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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Fig. 1

Schematic illustration of localized band formation in the axisymmetric compression test

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Fig. 2

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

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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

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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].

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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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