Formation Of Compaction Bands Research Articles

Mechanism of formation of wiggly compaction bands in porous sandstone: 1. Observations and conceptual model

AbstractField observations are combined with microscopic analyses to investigate the mechanism of formation of wiggly compaction bands (CBs) in the porous Jurassic aeolian Aztec Sandstone exposed at Valley of Fire State Park, Nevada. Among the three types of CBs (T1, T2, and T3), we focused on the wiggly CBs (T3), which show a chevron (T31) or wavy (T32) pattern with typical corner angles of approximately 90° or 130°, respectively. Where corner angles of wiggly CBs increase to 180°, they become straight CBs (T33). Image analyses of thin sections using an optical microscope show host rock porosity increases downslope in this dune, and the predominant type of wiggly CBs also varies from chevron to straight CBs. Specifically, band type varies continuously from chevron to wavy to straight where the porosity and grain sorting of the host rock increase systematically. Based on the crack and anticrack models, we infer that the change from chevron to straight CBs is due to increasing failure angle of the sandstone and this may correlate with increasing grain sorting. Wavy CBs with intermediate failure angle and host rock porosity are an intermediate stage between chevron and straight CBs. Previous sedimentological studies also have suggested that grain size and sorting degree increase downslope on the downwind side of sand dunes due to a sieving process of the wind‐blown grains. Therefore, the transition of wiggly CB types in this regard correlates with increasing sorting and perhaps with increasing porosity downslope.

Mechanism of formation of wiggly compaction bands in porous sandstone: 2. Numerical simulation using discrete element method

AbstractWiggly compaction bands in porous aeolian sandstone vary from chevron shape to wavy shape to nearly straight. In some outcrops these variations occur along a single band. A bonded close‐packed discrete element model is used to investigate what mechanical properties control the formation of wiggly compaction bands (CBs). To simulate the volumetric yielding failure of porous sandstone, a discrete element shrinks when the force state of one of its bonds reaches the yielding cap defined by the failure force and the aspect ratio (k) of the yielding ellipse. A Matlab code “MatDEM3D” has been developed on the basis of this enhanced discrete element method. Mechanical parameters of elements are chosen according to the elastic properties and the strengths of porous sandstone. In numerical simulations, the failure angle between the band segment and maximum principle stress decreases from 90° to approximately 45° as k increases from 0.5 to 2, and compaction bands vary from straight to chevron shape. With increasing strain, subsequent compaction occurs inside or beside compacted elements, which leads to further compaction and thickening of bands. The simulations indicate that a greater yielding stress promotes chevron CBs, and a greater cement strength promotes straight CBs. Combined with the microscopic analysis introduced in the companion paper, we conclude that the shape of wiggly CBs is controlled by the mechanical properties of sandstone, including the aspect ratio of the yielding ellipse, the critical yielding stress, and the cement strength, which are determined primarily by petrophysical attributes, e.g., grain sorting, porosity, and cementation.

Mechanical compaction and strain localization in Bleurswiller sandstone

AbstractWe performed a systematic investigation of mechanical compaction and strain localization in Bleurswiller sandstone. Our data show that the effective pressure principle can be applied in both the brittle faulting and cataclastic flow regimes, with an effective pressure coefficient close to but somewhat less than 1. Under relatively high confinement, the samples typically fail by development of compaction bands. X‐ray computed tomography (CT) was used to resolve preexisting porosity clusters, as well as the initiation and propagation of the compaction bands in deformed samples. Synthesis of the CT and microstructural data indicates that there is no casual relation between collapse of the porosity clusters in Bleurswiller sandstone and nucleation of the compaction bands. Instead, the collapsed porosity clusters may represent barriers for the propagation of compaction localization, rendering the compaction bands to propagate along relatively tortuous paths so as to avoid the porosity clusters. The diffuse and tortuous geometry of compaction bands results in permeability reduction that is significantly lower than that associated with compaction band formation in other porous sandstones. Our new data confirm that Bleurswiller sandstone stands out as the only porous sandstone associated with a compactive cap that is linear, and our CT and microstructural observation show that it is intimately related to collapse of the porosity clusters. We demonstrate that the anomalous linear caps and their slopes are in agreement with a micromechanical model based on the collapse of a spherical pore embedded in an elastic‐plastic matrix that obeys the Coulomb failure criterion.

Time‐dependent compaction band formation in sandstone

AbstractCompaction bands in sandstone are laterally extensive planar deformation features that are characterized by lower porosity and permeability than the surrounding host rock. As a result, this form of localization has important implications for both strain partitioning and fluid flow in the Earth's upper crust. To better understand the time dependency of compaction band growth, we performed triaxial deformation experiments on water‐saturated Bleurswiller sandstone (initial porosity = 0.24) under constant stress (creep) conditions in the compactant regime. Our experiments show that inelastic strain accumulates at a constant stress in the compactant regime, manifest as compaction bands. While creep in the dilatant regime is characterized by an increase in porosity and, ultimately, an acceleration in axial strain rate to shear failure, compaction creep is characterized by a reduction in porosity and a gradual deceleration in axial strain rate. The global decrease in the rates of axial strain, acoustic emission energy, and porosity change during creep compaction is punctuated at intervals by higher rate excursions, interpreted as the formation of compaction bands. The growth rate of compaction bands formed during creep is lower as the applied differential stress, and hence, background creep strain rate, is decreased. However, the inelastic strain associated with the growth of a compaction band remains constant over strain rates spanning several orders of magnitude (from 10−8 to 10−5 s−1). We find that despite the large differences in strain rate and growth rate (from both creep and constant strain rate experiments), the characteristics (geometry and thickness) of the compaction bands remain essentially the same. Several lines of evidence, notably the similarity between the differential stress dependence of creep strain rate in the dilatant and compactant regimes, suggest that as for dilatant creep, subcritical stress corrosion cracking is the mechanism responsible for compactant creep in our experiments. Our study highlights that stress corrosion is an important mechanism in the time‐dependent porosity loss, subsidence, and permeability reduction of sandstone reservoirs.

Visco‐poroelastic damage model for brittle‐ductile failure of porous rocks

AbstractThe coupling between damage accumulation, dilation, and compaction during loading of sandstones is responsible for different structural features such as localized deformation bands and homogeneous inelastic deformation. We distinguish and quantify the role of each deformation mechanism using new mathematical model and its numerical implementation. Formulation includes three different deformation regimes: (I) quasi‐elastic deformation characterized by material strengthening and compaction; (II) cataclastic flow characterized by damage increase and compaction; and (III) brittle failure characterized by damage increase, dilation, and shear localization. Using a three‐dimensional numerical model, we simulate the deformation behavior of cylindrical porous Berea sandstone samples under different confining pressures. The obtained stress, strain, porosity changes and macroscopic deformation features well reproduce the laboratory results. The model predicts different rock behavior as a function of confining pressures. The quasi‐elastic and brittle regimes associated with formation of shear and/or dilatant bands occur at low effective pressures. The model also successfully reproduces cataclastic flow and homogeneous compaction under high pressures. Complex behavior with overlap of common features of all regimes is simulated under intermediate pressures, resulting with localized compaction or shear enhanced compaction bands. Numerical results elucidate three steps in the formation of compaction bands: (1) dilation and subsequent shear localization, (2) formation of shear enhanced compaction band, and (3) formation of pure compaction band.

Dynamical effects during compaction band formation affecting their spatial periodicity

AbstractCompaction bands (CBs) are responsible for significant anisotropy alterations of permeability in geological materials; hence, understanding their formation conditions appears of key importance to all applications involving fluid extraction/injection from/into the ground. While most of the available models to understand CB formation are focused on interpreting the onset of a single CB, little effort has been so far dedicated to understand the documented periodicity of CBs. In this paper, the role of dynamical effects in inducing the post onset evolution of CBs is analyzed by means of a dedicated model for porous media with compressible constituents, with reference to a horizontal layer of sandy, water‐saturated material. Elastic waves are generated as a first CB occurs due to sudden, localized volumetric collapse. If the waves are reflected at the interface with a softer material or with a previously formed CB, they produce significant local effective stress concentrations, which can promote the formation of further CBs in a cascade fashion, according to a regular geometric pattern. The spatial distribution of dynamically generated CBs, as well as the extent of the phenomenon, depends on the geometry of the domain and on the material's permeability. Sensitivity analysis is also performed to assess the key properties that promote dynamical CB in situ formation, identifying as the most influential conditions large stratum stiffness (increasing with depth) and the presence of softer layers. In contrast, the presence of less permeable and/or stiffer layers is not believed to play a major role in the proposed mechanism.

Nano-scale mechanical properties and behavior of pre-sintered zirconia

This paper reports on the mechanical properties and material behavior of pre-sintered zirconia using nanoindentation with in situ scanning probe microscopy. Indentation contact hardness, Hc, and Young׳s modulus, E, were measured at loading rates of 0.1–2mN/s and 10mN peak load to understand the loading rate effect on its properties. Indentation imprints were analyzed using in situ scanning probe imaging to understand the indentation mechanisms. The average measured contact hardness was 0.92–1.28GPa, independent of the loading rate (ANOVA, p>0.05). Young׳s moduli showed a loading rate dependence, with average 61.25GPa and a great deviation at a low loading rate of 0.1mN/s, which was twice the average moduli at the loading rates of 0.5–2mN/s. Extensive discontinuities and the largest maximum penetration, final and contact depths were also observed on the load–displacement curves at the lowest loading rate. These phenomena corresponded to microstructural compaction (pore closure and opening) and kink band formation, indicating the loading rate dependence for microstructural changes during nanoindentation. The in situ scanning probe images of indentation imprints show plastic deformation without fracture at all loading rates, compaction at the low loading rate and pore filling at the high loading rate. The mechanical behavior studied provides physical insight into the abrasive machining responses of pre-sintered zirconia using sharp diamond abrasives.

Chemically induced compaction bands: Triggering conditions and band thickness

During compaction band formation, various mechanisms can be involved at different scales. Mechanical and chemical degradation of the solid skeleton and grain damage are important factors that may trigger instabilities in the form of compaction bands. Here we explore the conditions of compaction band formation in quartz- and carbonate-based geomaterials by considering the effect of chemical dissolution and grain breakage. As the stresses/deformations evolve, the grains of the material break, leading to an increase of their specific surface. Consequently, their dissolution is accelerated and chemical softening is triggered. By accounting for (a) the mass diffusion of the system, (b) a macroscopic failure criterion with dissolution softening, and (c) the reaction kinetics at the microlevel, a model is proposed and the conditions for compaction instabilities are investigated. Distinguishing the microscale (grain level) from the macrolevel (representative elementary volume) and considering the heterogeneous microstructure of the representative elementary volume, it is possible to discuss the thickness and periodicity of compaction bands. Two case studies are investigated. The first one concerns a sandstone rock reservoir which is water flooded and the second one a carbonate rock in which CO2 is injected for storage. It is shown that compaction band instabilities are possible in both cases.

Experimental study on formation mechanism of compaction bands in weathered rocks with high porosity

Since Mollema and Antonellini observed compaction bands in the field in 1996, different patterns of compaction bands have been found in laboratory experiments. There are some discrepancies between the laboratory experiments and the field observations: compared to the field observation, the stress levels required to induce compaction bands in laboratory experiments are usually higher than the inferred in the field, and the grain crushing are more intense in the laboratory experiments. In this paper, compaction bands were observed at the maximal principal stresses below 8 MPa, which is lower than the stress level inferred in the field, and there was no severe comminution inside the compaction bands. Experimental results indicate that the porosity and confining pressure have great impacts on the types of localization bands. Lower porosity and confining pressure can promote the growth of shear bands and high-angle shear bands. Higher porosity and confining pressure can promote the growth of discrete compaction bands. Intermediate porosity and confining pressure are favorable for the growth of hybrid modes involving two of the three, i.e., discrete compaction band, diffuse compaction band and high-angle shear band. The formation of discrete compaction bands is more unstable compared to diffuse compaction bands. The two types of compaction bands can appear in the same type rocks, and diffuse compaction bands are formed under lower confining pressure compared to discrete compaction bands. The reduction of permeability was within 2 orders of magnitude in this study, and it is 2-3 orders of magnitude lower than those obtained by other researchers.

2011 Drucker Medal Paper: Localized Compaction in Porous Sandstones

Compaction bands are narrow, roughly planar zones of localized deformation, in which the shear is less than or comparable to compaction. Although there are differences in their appearance in the field and in laboratory specimens, they have been observed in both for high-porosity (greater than about 15%) sandstones. Because the porosity in them is reduced and the tortuosity increased, they inhibit fluid flow perpendicular to their plane. Consequently, they can alter patterns of fluid movement in formations in which they occur and are relevant to applications involving fluid injection or withdrawal. Formation of compaction bands is predicted by a framework that treats localized deformation as a bifurcation from homogeneous deformation. This paper gives a brief overview of compaction localization but focuses on field and laboratory observations that constrain two parameters entering the bifurcation analysis: a friction coefficient μ and a dilatancy factor β. The inferred values suggest that normality (μ = β) is not satisfied, and compaction localization occurs on a transitional portion of the yield surface, where the local slope in a plot of Mises equivalent shear stress versus compressive mean normal stress changes from positive (μ > 0) to negative (μ < 0). These inferences are at odds with critical state and cap theories that typically assume normality and predict dilation on the portion of the surface where μ > 0. In addition, the values suggest that the critical state (μ = 0) does not necessarily correspond to zero volume change.

Effect of grain size distribution on the development of compaction localization in porous sandstone

Compaction bands are strain localization structures that are relatively impermeable and can act as barriers to fluid flow in reservoirs. Laboratory studies have shown that discrete compaction bands develop in several sandstones with porosities of 22–25%, at stress states in the transitional regime between brittle faulting and cataclastic flow. To identify the microstructural parameters that influence compaction band formation, we conducted a systematic study of mechanical deformation, failure mode and microstructural evolution in Bleurswiller and Boise sandstones, of similar porosity (∼25%) and mineralogy but different sorting. Discrete compaction bands were observed to develop over a wide range of pressure in the Bleurswiller sandstone that has a relatively uniform grain size distribution. In contrast, compaction localization was not observed in the poorly sorted Boise sandstone. Our results demonstrate that grain size distribution exerts important influence on compaction band development, in agreement with recently published data from Valley of Fire and Buckskin Gulch, as well as numerical studies.

Distribution of compaction bands in 3D in an aeolian sandstone: The role of cross-bed orientation

We report the occurrence of bed-parallel and high-angle compaction bands as well as crooked or wiggly compaction bands in the aeolian Aztec Sandstone exposed throughout the Valley of Fire State Park, Nevada. Field observations at several locations within the Park show that depositional domains (dune units characterized by cross-beds therein) with particular ranges of cross-bed orientations corresponding to certain deformational/structural domains (compaction bands of different orientations) occur adjacent to each other in a consistent pattern. We distinguish three architectural categories of depositional and structural domains: 1) cross-beds with bed-parallel compaction bands, 2) cross-beds with high-angle compaction bands, and 3) cross-beds with both bed-parallel and high-angle compaction bands overlapping in a relatively narrow transition zone. The field data demonstrates that the orientation of the cross-beds for each of these domains falls into a certain range. In fact, there is a strong correlation between the bottom set and high-angle compaction bands and the top set and the low-angle bed-parallel compaction bands. This implies that the cross-bed heterogeneity and the resulting mechanical anisotropy may play a significant role in the formation, orientation, distribution, and compartmentalization of compaction bands in the study area. Data sets on the dimensions of both depositional and structural domains indicate that they are interrelated and show a wide range of distributions.There is plenty of evidence for contemporaneous age relationships between compaction bands of various orientations. Based on this temporal relationship, we propose that at least one set of bands, and perhaps all of them, accommodated primarily localized compaction oblique to the principal planes of stress. Alternatively, if each set of the compaction bands represents the principal planes, then, the stress orientation must have varied spatially, perhaps due to the anisotropy of the aeolian medium with variable cross-bed orientation.

Conditions and implications for compaction band formation in the Navajo Sandstone, Utah

Observations from quartz-rich eolian Navajo Sandstone in the Buckskin Gulch site in southernmost Utah show that pure compaction bands only occur in sandstones where current porosity > 0.29 ± 3, permeability > 10 ± 7 darcy, and grain size > 0.4 mm – properties restricted to the lower and most coarse-grained and well-sorted parts of grain flow units within the dune units. Hence a direct correlation between stratigraphy and band occurrence has been established that can be used to predict deformation band occurrences in similar sandstone reservoirs. We show that the pure compaction bands formed perpendicular to a subhorizontal σ 1, bisecting conjugate sets of shear-enhanced compaction bands. The latter bands locally developed into shear-dominated bands that transect entire dune units, suggesting that an increase in the amount of simple shear promotes band propagation into less porous and permeable lithologies. Stress considerations indicate that, as a continuous and overlapping sequence of events, pure compaction bands in quartz-rich Navajo Sandstone initiated at 10–20 MPa (∼1 km depth), followed by shear-enhanced compaction bands that locally developed into more stratigraphically extensive shear-dominated bands. The rare combination of special lithologic and stress conditions may explain why pure compaction bands are rarely observed in naturally deformed sandstones.

Compaction bands due to grain crushing in porous rocks: A theoretical approach based on breakage mechanics

[1] Grain crushing and pore collapse are the principal micromechanisms controlling the physics of compaction bands in porous rocks. Several constitutive models have been previously used to predict the formation and propagation of these bands. However, they do not account directly for the physical processes of grain crushing and pore collapse. The parameters of these previous models were mostly tuned to match the predictions of compaction localization; this was usually done without validating whether the assigned parameters agree with the full constitutive behavior of the material. In this study a micromechanics-based constitutive model capable of tracking the evolving grain size distribution due to grain crushing is formulated and used for a theoretical analysis of compaction band formation in porous rocks. Linkage of the internal variables to grain crushing enables us to capture both the material behavior and the evolving grain size distribution. On this basis, we show that the model correctly predicts the formation and orientation of compaction bands experimentally observed in typical high-porosity sandstones. Furthermore, the connections between the internal variables and their underlying micromechanisms allow us to illustrate the significance of the grain size distribution and pore collapse on the formation of compaction bands.

X-ray imaging of water motion during capillary imbibition: A study on how compaction bands impact fluid flow in Bentheim sandstone

[1] To investigate the effect of compaction bands (CB) on fluid flow, capillary imbibition experiments were performed on Bentheim sandstone specimens (initial porosity ∼22.7%) using an industrial X-ray scanner. We used a three-step procedure combining (1) X-ray imaging of capillary rise in intact Bentheim sandstone, (2) formation of compaction band under triaxial tests, at 185 MPa effective pressure, with acoustic emissions (AE) recording for localization of the induced damage, and (3) again X-ray imaging of capillary rise in the damaged specimens after the unloading. The experiments were performed on intact cylindrical specimens, 5 cm in diameter and 10.5 cm in length, cored in different orientations (parallel or perpendicular to the bedding). Analysis of the images obtained at different stages of the capillary imbibition shows that the presence of CB slows down the imbibition and disturbs the geometry of water flow. In addition, we show that the CB geometry derived from X-ray density maps analysis is well correlated with the AE location obtained during triaxial test. The analysis of the water front kinetics was conducted using a simple theoretical model, which allowed us to confirm that compaction bands act as a barrier for fluid flow, not fully impermeable though. We estimate a contrast of permeability of a factor of ∼3 between the host rock and the compaction bands. This estimation of the permeability inside the compaction band is consistent with estimations done in similar sandstones from field studies but differs by 1 order of magnitude from estimations from previous laboratory measurements.

Porosity and grain size controls on compaction band formation in Jurassic Navajo Sandstone

Determining the rock properties that permit or impede the growth of compaction bands in sedimentary sequences is a critical problem of importance to studies of strain localization and characterization of subsurface geologic reservoirs. We determine the porosity and average grain size of a sequence of stratigraphic layers of Navajo Sandstone that are then used in a critical state model to infer plastic yield envelopes for the layers. Pure compaction bands are formed in layers having the largest average grain sizes (0.42–0.45 mm) and porosities (28%), and correspondingly the smallest values of critical pressure (∼22 MPa) in the sequence. The results suggest that compaction bands formed in these layers after burial to ∼1.5 km depth in association with thrust faulting beneath the nearby East Kaibab monocline, and that hardening of the yield caps accompanied compactional deformation of the layers.

Characterization of shear and compaction bands in a porous sandstone deformed under triaxial compression

The study of localized deformation in porous sandstones at the laboratory scale can yield valuable insights into the internal structures and mechanisms of shear zones and compaction bands that might impact on flow at a reservoir scale. Herein, we report results of a laboratory study of shear and compaction band formation in a porous sandstone using a range of full-field experimental techniques: acoustic emissions, ultrasonic tomography, X-ray tomography, and 3D volumetric digital image correlation, plus thin section and Scanning Electron Microscope observations. The two main mechanisms involved in shear and compaction band formation, grain breakage (damage) and porosity reduction (compaction), are both well captured by the combination of all these laboratory techniques. The combined use of these techniques demonstrated the processes of shear and compaction band generation and the associated strain components that developed in the laboratory, and potentially also increased understanding of the naturally developed equivalents. The physical mechanisms of shear and compaction involved seem to be similar, but at the laboratory scale they show differences in the proportions and the order of occurrence in time.

Pure and shear-enhanced compaction bands in Aztec Sandstone

We report on the occurrence of deformation bands in Jurassic eolian Aztec Sandstone at Valley of Fire, Nevada, that accommodated roughly equal amounts of shear and band-perpendicular compaction by grain rearrangement and porosity collapse. These bands, referred to as shear-enhanced compaction bands, differ in orientation, structural arrangement, and microtexture from pure compaction bands that form perpendicular to the shortening direction. Shear-enhanced compaction bands are planar over tens of meters, and commonly composed of multiple parallel thinner strands. Pure compaction bands are less commonly planar, typically wavy or chevron in geometry, and composed of single strands. Shear-enhanced compaction bands are inferred to form at 38–53° relative to the maximum compressive principal stress, and thus differ from compactive shear bands that form at distinctly lower angles. While shear offsets along shear-enhanced compaction bands are only about 1/10th of the band thickness, by contrast, shear offsets may be large for compactive shear bands with formation of slip surfaces. Based on inferred timing and burial conditions, we interpret that the formation of shear-enhanced and pure compaction bands requires large initial porosity close to the loose packing porosity, good sorting, and high effective maximum compressive principal stress of about 20 MPa.

Numerical Modeling of the Slit Mode of Cavity Evolution Associated With Sand Production

Summary This paper documents progress in the development of a numerical model to predict the amount and rate of sand production at the scale of a wellbore or perforation. The model uses a continuum hydro-mechanical description of the rock mass, coupled with a superficial erosion scheme with evolving geometry. Different modes of cavity evolution have been observed in laboratory experiments to study sand production (uniform, dog-ear, and slit), and the various modes have been associated with different rock failure types (tension, shear, and compaction). In this work, the sand-production model (which can accommodate tension and shear failure) is also expanded to account for the combination of volumetric collapse (compaction band formation) and transport of failed material by hydrodynamic forces. It is shown, using numerical experiments, that those two basic ingredients can lead to the development of the slit mechanism. In this paper, we review the basic conditions for the compaction mode of failure to occur by considering a simple cap constitutive law and give examples of numerical simulations that illustrate band formation in a (dry) hollow cylinder test. Also, using numerical experiments, we show that the sand-production model, enhanced with a constitutive law featuring a volumetric cap, is able to reproduce qualitatively the slit mode of cavity evolution that has been observed in laboratory settings. One key feature of the computational model is a sand-production curve giving sand-mass production versus simulation time. With the documented enhancement, the model can generate sand-production curves associated with tension, shear, and compaction failure. The sand-production model needs to be developed and validated further, and calibrated using laboratory experiments. However, at this stage, it shows good potential as an engineering tool to help characterize the impact of rock strength on sand production associated with oil production.

Influence of the intermediate principal stress on the strain localization mode in porous sandstone

Compaction bands and dilation bands are zones of either pure compaction or pure dilation, characterized by decreased or increased porosity, respectively. In contrast with commonly observed shear bands, there are relatively few reports of compaction bands or dilation bands, particularly in field settings. This work explores one possible explanation for these isolated observations: unique stress conditions, which occur infrequently, are required to form these bands. In particular, the influence of the intermediate principal stress on localization conditions is examined. Theoretical results, using a bifurcation approach to localization, reveal that conditions for compaction band formation are least restrictive when the intermediate principal stress is equal to the minimum compressive stress, while dilation band conditions are least restrictive when the intermediate principal stress is equal to the maximum compressive stress. However, the occurrence of one of these favorable stress states does not guarantee formation of one of these deformation modes, since certain conditions on the inelastic material parameters (i.e., friction factor and dilation coefficient) must also be satisfied. These material parameters vary with mean stress; thus satisfaction of compaction band or dilation band conditions requires not only a specific relationship between the principal stresses but also a loading path resulting in a favorable mean stress, such that inelastic material parameters fall in the required range. In a laboratory environment, where principal stresses are controllable, these conditions should be readily achievable. However, if these specialized stress conditions are uncommon in field settings, theory suggests that compaction bands and dilation bands may form infrequently.