HR: 0830h
AN: T41D-0254    [PDF]
TI: Formation of Compaction Bands in Sandstone as a Phase Decomposition Associated With a Non-convex Stress Potential
AU: * Olsson, W A
EM: waolsso@sandia.gov
AF: Sandia National Laboratories, MS 0751 POB 5800, Albuquerque, NM 87185-0751 United States
AU: Holcomb, D J
EM: djholco@sandia.gov
AF: Sandia National Laboratories, MS 0751 POB 5800, Albuquerque, NM 87185-0751 United States
AB: Permanent compaction of pore volume into localized regions, compaction bands, in sandstone has been observed in the outcrop and the laboratory. The current theoretical framework treats the onset of compaction banding as a bifurcation of the deformation field at a particular set of values of constitutive properties. A shortcoming of the theory as it exists is that it says nothing about the evolution of the specimen after the onset of banding. Stress-shortening curves for specimens undergoing compaction band formation and spread are characterized by a plateau of nearly constant stress during shortening. During this plateau the compaction bands form and spread throughout the specimen, in effect, changing the specimen from the original porosity (density) to a new, lower porosity (higher density). This type of curve is characteristic of many materials that show band formation and spread (interface propagation). Such a stress-deformation relation arises from the global minimization of an associated non-convex, multi-well stress potential curve that is characterized by three numbers $\lambda_1$, $\lambda_2$ and $p_M$ (note: three numbers only if there are just two wells in the energy curve) that may be construed as constitutive parameters of the original porous rock. The deformation state at the onset of banding is characterized by $\lambda_1$, deformation at the completion of banding by $\lambda_2$ and the plateau stress is the Maxwell stress $p_M$. During a triaxial test on a specimen of porous sandstone, the stress difference first increases from zero to peak stress where the deformation is $\lambda_1$. At this point a new phase of deformation characterized by $\lambda_2$ appears. Throughout the plateau, there is a continuous rearrangement of phases, $\lambda_1$ being replaced by $\lambda_2$. The volume fractions of the two $\lambda$'s are related to the overall shortening $\bar{\lambda}$ by the standard mixture rule. Nothing is predicted about the distribution of phases, only the relative amounts. Thus deformation could proceed as one thickening band or a series of intercalated bands of compacted and uncompacted material. Furthermore, the bands could be few in number and thick, or multitudinous and thin. All that is required is that the mixture rule be obeyed. Currently, we are examining a Hertzian fracture mechanism as the possible origin of the energy non-convexity. Identification of the appropriate micro-mechanism may lead to better understanding of the effects of such variables as grain size and distribution of sizes on the type of compaction observed---thick bands, thin bands, or homogeneous deformation.
DE: 5100 PHYSICAL PROPERTIES OF ROCKS
DE: 5104 Fracture and flow
DE: 5114 Permeability and porosity
DE: 8010 Fractures and faults
DE: 8020 Mechanics
SC: Tectonophysics [T]
MN: 2003 Fall Meeting