Abstract. Usually several deformation mechanisms interact to accommodate plastic deformation. Quantifying the contribution of each to the total strain is necessary to bridge the gaps from observations of microstructures, to geomechanical descriptions, to extrapolating from laboratory data to field observations. Here, we describe the experimental and computational techniques involved in microscale strain mapping (MSSM), which allows strain produced during high-pressure, high-temperature deformation experiments to be tracked with high resolution. MSSM relies on the analysis of the relative displacement of initially regularly spaced markers after deformation. We present two lithography techniques used to pattern rock substrates at different scales: photolithography and electron-beam lithography. Further, we discuss the challenges of applying the MSSM technique to samples used in high-temperature and high-pressure experiments. We applied the MSSM technique to a study of strain partitioning during creep of Carrara marble and grain boundary sliding in San Carlos olivine, synthetic forsterite, and Solnhofen limestone at a confining pressure, Pc, of 300 MPa and homologous temperatures, T∕Tm, of 0.3 to 0.6. The MSSM technique works very well up to temperatures of 700 °C. The experimental developments described here show promising results for higher-temperature applications.
Using high‐resolution surface imaging and a split‐cylinder technique, we mapped the strain heterogeneity in Carrara marble samples deformed to bulk strains <25%, under conventional triaxial loading, at 400–700°C, 300 MPa confining pressure, and strain rates of 10 −4 to 10 −5 s −1 . To map strain, we deposited grid markers on the polished surface of a half cylinder, performed mechanical tests on composites of two half cylinders, compared the positions of each marker in undeformed and deformed samples, and computed the spatial distribution of strain. Strains over the scale of a few microns varied by as much as 300%. Localized deformation occurred along twins and grain boundaries but was also present as patches in intragranular regions. The heterogeneity is more pronounced at scales smaller than grains, but the strain averaged over individual grains also varied by 50%. After deformation, the crystallographic orientation of individual grains relative to the compression direction was measured by electron backscattered diffraction. Inverse pole figures of the aggregate lattice‐preferred orientation (LPO) have a maximum near e (01 8) and are consistent with previous studies. The observed LPO is qualitatively consistent with that produced by simulations using a simple viscoplastic self‐consistent (VPSC) code that did not include mechanisms other than slip or twinning. The qualitative comparison of observed and simulated LPO was not sensitive to the model for the crystallographic resolved shear stresses for slip. However, the VPSC simulation was ineffective in predicting individual grain rotations.
Fluid inclusions break, or decrepitate, when the fluid pressure exceeds the least principal lithostatic stress by a critical amount. After decrepitation, excess fluid pressure is relaxed, resulting in crack arrest; subsequently, crack healing may occur. Existing models of decrepitation do not adequately explain several experimentally observed phenomena. We developed a linear elastic fracture mechanics model to analyze new data on decrepitation and crack arrest in San Carlos olivine, compared the model with previous fluid inclusion investigations, and used it to interpret some natural decrepitation microstructures. The common experimental observation that smaller inclusions may sustain higher internal fluid pressures without decrepitating may be rationalized by assuming that flaws associated with the inclusion scale with the inclusion size. According to the model, the length of the crack formed by decrepitation depends on the lithostatic pressure at the initiation of cracking, the initial sizes of the flaw and the inclusion, and the critical stress intensity factor. Further experiments show that microcracks in San Carlos olivine heal within several days at 1280 to 1400°C; healing rates depend on the crack geometry, temperature, and chemistry of the buffering gas. The regression distance of the crack tip during healing can be related to time through a power law with exponent n = 0.6. Chemical changes which become apparent after extremely long heat‐treatments significantly affect the healing rates. Many of the inclusions in the San Carlos xenoliths stretched, decrepitated, and finally healed during uplift. The crack arrest model indicates that completely healed cracks had an initial fluid pressure of the order of 1 GPa. Using the crack arrest model and the healing kinetics, we estimate the ascent rate of these xenoliths to be between 0.001 and 0.1 m/s.
Triaxial experiments were performed at room temperature and confining pressures up to 450 MPa on four pure, dense calcite rocks whose average grain sizes range over four orders of magnitude. Volumetric strain was measured during some of the experiments and microstructural studies were conducted to identify the active deformation mechanisms. The brittle fracture strength and macroscopic initial “plastic” yield stress in the semibrittle field follow empirical Hall‐Petch relations. The confining pressure at the brittle‐ductile transition depends inversely on grain size, but the stress ratio σ 3 /σ 1 at the transition is nearly the same for the different rocks. We assume that the initial flaw size scales with grain size and compare our experimental data to the fracture mechanics models of Ashby and Hallam (1986) for brittle fracture and Horii and Nemat‐Nasser (1986) for the brittle‐plastic transition in compression. The first model predicts that small confining pressures are sufficient to inhibit work softening behavior; however, our data indicate that localization occurs for significantly higher values of confining pressure than predicted. Furthermore, we find that localization is inhibited with increased confining pressure because of the increased activity of plastic flow mechanisms, rather than because of the increased difficulty of crack propagation alone. With certain assumptions, the model predicts the experimentally determined slope of the Hall‐Petch relation in the brittle field, although it underestimates the compressive strength of the rocks. The second model predicts that the stress ratio σ 3 /σ 1 at the brittle‐plastic transition scales with the, square root of the grain size; however, the experimental data do not corroborate the model unless the square of the ratio of the mode I fracture toughness to the plastic yield stress in shear scales with the grain size. The stress ratio at the brittle‐ductile transition is apparently a constant for many different rock types; we suggest that the physical basis for this relationship is that the ductility of most mineral aggregates falls within a small range.
Pore connectivity is likely one of the most important factors affecting the permeability of reservoir rocks. Furthermore, connectivity effects are not restricted to materials approaching a percolation transition but can continuously and gradually occur in rocks undergoing geological processes such as mechanical and chemical diagenesis. In this study, we compiled sets of published measurements of porosity, permeability and formation factor, performed in samples of unconsolidated granular aggregates, in which connectivity does not change, and in two other materials, sintered glass beads and Fontainebleau sandstone, in which connectivity does change. We compared these data to the predictions of a Kozeny-Carman model of permeability, which does not account for variations in connectivity, and to those of Bernabé et al. (2010, 2011) model, which does [Bernabé Y., Li M., Maineult A. (2010) Permeability and pore connectivity: a new model based on network simulations, J. Geophys. Res. 115, B10203; Bernabé Y., Zamora M., Li M., Maineult A., Tang Y.B. (2011) Pore connectivity, permeability and electrical formation factor: a new model and comparison to experimental data, J. Geophys. Res. 116, B11204]. Both models agreed equally well with experimental data obtained in unconsolidated granular media. But, in the other materials, especially in the low porosity samples that had undergone the greatest amount of sintering or diagenesis, only Bernabé et al. model matched the experimental data satisfactorily. In comparison, predictions of the Kozeny-Carman model differed by orders of magnitude. The advantage of the Bernabé et al. model was its ability to account for a continuous, gradual reduction in pore connectivity during sintering or diagenesis. Although we can only speculate at this juncture about the mechanisms responsible for the connectivity reduction, we propose two possible mechanisms, likely to be active at different stages of sintering and diagenesis, and thus allowing the gradual evolution observed experimentally.
Experimental measurements of dihedral angles formed at the junction of calcite/fluid interfaces with high‐angle grain boundaries suggest that the two fluids used in these experiments, water and carbon dioxide, do not wet high‐angle grain boundaries. Four types of carbonate samples were used: Solnhofen limestone, Oak Hall limestone, synthetic calcite bicrystals fabricated in a dry environment at 880°C and a carbon dioxide atmosphere of 0.1 MPa with 5‐MPa uniaxial stress, and synthetic calcite bicrystals fabricated in a wet environment at 600°C with a confining pressure of 120 to 170 MPa and a pore water pressure 15 to 50 MPa lower. The ratio between grain boundary energy and surface energy obtained from measurements of dihedral angle (Θ) along grain boundary grooves was 0.46 ± 0.24 for dry bicrystals grooved at 760° to 880°C in 0.1 MPa carbon dioxide, and 0.75 ± 0.15 for those grooved at 450° to 500°C in 200 MPa H 2 O. Measurements of Θ from pore/grain boundary junctions in the limestones and wet synthetic bicrystals also suggest the ratio of grain boundary energy to surface energy is about 1. Using this evidence and published values of calcite surface energy, the energy of high‐angle grain boundaries is roughly estimated to be 80 mJ/m 2 at 20°C. About 60 boundaries were examined using lattice fringe imaging, a high‐resolution electron microscope technique. In all cases where satisfactory images were obtained, there was no evidence of a second phase along the boundary. These results imply that waterrich pore fluids in natural carbonates will tend to form isolated pores along grain boundaries and three‐and four‐grain junctions; interconnected networks, including fluid‐wetted grain boundaries and three‐grain junctions, are probably unstable. Therefore local mass transport in unjointed carbonates is probably dominated by the properties of semicoherent grain boundaries, and not by pore‐fluid properties.
