi.org/10.1130/B25820.1 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyGSA Bulletin Search Advanced Search Abstract The propagation of deformation bands into compressive and extensional stepover geometries is investigated by integrating field observations with numerical model simulations of the effective stress state due to shear along the bands. Deformation bands are tabular discontinuities, with mm- to cm-scale thicknesses, of localized volumetric strain and shear. Deformation bands are precursors to frictional slip (i.e., faulting) in porous granular rocks and soils. Systematic rotations in near-tip principal stress orientation due to shear along the overlapping deformation bands are shown to predict band propagation paths that are consistent with characteristic stepover geometries as viewed in the mode II direction, the orientation in which the observation plane is parallel with the displacement direction. Therefore, propagation paths for deformation bands can be predicted from knowledge of the effective near-tip stress state. These results establish a mechanics-based framework for investigations of fault growth and fault-controlled fluid flow in porous granular rocks and soils. You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

Overview of the Spirit Mars Exploration Rover Mission to Gusev Crater: Landing site to Backstay Rock in the Columbia Hills

Spirit landed on the floor of Gusev Crater and conducted initial operations on soil‐covered, rock‐strewn cratered plains underlain by olivine‐bearing basalts. Plains surface rocks are covered by wind‐blown dust and show evidence for surface enrichment of soluble species as vein and void‐filling materials and coatings. The surface enrichment is the result of a minor amount of transport and deposition by aqueous processes. Layered granular deposits were discovered in the Columbia Hills, with outcrops that tend to dip conformably with the topography. The granular rocks are interpreted to be volcanic ash and/or impact ejecta deposits that have been modified by aqueous fluids during and/or after emplacement. Soils consist of basaltic deposits that are weakly cohesive, relatively poorly sorted, and covered by a veneer of wind‐blown dust. The soils have been homogenized by wind transport over at least the several kilometer length scale traversed by the rover. Mobilization of soluble species has occurred within at least two soil deposits examined. The presence of monolayers of coarse sand on wind‐blown bedforms, together with even spacing of granule‐sized surface clasts, suggests that some of the soil surfaces encountered by Spirit have not been modified by wind for some time. On the other hand, dust deposits on the surface and rover deck have changed during the course of the mission. Detection of dust devils, monitoring of the dust opacity and lower boundary layer, and coordinated experiments with orbiters provided new insights into atmosphere‐surface dynamics.

A general framework for the occurrence and faulting of deformation bands in porous granular rocks

Deformation bands form in porous granular rocks by localized inelastic yielding that is well described by a modified Cam cap model. All five kinematic varieties of bands observed in the field, including dilation bands, dilation bands with shear, shear bands, compaction bands with shear, and compaction bands, can be explained by this unifying mechanical framework once their localization criteria are also specified. The growth of dilation bands with shear has been observed in the field and in the laboratory for low-pressure conditions. More commonly, however, strain hardening of compaction bands with shear will lead to faulting within, and eventually through, the resulting damage zone if the associated yield cap grows outward sufficiently to intersect the frictional strength surface. This sequence is best explained by replacing the critical state line with a frictional failure criterion in the general Cam cap approach. Given recent advances in localization theory and continuing refinement of field observations, the term “fracture” must now be expanded to include both weak and strong discontinuities, or deformation bands and displacement discontinuities (i.e., cracks, joints, veins, solution surfaces, anticracks, dikes, sills, faults), respectively. Shear zones and fault zones that accommodate both continuous and discontinuous changes in shear offset within them should also be considered as fractures according to this expanded definition.

Geological and mathematical framework for failure modes in granular rock

We synthesize all the available data on failure processes in granular rock and provide a geological framework for the corresponding structures. We describe two categories: (1) sharp discontinuities made up of two surfaces similar to elastic crack models, and (2) tabular structures resulting from strain localization into narrow bands. Each of these categories includes types predominated by shear and/or volumetric deformation. While shear failure can be in two different modes as sliding and tearing, the volumetric failure has two diametrically opposite types: compaction (contraction) and dilation (extension). Thus, we distinguish among bands predominantly by shearing, shortening, and extension. Slip surfaces, pressure solution surfaces, and joints represent corresponding sharp discontinuities. A survey of observations and measurements from naturally occurring structures indicates that although isochoric shear and pure volumetric deformation types represent end members, a complete spectrum of combined shear and volumetric deformation occurs in nature. Field observations also show that sharp structures overlap older narrow tabular structures in the same rock. This switch in failure modes is attributed to changing rock rheology and/or loading conditions. In the mathematical modeling, we focus on the strain localization into narrow tabular bands using classical bifurcation theory combined with nonlinear continuum mechanics and plasticity. We formulate a family of three invariant plasticity models with a compression cap and capture the entire spectrum of failure of geomaterials. In addition, we draw an analogy between the concepts of ‘strong’ and ‘sharp’ discontinuity and classic elastic crack representations to complement the mathematical treatment of the failure modes.