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The Stanford Rock Fracture Project
Field data, 3D geometrical modelling, quantification of micropores are combined with numerical simulation to investigate the mechanism of wiggly compaction bands in high-porosity aeolian sandstone. Field data show that the segments of wiggly compaction bands have similar orientations as that of preexisting shear-enhanced compaction bands H1 and H2. The wiggly bands are inferred to propagate and switch orientations between H1 and H2. Based on the geometry of band, the direction of greatest compression (ε3) is interpreted as perpendicular to the overall strike of wiggly compaction bands. And the band segments perpendicular to ε3 are the pure compaction bands. Analysis of micropores shows that the pure compaction bands have the greatest porosity in the host rock, and may have a different failure envelope. In discrete element modelling, a discrete particle is used to represent a pore structure that surrounded by several quartz grains. Similar to the collapse and compaction of a pore structure, the breakable particle may be compacted (shrink) when the force status exceeds the yielding cap determined by failure force (Ff) and aspect ratio (k). Discrete element model built by the breakable particles is compressed to simulate the formation of compaction bands. The direction of compaction bands is determined by the aspect ratio (k) of the cap. When k=0.5, compacted zone tends to propagate perpendicular to the greatest compression direction, which corresponds to pure compaction bands. When k=2, two 45-degree directions are the predominant directions of the compacted zones. Compacted zones propagate along one inclined direction, and may switch to the other direction when the stress state is changed. As a result, the wiggly compacted zone shows a chevron pattern. To conclude, the direction of compaction bands is determined by the failure envelope of the host rock and the local stress; the pure compaction bands formed at higher rock porosity; and the wiggly compaction bands composed of segments of shear-enhanced bands are perpendicular to the direction of greatest compression.
Collection
The Stanford Rock Fracture Project
Examination of the host rock around magmatic dikes at Ship Rock, NM, reveals two sets of joints in the Mancos shale in the immediate vicinity of the dikes. One set is parallel to the dike contact and is believed to have formed just ahead of the dike as it was propagating (Delaney et al. 1986). The other joint set is sub-perpendicular to the dike contact and is the focus of this paper. A high-resolution aerial map of a segment of the northeastern dike at Ship Rock was made using Structure from Motion (SfM), where a camera attached to a helium balloon collects photographs, which are automatically orthorectified and stitched together in Agisoft LLC. Measurements from this map, combined with other field data, shows that the joint set remains perpendicular to the contact along the length of the dike, even when the orientation of the dike changes. Furthermore there is a significant decrease in the fracture spacing towards the center of the dike. We interpret the joints to have formed as a result of heat flow from the dike, and we investigate the role of thermal pore-pressurization in this process. Understanding the formation of these joints is critical to our understanding of brecciation and erosion of host rock around fissure eruptions to produce sustained eruptions through larger cylindrical volcanic vents.
Collection
The Stanford Rock Fracture Project
We measured the permeabilities of 30 samples extracted from six sets of compaction bands and the adjacent host rocks of aeolian Aztec Sandstone using core flooding experiments. The results show that the permeability within the high-angle compaction bands (three sets) is consistently three orders of magnitude lower than that of the host rocks. For the bed-parallel compaction bands, the measured permeability reduction is about half an order to three orders of magnitude for two sets of bands, and there is no detected permeability reduction for the samples from one set. For the samples that show permeability reduction within high-angle and bed-parallel compaction bands, the results are generally consistent with the data estimated from 2D segmented image analyses in previous studies. Permeabilities of the samples used in the laboratory experiments were also obtained numerically based on 3D tomographic images scanned from micro-samples and lattice-Boltzmann flow simulations. In addition, Backscatter Electron Images (BEI) and Energy Dispersive Spectroscopy Images (EDSI) of thin-sections were used to estimate the clay content inside and outside the bands. Large differences exist between the lab-based and image-based permeability and porosity measurements of compaction bands and host rocks. Possible factors causing these differences are different sample sizes and heterogeneities within the host rocks, calibration on the image segmentation, incomplete characterization of clay minerals and fines migration during lab-based experiments. Given the wide range of permeability reductions within compaction bands of different orientations by different investigators, their impact on fluid flow should be evaluated case by case also considering their dimensions and distributions.
Collection
The Stanford Rock Fracture Project
Faults influence groundwater flow paths. Of interest here is the transport of contaminants within the faulted sandstones and shales of Chatsworth Formation exposed in southern California. Structural and hydrogeological data are combined to interpret the hydraulic head drop measured across a fault with tens of meters of oblique-slip. The fault zone architecture was delineated at two locations: the first one is an outcrop and the second one is a borehole intersecting the fault at depth. At the first station, the fault juxtaposes sandstones against shales with a fault core mostly consisting of deformed shale. A series of shale beds striking parallel to the fault zone and dipping by 50° towards the fault zone provides evidence that the shale was incorporated into the fault zone. At the second station, borehole images show a plane juxtaposing fractured sandstone against shale-rich fault rock. Hydraulic heads measured at 30 wells show a drop of 75 meters across the fault, which is interpreted to be a result of low-permeability shaley fault rock. It is proposed that the shale was incorporated into the fault zone by shale smearing. The results of this work provide constraints for modeling the migration of contaminates in the groundwater system.
Collection
The Stanford Rock Fracture Project
A 2-D mechanical model shows the effect that geometries, limestone material properties, boundary conditions, and pressure solution seam displacements have on echelon fracture propagation and vein shape. We present a range and combination of geologically substantiated values for these physical parameters to reproduce the geometries of echelon veins observed in the field. Particularly, triangular vein shapes and straight vein traces angled to the remote maximum principal compressive stress direction. A complete description of echelon vein and pressure solution seam formation reveals that limestone stiffness, pressure solution seam displacement, and vein interaction, in terms of vein length, vein spacing, and vein-array angle, are significant parameters. For veins in a left-stepping geometry oriented clockwise from the 𝜎! direction, straight vein propagation requires a specific amount of seam displacement. Displacement of the pressure solution seam is a function of the limestone stiffness. We find that for cracks at 0° (in line with 𝜎!), E must be relatively soft with a value of 1.5 GPa. Cracks that are at 10° (𝛼 = 35°) to the 𝜎! direction, E can be much stiffer (19 GPa). Echelon veins angled to the remote maximum principal compression direction are more likely to propagate in their own plane than veins oriented parallel to the maximum compression direction when they are coupled with pressure solution seams. This implies that for the formation of veins in echelon arrays, such as those identified at the eastern Monument Upwarp, pressure solution seam displacements can cause veins to be straight and angled to the remote maximum principal compressive direction. These results explain the common interpretation of 𝜎! bisecting the acute angle between conjugate array sets to cause their synchronous formation using the method that explicitly relates deformation (displacements and strain) to the causative forces as functions of the material properties. Small vein spacing provides clues about limestone stiffness. Limestone stiffness can be greater for straight propagation of veins with smaller spacing. Smaller vein spacing requires less pressure solution seam displacement for straight vein propagation than larger vein spacing. With a vein spacing of 8 mm, the limestone stiffness needs to be 3 GPa and admit 0.3 mm of pressure solution seam displacement. In contrast, a 19 GPa limestone stiffness (us = 0.1 mm) produces straight vein propagation when vein spacing is 5 mm. We observe most vein spacing to be less than the crack geometries that we model, therefore suggesting that the limestone could have been stiffer than 20 GPa.
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The Stanford Rock Fracture Project
Fault-related deformation in the Bear Creek field area (central Sierra Nevada, CA) provides an exceptional opportunity to investigate the constitutive equations that govern mid-crustal rheology. This paper focuses on a contractional fault step located in the Seven Gables outcrop, which is cross-cut by a leucocratic dike. Within the step, the dike is stretched and rotated, providing a graphic measure of the deformation. In addition, a mylonitic foliation develops within the dike and the surrounding granodiorite between the step-bounding faults. The geometry and conceptual model for the Seven Gables step are used as a basis for a finite element model of the deformation. Using this model, we test five possible constitutive equations for characterizing brittle-ductile deformation: Von Mises elastoplasticity, Drucker- Prager elastoplasticity, power law creep, two-layer elastoviscoplasticity, and coupled elastoviscoplasticity. Of the models tested, the coupled elastoplasitity with a relaxation time of t = 5e6 s provides the most accurate representation of the deformation within the step. It appears that a frictional plastic yield criterion (i.e., Drucker-Prager) is incapable of reproducing the outcrop deformation due to the elevated mean normal stress within the step. Furthermore, the symmetry of the intermediate and minimum principal deviatoric stress distributions across faults likely prevents the power-law creep model from localizing deformation within the fault step. Models with yield criteria based on the Mises equivalent stress are most successful in matching the outcrop deformation. Microstructural analysis, including electron backscatter diffraction analysis, indicates that deformation mechanisms within the step included brittle fracturing, crystal plasticity and viscous flow, consistent with elastoviscoplastic behavior. Furthermore, the dike appears to have been weaker than the granodiorite during deformation, due to the formation of interconnected and continuous layers of plastically deforming quartz.
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The Stanford Rock Fracture Project
We propose a close relationship between the orientations of cross-beds and the cross-bed package confined joints in the Jurassic aeolian Aztec Sandstone cropping out in the Valley of Fire State Park (NV) and Navajo Sandstone in Zion National Park (UT). The field data demonstrates that the orientation of cross- bed package confined joints is related to the orientation of cross-beds, suggesting that in addition to the distribution of compaction bands, cross-bed orientation and the associated anisotropy also exert a strong control on the formation, and orientation of the joints. These results may have important implications for fluid flow through aeolian sandstones in reservoirs and aquifers.
Collection
The Stanford Rock Fracture Project
In this study, we directly measured the permeabilities of six sets of compaction bands and the adjacent host rocks. The results show that the permeability within the three sets of high-angle compaction bands is consistently three orders of magnitudes lower than that of the host rocks. For bed- parallel compaction bands, the permeability reduction is about one to three orders of magnitudes within the bands, except that there is no detected permeability reduction within one set of the samples of the bed- parallel compaction bands. Future work on the composition analysis and microstructural attributes of the compaction bands and host rocks will be conducted to better understand the variation. Given the fact that this is the first study on directly measuring the permeability of compaction bands, the results obtained provide important constraints for the permeability reduction associated with compaction bands in aeolian Aztec Sandstone.
Collection
The Stanford Rock Fracture Project
Eshelby’ s solution for an ellipsoidal inhomogeneous inclusion in an infinite elastic body is applied to compaction bands and shear enhanced compaction bands in the Aztec sandstone at Valley of Fire State Park, NV. The inclusion and matrix are linear elastic and isotropic, and a remote stress field represents tectonic loading. Uniform eigen- strain in the inclusion accounts for inelastic compaction with porosity change from 25% to 10%. Differences in elas- tic moduli between the matrix and inclusion are based on laboratory data. We generalize earlier results, limited to 2D and axisymmetric geometries, by considering an ellip- soid with three unequal axes with intermediate and greatest axes different by a factor of 10, accounting for field obser- vations. Stiffness contrasts between inclusion and matrix produce a modest concentration or diminution of the re- mote stress components, but plastic strains of 1% to 10%, due to compaction, produce a significant triaxial compres- sive stress concentration, which presumably is responsible for band propagation. We use an iterative algorithm to es- timate the plastic strain and find that it is triaxial, but dom- inated by the normal strain acting across the inclusion. The stress diminution on the flank of a band is easily overcome by minor increases in the tectonic loading, enabling bands to be closely spaced relative to intermediate axis lengths. We use an iterative algorithm to identify the plastic strain in the shear-enhanced inclusion. If the plastic shear and normal strains are approximately equal, the ratio of shear to normal stress is about 1.3 at the tip.
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The Stanford Rock Fracture Project
Deformation within fault steps contributes to many important geologic phenomena, including earthquakes, mountain building, and basin development, and has previously been investigated using both kinematic and mechanical models. This paper provides a direct comparison of these modeling techniques in the context of a meter-scale contractional fault step located in the Seven Gables outcrop (Bear Creek field area, Sierra Nevada, CA). The Seven Gables fault step contains locally foliated granodiorite and a stretched and rotated dike, which serve as three-dimensional deformation markers. Kinematic models in previous studies have assumed one of two possible shear plane orientations: (i) shear plane parallel to the step- bounding faults; (ii) shear plane parallel to an internal fault, which is oblique to and connects the step- bounding faults. This study presents kinematic models for the Seven Gables fault step using each of these geometries. Kinematic modeling is accomplished by use of the deformation matrix, which is first formulated for simple shear and then for transtension/transpression. The components of the deformation matrix are based on outcrop measurements and the assumption of constant volume. Both models result in dike orientations with significant misfit (model 1: 28% total misfit; model 2: 44% total misfit) compared to the dike measured in outcrop. An interesting result of the kinematic analysis is that the contractional step may be classified as either transtensional or transpressional, depending on which model geometry is used, suggesting that these terms may not be appropriate descriptors of deformation within fault steps. The ambiguity of the kinematic results motivates the use of a mechanics-based finite element model of deformation in the Seven Gables fault step. The results of this mechanical model indicate that plastic strain localizes along a narrow zone that runs diagonally through the step (consistent with the orientation of the shear plane in the second kinematic model). The mechanical model provides additional insights into the heterogeneous nature of deformation within the step, including the spatial variability of plastic strain, slip gradient along the faults, and non- uniform dike thinning. The ability to characterize heterogeneous deformation represents a significant advantage of the mechanical model over the kinematic models. In addition, the mechanical model provides a means to investigate the underlying physics of the problem, including the governing constitutive laws, causative tectonic stress states, and frictional contact boundary conditions on the fault. In contrast, the kinematic model is constrained only by the geometry of the structure in the final state and the assumption of constant volume. The comparison between kinematic and mechanical models presented here should compel future investigators to use the latter when considering deformation within fault steps.
Collection
The Stanford Rock Fracture Project
This study has been designed to investigate and monitor a groundwater system that was highly contaminated by past military and industrial activities. In this proposal we describe a methodology to assess the effect of a fault and fracture system on the groundwater flow through the turbidite sequence underlying the study area near Los Angeles, California. This formation is composed of alternating sandstone and shale units. Using a process-based methodology we intend to decipher the architecture and the lateral and vertical continuity of the faults and fracture zones. In addition to a quantitative characterization of the fault and fracture system in the outcrop, we will use existing and new wellbore data to determine the 3D geometry of the observed faults and fractures. The knowledge gained will be useful for assessing the role of these structures in the flow of the groundwater in the site.
Collection
The Stanford Rock Fracture Project
This proposal suggests the use of field work, laboratory work, and modeling to investigate thermal pore pressurization around recently emplaced dikes as it relates to the formation of breccias and dike- perpendicular joint sets in the host rock adjacent to dikes that intrude fluid-saturated sedimentary rocks. The formation of dike-perpendicular joints and breccias is a necessary precursor to erosion and sustained flow through a conduit; thus, understanding their formation is critical to the outstanding question of how dikes and fissures evolve into larger volcanic plugs. Field work will be carried out at Ship Rock, New Mexico, an Oligocene-aged diatreme surrounded radially by minette dikes and smaller plugs. Ship Rock and other intrusions of the Navajo Volcanic Field cut through a sequence of Cretaceous sediments of the San Juan Basin, and hence are an excellent natural laboratory for studying the effect of lithology on thermal pore pressurization. Three projects will seek to characterize the dike-perpendicular joints, examine the role of thermal pore pressurization in their formation, and understand how their formation in turn affects the pore pressure field. Completion of these projects should provide the basis for future work on the subsequent stages in conduit geometry evolution, for example host rock erosion and magma flow problems.
Collection
The Stanford Rock Fracture Project
At Favignana Island (southern Italy), several quarries provide an excellent 3D view of Lower- Pleistocene grainstones crosscut by a strike-slip fault system. This fault system is made up of two conjugate sets of strike-slip structural features such as Compactive Shear Bands, Zones of Compactive Shear Bands and larger faults with discrete slip surfaces. This contribution integrates structural analysis and numerical modeling to build up a 3D Discrete Fracture Network model, which is used for fluid flow simulations of a carbonate reservoir analogue. This new workflow appears to be promising for reservoir-scale assessment of sub-seismic structures and their impact on the bulk permeability of porous carbonate reservoirs.
Collection
The Stanford Rock Fracture Project
Faults are often idealized as planar structures, although abundant evidence from geological and geophysical investigations confirm that they are geometrically complex and exhibit geometric irregularities on many scales. Understanding the relationships between geometric irregularities of fault surfaces and slip distributions, fault opening at depth, and off-fault damage is of practical importance for disciplines such as rock mechanics, geotechnical engineering, earthquake science, and economic geology. Here we show how working through simplified non-planar fracture problems can provide a foundation from which to better understand the much more complicated mechanical behavior of non-planar faults. This contribution is an overview of Elizabeth Ritz's dissertation, and focuses on slip surface deformation. Incorporating a complementarity algorithm into the displacement discontinuity boundary element method (DDM) merges two existing computational tools and provides an effective numerical method to investigate the mechanical behavior of faults and fractures in a wide range of frictional contact problems. The circular arc crack problem has served as a catalyst for testing new numerical approaches. The DDM with complementarity is employed to define when the analytical solution is not applicable and to better understand the mechanism that causes partial closure under various loading conditions. The DDM with complementarity is also used to investigate idealized sinusoidal fault shapes. The analytical solution for an infinite sinusoidal interface does not accurately reflect important fault characteristics that influence its mechanical behavior; this necessitates use of a numerical model and precludes use of an analytical model for wavy faults. Stick, slip, and opening distributions along wavy faults with a range of uniform coefficients of friction, amplitude to wavelength ratios, and wave numbers are provided. Lastly, natural fault traces are modeled with an updated DDM with complementarity to demonstrate the differences between the mechanical behavior of natural fault geometries with that of simplified shapes. Field observations of meter-scale, subvertical strike-slip fault traces mapped in the Lake Edison Granodiorite, central Sierra Nevada, California, provide model geometries and parameter constraints for the modeling, and new field observations help to elucidate slip surface deformation in this study area.
Collection
The Stanford Rock Fracture Project
Two sets of bed-perpendicular, echelon vein arrays with complementary echelon pressure solution seams were mapped and sampled within folded Pennsylvanian to Permian period limestones at Raplee anticline and Comb monocline, Utah. We show how each physical quantity of these structures (vein dimensions, vein spacing, vein and array angles, traction boundary conditions, elastic moduli, and shortening due to pressure solution seams) influence the displacements at the crack boundaries and affect the stress concentration at crack tips. We use Abaqus FEA, a commercial finite element software, to evaluate the displacement, strain, and stress fields in a 2D model limestone having material properties determined from experimental rock mechanics literature. The model inherently conserves mass and momentum through the governing equations of motion. The range of tested values for model crack dimensions and crack orientations come from field measurements. The remote boundary conditions and crack boundary conditions used in the model are based on the tectonic conditions inferred from the published burial history profile of the stratigraphy, and have a combination of stress magnitudes that allow the model cracks to open. The resulting crack surface displacements and the maximum in-plane principal stress field at the crack tips are model results that can be directly compared with field and petrographic measurements of vein deformation; that is vein shape and relative displacements of the vein walls. Those physical attributes that encourage opening include a decrease in crack spacing, an increase in crack overlap, and an increase in the number of cracks in an array. Crack orientation that is perpendicular to the remote least compressive stress, and an increase in shortening of an intersecting, perpendicular pressure solution seam also encourage opening. The opening distribution profile of a crack with a pressure solution seam is more triangular than elliptical. Physical attributes that increase the magnitude of shear across a model crack include a decrease in spacing, an increase in crack overlap, and an increase in crack angle to the remote greatest compressive stress. Increasing the number of cracks in an array has little effect on relative shearing along a crack. However, for minor amounts (~0.04 mm) of pressure solution seam shortening along a crack not in line with a principal stress direction, relative shear along a crack switches sign (e.g. from left-lateral to right-lateral).
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The Stanford Rock Fracture Project
The field observations indicate that the low-angle bed-parallel compaction bands and the high-angle-to- bedding compaction bands occur only in cross-beds with certain range of bedding orientations in the Aztec Sandstone at the Valley of Fire State Park (NV). The most important underlying mechanical reason for this phenomenon is the strength anisotropy of localized compaction in anisotropic sandstones. In this paper, we used a quadratic failure criterion to describe the strength anisotropy of localized compaction and compared the results with the field data. The results show a clear relationship among the cross-beds with (or without) compaction bands of certain orientations and the cross-beds with relatively lower (or higher) calculated strength of localized compaction. These findings indicate that (1) the application of the quadratic failure criterion to the formation of compaction bands in anisotropic sandstones is promising and that (2) the strength anisotropy of localized compaction is an important factor controlling the compartmentalized distribution of compaction bands of various orientations in the aeolian sandstones.
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The Stanford Rock Fracture Project
This paper is a prelude to our field trip and includes a summary of the contributions to the structural history of the Valley of Fire State Park and its surroundings.
Collection
The Stanford Rock Fracture Project
Although significant geological and geophysical processes, including earthquake nucleation and propagation, occur in the brittle-ductile transition, earth scientists struggle to identify appropriate constitutive laws for brittle-ductile deformation. This paper investigates outcrops from the Bear Creek field area that record deformation at approximately 4-15 km depth and 400-500oC. We focus on the Seven Gables outcrop, which contains a ~10cm thick aplite dike that is displaced ~45 cm through a contractional step between two sub-parallel left-lateral faults. Stretching and rotation of the aplite dike, in addition to local foliation development in the granodiorite, provides an excellent measure of the strain within the step. We use the geometry of this well-constrained outcrop to motivate the geometry and boundary conditions of a finite element model of the deformation. The model is then used to test the ability of six constitutive laws (von Mises elastic-plasticity, Drucker-Prager elastic-plasticity, Drucker-Prager Cap elastic-plasticity, power-law creep, hyperbolic-sine creep, and viscoplasticity) to reproduce the deformation features observed in outcrop. The results indicate that the constitutive behavior is likely frictionless and has a yield criterion that depends on the hydrostatic stress. In addition, the flow rule should not contain a volumetric strain component, as this results in volume loss in the modeled aplite dike. Of the constitutive laws tested, the viscoplasticity law most accurately depicts the outcrop deformation. This result should motivate future laboratory research into the creep properties of granitic rock. The results of this study help to eliminate constitutive laws (e.g.., frictional plasticity) that could potentially describe brittle-ductile deformation, which leads to a better understanding of the rheology of the continental crust in the brittle-ductile transition.
Collection
The Stanford Rock Fracture Project
The McKim Limestone is a 1m to 3m thick sedimentary rock stratum that is well-exposed across large portions of Raplee anticline and Comb monocline; a pair of kilometer-scale folds that mark the eastern Monument Upwarp of the Colorado Plateau in southeastern Utah. Two conjugate sets of echelon vein arrays, with complementary echelon pressure solution seam arrays, occur as bed-perpendicular, systematic deformation features. Based on large vein to vein array angles, large vein aperture to length ratios, and the presence of vein-perpendicular pressure solution seams, these structures are interpreted to have developed within localized, brittle-ductile shear zones in low-temperature and shallow burial conditions. The formation mechanism of these structures are often founded on geometric observations and kinematic models of deformation (e.g. simple shear) that are independent of the constitutive properties of the rock, the equations of motion, and the boundary conditions on the vein surfaces. Here we show a more realistic representation of brittle-ductile shear zone formation by introducing numerical models that consider the mechanical properties of limestone, are constrained by the equations of motion, and explicitly define the vein surfaces and their boundary conditions. The commercial finite element software, Abaqus FEA®, is used to investigate the deformed geometry of model echelon vein arrays as a function of the remotely applied stress, the initial geometry of the vein arrays, and the constitutive properties of the solid. These geometric patterns are compared to those mapped on the McKim Limestone stratum.
Collection
The Stanford Rock Fracture Project
We have developed a MatlabTMcode to evaluates Eshelby’s solution for an arbitrary ellipsoidal inclusion or heterogeneity embedded in an elastic, isotropic and infinite body. The code evaluates the elastic fields (i.e. strain, stress and displacement) inside and outside an ellipsoidal inclusion/heterogeneity. With this code, we review some of the research on localized volumetric deformation in earth’s crust that used some special cases of Eshelby’s solution, e.g. a heterogeneity modeled as a 2D ellipse or an ellipsoid that has two equal axes known as a spheroid. We discuss how the arbitrary ellipsoidal geometry would improve the results. One application of the code is to evaluate the stress fields about the tip-line of a compaction band or shear enhanced compaction band modeled as a flat ellipsoidal geometry to understand the propagation mechanism. Unlike numerical methods, e.g. finite element and boundary element methods, the accuracy is not affected by the distance-to-tip at which the stress is evaluated. This feature enables us to accurately evaluate the stress field in an arbitrary near-tip region. The previous criterion for the in/off- plane growth of the deformation is restricted to a straight tip-line. With this code, we investigate how the varying tip- line curvature would affect the near-tip stress and further the deformation growth.