Jörg Renner

On the rheologically critical melt fraction

Abstract With increasing melt fraction (φ), the strength of partially molten granite decreases from a value characteristic of solid, competent rock to a value nearly equal to that of the melt. Previously published mechanical and microstructural data indicate that deformation in partially molten rocks often involves brittle processes. Thus, the pressure in the melt is expected to be important in determining strength. When the volume changes during deformation, strength and fluid flow will be coupled by such parameters as permeability (k), storage capacity per unit volume or storativity (βs), melt compressibility (βf), grain size (d), fluid viscosity (η), and strain rate ( ϵ ). Experiments on brittle rock at low temperatures show that the strain rate at which the internal fluid pressure can be maintained constant is approximately proportional to k/(ηβs). An evaluation of published experimental data suggests that this relation also holds for partially molten granites, indicating that the strength of these rocks depends on their transport properties. Since the permeability is related to φ, below a critical melt fraction (φrcmf), the melt pressure will change if deformation is not iso-volumetric. By assuming a power-law relationship between k and φ, we estimate that φ rcmf ∝( ϵ ηβ f /d m ) 1/(n−1) where m and n relate permeability to grain size and φ, respectively.

Rheology of Crustal Rocks at Ultrahigh Pressure

An improved understanding of tectonic processes in the deep levels of subduction zones and collisional belts requires information on the mechanical behavior of continental crust during ultrahigh-pressure (UHP) metamorphism. Predictions are based on the results of experimental deformation of minerals stable at ultrahigh pressure and on the anticipated effect of pressure on deformation mechanisms. Flow laws for dislocation creep of coesite and aragonite indicate that, at ultrahigh pressure, the strength of continental material remains well below a few MPa at natural strain rates. We question the high strength that has been inferred for eclogites, based on preliminary experimental data on jadeite and on natural microstructures of omphacite. The (micro)structural record of natural UHP rocks indicates that strain localization into weak shear zones, albeit not yet identified, must be common. We propose that the presence of dense fluids or hydrous melts at grain and solid phase boundaries could accomplish deformation analogous to liquid phase sintering in ceramics. The low strength of continental material at ultrahigh pressure precludes notable shear heating, thus cool geotherms and P-T paths are implied. The low strength also places upper bounds on the stress drop of seismic events in presently subducted continental crust and limits the size of coherent subducted continental slices.

Self‐potential signals induced by periodic pumping tests

[1] We measured the variations of the self-potential (SP) during periodic pumping tests performed at a test site located near a freshwater reservoir (Kemnader See, Bochum, Germany). Successions of injection and production intervals were applied in a borehole penetrating a jointed sandstone aquifer. We report the SP observations for tests with periods ranging between 10 and 60 min and flow rates between 10 and 25 L min -1 . The SP responses at the surface exhibit the imposed period but are not truly harmonic contrary to the hydraulic pressure and SP measured in monitoring wells. In the grassy zone around the injection well, the amplitude of the SP signals decreases with distance from the injection well (around one order of magnitude at 10 m) in rough agreement with predictions for radial flow in a homogeneous medium around an infinite source. The shape of the SP responses also evolves with distance. Fourier spectral analysis reveals that the surface signals generally contain two main components at the main period and at half the period with the relative weight of the subperiodic components increasing with distance. Furthermore, the characteristics of the SP responses depend on whether the boreholes are left open or closed by packers. The comparison between surface and borehole measurements suggests that nonlinear phenomena are acting, probably related to the saturation and desaturation processes occurring in the vadose zone.

An experimental study into the rheology of synthetic polycrystalline coesite aggregates

Coesite has been found as a relic in ultrahigh pressure metamorphic (UHPM) crust worldwide and is expected to play a major role in the mechanical behavior of continental crust at UHPM conditions. We performed triaxial compression tests on synthetic polycrystalline coesitite in a solid medium apparatus at confining pressures of 3.1 to 3.7 GPa, temperatures of 700° to ∼1160°C, and strain rates betweeen 6×10−7 and 1×10−3 s−1. The problem of the limited stress resolution of the solid medium apparatus was addressed by applying two extreme friction corrections that yield lower and upper bounds to the differential stress. The correlation between the mechanical data and the microstructural record of the deformed samples, as a function of temperature and imposed strain rate, is consistent with deformation by dislocation creep. We deduced parameters of a power law as n ≈ 3±1 and Q ≈ 275±50 kJ mol−1. Extrapolation of the experimental data to natural conditions cannot be constrained by comparison with natural microstructures, due to the lack of preserved coesite other than as single crystal inclusions. Nevertheless, the extrapolation indicates a low strength (of order 10 MPa) for natural strain rates at typical UHPM conditions. Absent deformation of the UHPM Brossasco granite (Dora Maira Massif, Western Alps) thus implies low stresses; deformation must have been localized in very weak shear zones during burial and exhumation.

On estimating the strength of calcite rocks under natural conditions

Abstract Field studies of calcite mylonites often document microstructures produced by dislocation creep. In contrast, flow laws derived from experiments predict that calcite rocks should deform mostly by diffusion creep during tectonic processes. To investigate this apparent discrepancy, we compare stresses estimated by microstructural piezometers to those obtained by extrapolation of experimentally derived flow laws. Considering shear zones from different geological settings, a clear trend is observed of increasing recrystallized grain size with increasing temperature. However, there is a large spread in grain size and associated stress. Because separate flow laws have been defined for various different marbles and limestones, the strengths predicted for a given set of conditions differ significantly. The stress estimates based on the piezometers and strength extrapolated from the various experimentally derived dislocation creep flow laws agree qualitatively, but no single flow law predicts all the palaeostress estimates. Even if experimental data are disregarded, the field observations are not consistent with a hypothetical law for Coble creep; they are consistent with a power law for dislocation creep, but only if the material constants are different from those currently determined in laboratory experiments.

The effect of experimental and microstructural parameters on the transition from brittle failure to cataclastic flow of carbonate rocks

Abstract Triaxial compression tests were conducted on cold-pressed calcite, aragonite and limestone aggregates and on Solnhofen limestone specimens to study the effect of experimental and microstructural parameters on the transition from brittle failure to cataclastic flow. The tests were performed at confining pressures up to 195 MPa and at strain rates between 5 · 10−4 s−1 and 5 · 10−6 s−1. Axial as well as volumetric strain were measured. Samples were produced by cold-pressing powders of crushed calcite and aragonite crystals and of crushed Solnhofen limestone. Sample porosity ranged between 5 and 25% and the average grain size varied between 5 and 400 μm. For both the cold-pressed aggregates and the intact limestone specimens, the confining pressure at the transition from localized brittle failure to non-localized cataclastic flow decreases with increasing porosity and grain size. The transition is characterized by a zero work-hardening coefficient, by dilation for low porosity and compaction for high porosity rocks, by a constant ratio between axial stress and confining pressure, and by decreasing yield strength for increasing confining pressure. The experimental results disagree with the critical state concept over most of the porosity range investigated, and indicate non-associated material behaviour. These properties of the brittle-ductile transition are addressed on the basis of continuum mechanics or by models suggested for granular materials. The problems discussed and the results obtained are of fundamental interest to rock deformation and structural geology.

Transport Processes at α‐Quartz–Water Interfaces: Insights from First‐Principles Molecular Dynamics Simulations

Car-Parrinello molecular dynamics (CP-MD) simulations are performed at high temperature and pressure to investigate chemical interactions and transport processes at the alpha-quartz-water interface. The model system initially consists of a periodically repeated quartz slab with O-terminated and Si-terminated (1000) surfaces sandwiching a film of liquid water. At a temperature of 1000 K and a pressure of 0.3 GPa, dissociation of H(2)O molecules into H(+) and OH(-) is observed at the Si-terminated surface. The OH(-) fragments immediately bind chemically to the Si-terminated surface while Grotthus-type proton diffusion through the water film leads to protonation of the O-terminated surface. Eventually, both surfaces are fully hydroxylated and no further chemical reactions are observed. Due to the confinement between the two hydroxylated quartz surfaces, water diffusion is reduced by about one third in comparison to bulk water. Diffusion properties of dissolved SiO(2) present as Si(OH)(4) in the water film are also studied. We do not observe strong interactions between the hydroxylated quartz surfaces and the Si(OH)(4) molecule as would have been indicated by a substantial lowering of the Si(OH)(4) diffusion coefficient along the surface. No spontaneous dissolution of quartz is observed. To study the mechanism of dissolution, constrained CP-MD simulations are done. The associated free energy profile is calculated by thermodynamic integration along the reaction coordinate. Dissolution is a stepwise process in which two Si--O bonds are successively broken. Each bond breaking between a silicon atom at the surface and an oxygen atom belonging to the quartz lattice is accompanied by the formation of a new Si--O bond between the silicon atom and a water molecule. The latter loses a proton in the process which eventually leads to protonation of the oxygen atom in the cleaved quartz Si--O bond. The final solute species is Si(OH)(4).

Do calcite rocks obey the power-law creep equation?

Abstract The power-law creep equation, ε̇ ∞ σn exp(−Q/RT), is commonly used to relate strain rate, ε̇, stress, σ, and temperature, T, for thermally activated dislocation creep in rocks. When triaxial deformation experiments on marble and limestone samples are performed at temperatures of 400–1050°C, to strains <0.2, and with strain rates between 10−3 and 10−7s−1, the variations in strength among different rocks at nominally identical conditions are much larger than the experimental uncertainty. During dislocation creep, the strengths of various limestones and marbles decrease with increasing grain size, similar to the Hall-Petch effect in metals. The stress sensitivity of strain rate, n′ = ∂ln ε̇/∂lnσ, and the temperature sensitivity of strain rate, Q′ = −R∂lnε̇/∂(1/T), differ greatly for the various calcite aggregates. There is a systematic dependence of n′ and Q′ on stress, grain size, and perhaps, temperature, and there is no interval in stress where n′ is constant. Thus, the steady-state power-law equation is an inadequate description of dislocation creep in calcite rocks. To improve the constitutive law, it may be necessary to include at least one additional state variable that scales with grain size.

A hybrid-dimensional approach for an efficient numerical modeling of the hydro-mechanics of fractures

Characterization of subsurface fluid flow requires accounting for hydro-mechanical coupling between fluid-pressure variations and rock deformation. Particularly, flow of a compressible fluid along compliant hydraulic conduits, such as joints, fractures, or faults, is strongly affected by the associated deformation of the surrounding rock. We investigated and compared two alternative numerical modeling approaches that describe the transient fluid-pressure distribution along a single deformable fracture embedded in a rock matrix. First, we analyzed the coupled hydro-mechanical problem within the framework of Biots poroelastic equations. Second, in a hybrid-dimensional approach, deformation characteristics of the surrounding rock were combined with a one-dimensional approximation of the fluid-flow problem to account for the high aspect ratios of fractures and the associated numerical problems. A dimensional analysis of the governing equations reveals that the occurring physical phenomena strongly depend on the geometry of the hydraulic conduit and on the boundary conditions. For the analyzed geometries, hydro-mechanical coupling effects dominate and convection effects can be neglected. Numerical solutions for coupled hydro-mechanical phenomena were obtained and compared to field data to characterize the fractured rock in the vicinity of an injection borehole. Either approach captures convection, diffusion, and hydro-mechanical effects, yet the hybrid-dimensional approach is advantageous due to its applicability to problems involving high-aspect-ratio features. For such cases, the modeling of pumping tests by means of the hybrid-dimensional approach showed that the observed inverse-pressure responses are the result of the coupling between the fluid flow in the fracture and the rock deformation caused by fluid-pressure variations along the fracture. Storage capacity as a single parameter of a fracture is insufficient to address all aspects of the coupling.

Microstructures of synthetic polycrystalline coesite aggregates. The effect of pressure, temperature, and time

The preservation of coesite-bearing ultrahigh-pressure metamorphic rocks in orogenic belts indicates that continental crust can be buried to a depth exceeding its present thickness. The exhumation of these rocks requires large scale flow patterns not yet understood. By analogy to the use of flow laws for quartz for the higher crustal levels, rheological data and a flow law for coesite are required for the reconstruction and modelling of these important deep processes. The first aim of the present study was the synthesis of ‘coesitite’ samples appropriate for deformation experiments. Synthesis of coesite from silica glass follows the Ostwald step rule, with an interface-controlled slow second step from metastable α-quartz tocoesite. Normal grain growth of coesite crystals is not possible at temperatures up to 1100°C, because of the dependence of interfacial energy on crystallographic orientation. This energy becomes independent of orientation at 1170°C and a foam microstructure tends to develop, allowing for normal grain growth. This temperature dependence should also hold true for natural rocks. However, normal grain growth was not measurably observed in an experiment with 1080 min duration at a temperature of 1170°C. Consequently, the desired grain size of synthetic ‘coesitite’ samples had to be achieved by controlling the nucleation rate, which was successfully done by choosing appropriate p—T—t paths in the synthesis experiments.