Research Papers

2011 Drucker Medal Paper: Localized Compaction in Porous Sandstones

[+] Author and Article Information
J. W. Rudnicki

Fellow ASME
Departments of Civil and Environmental
Engineering and Mechanical Engineering,
Northwestern University,
Evanston, IL 60201
e-mail: jwrudn@northwestern.edu

Manuscript received June 26, 2013; final manuscript received July 31, 2013; accepted manuscript posted August 2, 2013; published online September 6, 2013. Editor: Yonggang Huang.

J. Appl. Mech 80(6), 061025 (Sep 06, 2013) (6 pages) Paper No: JAM-13-1263; doi: 10.1115/1.4025176 History: Received June 26, 2013; Accepted July 31, 2013; Revised July 31, 2013

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.

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Sun, W., Andrade, J. E., Rudnicki, J. W., and Eichhubl, P., 2011, “Connecting Microstructural Attributes and Permeability From 3D Topographic Images of In Situ Shear-Enhanced Compaction Bands Using Multiscale Computations,” Geophys. Res. Lett., 38, p. L10302. [CrossRef]
Hill, R. E., 1989. “Analysis of Deformation Bands in the Aztec Sandstone, Valley of Fire State Park, Nevada,” Master's thesis, University of Nevada, Las Vegas.
Mollema, P., and Antonellini, M. A., 1996, “Compaction Bands: A Structural Analog for Anti-Mode I Cracks in Aeolian Sandstone,” Tectonophysics, 267, pp. 209–228. [CrossRef]
Schultz, R. A., 2009, “Scaling and Paleodepth of Compaction Bands, Nevada and Utah,” J. Geophys. Res., 114, p. B03407. [CrossRef]
Sternlof, K. R., Chapin, J. R., Pollard, D. D., and Durlofsky, L. J., 2004, “Permeability Effects of Deformation Band Arrays in Sandstone,” Am. Assoc. Pet. Geol. Bull., 88(9), pp. 1315–1329.
Sternlof, K. R., Rudnicki, J. W., and Pollard, D. D., 2005, “Anti-Crack Inclusion Model for Compaction Bands in Sandstone,” J. Geophys. Res., 110, p. B11403. [CrossRef]
Aydin, A., and Ahmadov, R., 2009, “Bed-Parallel Compaction Bands in Aeolian Sandstone: Their Identification, Characterization and Implications,” Tectonophysics, 479, pp. 277–284. [CrossRef]
Ballas, G., Soliva, R., Sizun, J.-P., Fossen, H., Benedicto, A., and Skurtveit, E., 2013, “Shear-Enhanced Compaction Bands Formed at Shallow Burial Conditions: Implications for Fluid Flow (Provence, France),” J. Struct. Geol., 47, pp. 3–15. [CrossRef]
Baud, P., Klein, E., and Wong, T.-F., 2004, “Compaction Localization in Porous Sandstones: Spatial Evolution of Damage and Acoustic Emission Activity,” J. Struct. Geol., 26, pp. 603–624. [CrossRef]
Wong, T.-F., Baud, P., and Klein, E., 2001, “Localized Failure Modes in a Compactant Porous Rock,” Geophys. Res. Lett., 28(13), pp. 2521–2524. [CrossRef]
Tembe, S., Baud, P., and Wong, T.-F., 2008, “Stress Conditions for the Propagation of Discrete Compaction Bands in Porous Sandstone,” J. Geophys. Res., 113, p. B09409. [CrossRef]
Olsson, W. A., 2001, “Quasistatic Propagation of Compaction Fronts in Porous Rocks,” Mech. Mater., 33, pp. 659–668. [CrossRef]
Papka, S. D., and Kyriakides, S., 1998, “Experiments and Full-Scale Numerical Simulations of In-Plane Crushing of a Honeycomb,” Acta Metall., 46(8), pp. 2765–2776. [CrossRef]
Rudnicki, J. W., and Rice, J. R., 1975, “Conditions for the Localization of Deformation in Pressure-Sensitive Dilatant Materials,” J. Mech. Phys. Solids, 23, pp. 371–394. [CrossRef]
Issen, K. A., and Rudnicki, J. W., 2000, “Conditions for Compaction Bands in Porous Rock,” J. Geophys. Res., 105, pp. 21529–21536. [CrossRef]
Bésuelle, P., and Rudnicki, J. W., 2004, “Localization: Shear Bands and Compaction Bands,” Mechanics of Fluid Saturated Rocks (International Geophysics Series, Vol. 89), Y.Guéguen and M.Boutéca, eds., Academic, New York, pp. 219–321.
Rudnicki, J. W., 2004, “Shear and Compaction Band Formation on an Elliptic Yield Cap,” J. Geophys. Res., 109, p. B03402. [CrossRef]
Challa, V., and Issen, K. A., 2004, “Conditions for Compaction Band Formation in Porous Rock Using a Two-Yield Surface Model,” J. Eng. Mech., 130(9), pp. 1089–1097. [CrossRef]
Bernard, X. D., Eichhubl, P., and Aydin, A., 2002, “Dilation Bands: A New Form of Localized Failure in Granular Media,” Geophys. Res. Lett., 29(4), p. 2176. [CrossRef]
Bésuelle, P., 2001, “Compacting and Dilating Shear Bands in Porous Rock: Theoretical and Experimental Conditions,” J. Geophys. Res., 106(B7), pp. 13435–13442. [CrossRef]
Eichhubl, P., Hooker, J. N., and Laubach, S., 2010, “Pure and Shear-Enhanced Compaction Bands in Aztec Sandstone,” J. Struct. Geol., 32, pp. 1873–1886. [CrossRef]
Schofield, A. N., and Wroth, P., 1968, Critical State Soil Mechanics, McGraw-Hill, New York.
Dimaggio, F. L., and Sandler, I. S., 1971, “Material Model for Granular Soils,” J. Engrg. Mech. Div., 97, pp. 935–950.
Baud, P., Vajdova, V., and Wong, T.-F., 2006, “Shear-Enhanced Compaction and Strain Localization: Inelastic Deformation and Constitutive Modeling of Four Porous Sandstones,” J. Geophys. Res., 111, p. B12401. [CrossRef]
Wong, T., 2011, private communication
Carroll, M. M., 1991, “A Critical State Plasticity Theory for Porous Reservoir Rock,” Recent Advances in Mechanics of Structured Continua, Vol. 117, M.Massoudi and K. R.Rajagopal, eds., Applied Mechanics Division, ASME, New York, pp. 1–8.
Rudnicki, J. W., 2007, “Models for Compaction Band Propagation,” Geol. Soc., London, Spec. Pub., 284, pp. 107–125. [CrossRef]
Sternlof, K. R., 2006, “Structural Geology, Propagation Mechanics and Hydraulic Effects of Compaction Bands in Sandstone,” Ph.D. thesis, Stanford University, Stanford, CA.
Sternlof, K., and Pollard, D., 2002, “Numerical Modeling of Compactive Deformation Bands as Granular Anti-Cracks,” EOS Trans. Am. Geophys. Union, 83, p. F1347.
Fletcher, R. C., and Pollard, D. D., 1981, “Anticrack Model for Pressure Solution Surfaces,” Geology, 9, pp. 419–424. [CrossRef]
Rudnicki, J. W., Tembe, S., and Wong, T.-F., 2006, “Relation Between Width and Length of Compaction Bands in Porous Sandstones,” EOS Trans. Am. Geophys. Union, Vol. 87, Fall Meet. Suppl., Abstract T43A-1633.
Fortin, J., Schubnel, A., and Guéguen, Y., 2005, “Elastic Wave Velocities and Permeability Evolution During Compaction of Bleuswiller Sandstone,” Int. J. Rock Mech. Min. Sci., 42(7-8), pp. 873–889. [CrossRef]
Rice, J. R., 1968, “Mathematical Analysis in the Mechanics of Fracture,” Fracture: An Advanced Treatise, Vol. 2, H.Liebowitz, ed., Academic, New York, pp. 191–311.
Rice, J. R., 1968, “A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks,” ASME J. Appl. Mech., 35, pp. 379–386. [CrossRef]
Vajdova, V., and Wong, T.-F., 2003, “Incremental Propagation of Discrete Compaction Bands and Microstructural Observations on Circumferentially Notched Samples of Bentheim Sandstone,” Geophys. Res. Lett., 30(14), p. 1775. [CrossRef]
Tembe, S., Vajdova, V., Wong, T.-F., and Zhu, W., 2006, “Initiation and Propagation of Strain Localization in Circumferentially Notched Samples of Two Porous Sandstones,” J. Geophys. Res., 111, p. B02409. [CrossRef]


Grahic Jump Location
Fig. 1

Schematic illustration of localized band formation in the axisymmetric compression test

Grahic Jump Location
Fig. 2

Schematic illustration of a yield surface for a high-porosity sandstone

Grahic Jump Location
Fig. 3

Predicted variation of the angle between the normal to the plane of localization and the most compressive principal stress against the average of β and μ for axisymmetric compression and Poisson's ratio ν = 0.2

Grahic Jump Location
Fig. 4

Dilatancy angle Ψ defined by Ref. [20] against the difference β − μ. The shaded rectangle corresponds to compactive localization (Ψ < 0) and the range of fault angles, 37–53, reported by Ref. [21] for compacting shear bands in Valley of Fire State Park, Nevada. Modified from Fig. 5.16a of Ref. [16].

Grahic Jump Location
Fig. 5

Modified from Fig. 5.17b of Ref. [16]. Contours of constant dilatancy angle Ψ and fault angle θcrit on a plot of dilatancy factor β against friction coefficient μ. Shaded rectangle shows the range of β and μ for compacting bands from Fig. 9 of Refs. [24,25].

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Fig. 6

Compilation of field and laboratory data for midpoint thickness (mm) versus band half-length (m)

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Fig. 7

Schematic of a combined anticrack and antidislocation model for compaction band propagation [27]. Because of the very small aspect ratios of the bands, the actual thickness of the zone (shaded area) is neglected. Consequently, the compactive displacement shown corresponds to interpenetration in the model.




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