Frictional Rheology Research Articles

Complete dynamic modeling calibration for the Thurwieser rock avalanche (Italian Central Alps)

Few rock avalanches have been witnessed and no exact real time description is available. The 2.5 M m 3 Punta Thurwieser rock avalanche (September 2004, Italian Central Alps) is a unique event for which many quantitative observations have been gathered. This is the first case ever of a natural rock avalanche being recorded on video, and for which an almost exact value of the total time duration, from initial detachment to final deposition, is available. The landslide travelled over 2.9 km from its source partially in a glacial environment. The initial failure and the time for the complete evacuation of the source area were studied and assessed by a series of photos. The mean front velocities along the path have been estimated from the video. The final geometry and the characteristics of the deposit have been obtained by GPS measurements, aerial photos, field surveys and laboratory tests. A quasi-3D continuum dynamic analysis of the landslide motion has been performed assuming both a Voellmy and a frictional rheology in the model DAN 3D. For the first time the landslide front velocities have been used for back analyses and calibration of the rheological parameters, together with the final shape and thickness of the deposit, and its developing extension. The dynamic flow resistance parameters, initially calibrated with DAN, were adopted and validated in DAN 3D, showing good consistency. They are consistent with the existing database for calibrated landslides of similar type and scale. Flow velocities on the path segment underlain by glacial deposits (up to 55–65 m s − 1 ) are more accurately predicted by adopting a frictional rheology (up to 50–55 m s − 1 ) with zero pore pressure and a 26° friction angle than by a Voellmy rheology (up to 40–45 m s − 1 ). Both observations and modelling show that glacial ice plays a substantial role in increasing the rock avalanche mobility.

Extension during active collision in thin-skinned wedges: Insights from laboratory experiments

The occurrence of strike-normal extension in mountain belts undergoing active contraction is not predicted by analytical solutions for the mechanics of purely frictional orogens. To test the idea that ductile rocks at depth might allow extensional deformation to occur in otherwise frictional and contractional orogens, we have conducted a series of analog experiments with purely frictional and layered frictional-ductile rheologies. By precisely measuring the horizontal deformation field, we have quantitatively confirmed the qualitative observation that analog frictional wedges do not extend. This is consistent with published numerical models, and is in contrast to purely viscous models that commonly display coeval extension with contraction. Our modeling also demonstrates that layered frictional-ductile models can, during active convergence, result in discrete extensional normal faulting even when only a relatively thin ductile layer is present. The resulting extension, though relatively small in magnitude compared to the active contraction, can greatly modify the final profile of a convergent orogen and can lead to the formation of a broad plateau between the pro-wedge and the retro-wedge.

Results of Back-Analysis of the Propagation of Rock Avalanches as a Function of the Assumed Rheology

Numerical simulation can provide a useful tool for investigating the dynamics of phenomena like rock avalanches, within realistic geological contexts and in the framework of a better risk assessment and decision making. Difficulties in numerical modelling of a heterogeneous moving mass are mainly linked to the simulation of the complex behaviour assumed by the mass during propagation. The numerical code RASH3D, based on a continuum mechanics approach and on the long wave approximation, is used to back-analyse two cases of rock avalanches: Frank (1903, Canada) and Val Pola (1987, Italy). The two events are characterised by approximately the same volume (about 30 × 106 m3) while the run out area morphologies are widely different. Three alternative “rheologies” (Frictional, Voellmy and Pouliquen) are used. Comparison among obtained results underlines that the validation of a “rheology” requires not only a good agreement between the numerical simulation results and the run out area boundaries but also in term of depth distribution of the mass in the deposit. In case of a Frictional rheology, the obtained calibrated dynamic friction angle values are in a range of 15 ± 1° for both the cases; while assuming a Pouliquen or a Voellmy rheology it emerges a different behaviour of rheological parameters for each of the considered events. Besides the calibration of rheological parameters to better back-analyse each of the considered events, it is investigated how the behaviour due to the assumed rheology is influenced by the geometry of the run out area (e.g. narrow or broad valley).

Laminar flow of soursop juice through concentric annuli: Friction factors and rheology

Laminar axial flow of a pseudoplastic fluid food (soursop juice) in annular ducts has been experimentally investigated. In the first part of the manuscript, the rheological behavior of soursop juice, being essential for the annular flow analysis, was completely determined from 9.3 to 49.4 °Brix and temperatures from 0.4 °C to 68.8 °C, using a rotational rheometer equipped with coaxial cylinders. In order to test the adequacy of the rheology results, pressure loss data in the laminar pipe flow were collected and then experimental and theoretical friction factors were compared, showing excellent agreement, which indicated the reliability of the Power-Law model for describing the soursop juices. In the second part, pressure loss in annular regions was measured and used to estimate friction factors, which were then compared to those resulted from analytical and semi-analytical equations. The principal contributions of this article are to provide a review on the determination of friction factors-Reynolds number of pseudoplastic fluids in annuli, and also supply extensive new experimental data on the rheological properties and pressure loss of an important shear-thinning fluid food, which is of particular interest for the food engineering process design.

Non-Amontons behavior of friction in single contacts

We report on the frictional properties of a single contact between a glassy polymer lens and a flat silica substrate covered either by a disordered or by a self-assembled alkylsilane monolayer. We find that, in contrast to a widely spread belief, the Amontons proportionality between frictional and normal stresses does not hold. Besides, we observe that the velocity dependence of the sliding stress is strongly sensitive to the structure of the silane layer. Analysis of the frictional rheology observed on both disordered and self-assembled monolayers suggests that dissipation is controlled by the plasticity of a glass-like interfacial layer in the former case, and by pinning of polymer chains on the substrate in the latter one.

Volcanotectonic interactions between Mauna Loa and Kilauea: Insights from 2-D discrete element simulations

Numerical simulations using the discrete element method (DEM) are carried out to examine the dynamics and internal deformation of overlapping volcanoes constructed upon a weak décollement horizon, as analogs to the Kilauea–Mauna Loa system of volcanoes in Hawaii. Employing a frictional rheology, the DEM simulations capture much of the complex deformation behavior of Mauna Loa and Kilauea volcanoes, here referred to as the primary and secondary edifices, respectively. The models demonstrate incremental displacements of the outer flanks of the volcanoes and concurrent summit subsidence, leading to characteristic low slopes and inward dipping strata. Slip discontinuities that develop within the piles define steeply dipping normal faults along the upper flanks and beneath the edifice summits, that accommodate subsidence and flank spreading. Edifice overlap influences dynamic behavior significantly; even small topographic perturbations restrict the internal deformation and spreading of the confined flanks. The degree of buttressing depends on the relative positions of the two edifices. If the secondary edifice grows high upon the flanks of the primary edifice, outward spreading of the underlying flank is enhanced; if the secondary edifice is built low upon the primary flanks, spreading of the underlying flank is effectively prevented, or possibly reversed. Furthermore, as the second edifice grows, it subsides into the underlying flank, partitioning it into a mobile downslope region entrained by spreading of the second edifice, and a comparatively stable upper flank region. These results suggest that much of the mass of Kilauea volcano may lie deeply buried within the underlying flank of Mauna Loa, while older Mauna Loa rocks may lie far from their source beneath the mobile flank of the younger volcano.

Controls on the strength of coupling among climate, erosion, and deformation in two‐sided, frictional orogenic wedges at steady state

Many important insights regarding the coupling among climate, erosion, and tectonics have come from numerical simulations using coupled tectonic and surface process models. However, analyses to date have left the strength of the coupling between climate and tectonics uncertain and many questions unanswered. We present an approximate analytical solution for two‐sided orogenic wedges obeying a frictional rheology, and in a condition of flux steady state, that makes explicit the nature and sensitivity of the coupling between climate and deformation. We make the simplifying assumption that the wedge grows in a self‐similar fashion consistent with Airy isostasy such that topographic taper is invariant with orogen width, tectonic influx rate, and climate. We illustrate first how and why the form of the erosion rule matters to orogen evolution and then derive a physically based orogen‐scale erosion rule. We show that steady state orogen width, crest elevation, and crustal thickness are controlled by the ratio of accretionary flux to erosional efficiency to a power dictated by the erosion process. Remarkably, we show that for most combinations of parameters in the erosion law, rock uplift rate is more strongly controlled by erosional efficiency than it is by the accretionary flux. Further, assuming frontal accretion with no underplating, the spatial distribution of erosional efficiency dictates the relative rock uplift rates on the pro‐wedge and retro‐wedge and the time‐averaged trajectories of rocks through the orogen. The restriction to invariant frictional properties is conservative in these respects; systems subject to positive feedback between erosion and rheology will exhibit even stronger coupling among climate, erosion, and deformation than shown here.

Strain localization as a key to reconciling experimentally derived flow-law data with dynamic models of continental collision

Published strength profiles predict strength discontinuities within and/or at the base of continental crust during compression. We use finite element models to investigate the effect of strength discontinuities on continental collision dynamics. The style of deformation in model crust during continued subduction of underlying mantle lithosphere is controlled by: (1) experimental flow-law data; (2) the crustal geotherm; (3) strain localization by erosion; (4) strain-softening and other localization effects. In the absence of erosion and other factors causing strain localization, numerical models with typical geothermal gradients and frictional/ductile rheologies predict diffuse crustal deformation with whole-scale detachment of crust from mantle lithosphere. This prediction is at odds with earlier model studies that only considered frictional crustal rheologies and showed asymmetric, focused crustal deformation. Without localization, model deformation is not consistent with that observed in small collisional orogens such as the Swiss Alps. This suggests that strain localization by a combination of erosion and rheological effects such as strain softening must play a major role in focusing deformation, and that strength profiles derived under constant strain rates and uniform material properties cannot be used to infer crustal strength during collision dynamics.

Slip rates on San Francisco Bay area faults from anelastic deformation of the continental lithosphere

Long‐term slip rates on major faults in the San Francisco Bay area are predicted by modeling the anelastic deformation of the continental lithosphere in response to regional relative plate motion. The model developed by Bird and Kong [1994] is used to simulate lithospheric deformation according to a Coulomb frictional rheology of the upper crust and a dislocation creep rheology at depth. The focus of this study is the long‐term motion of faults in a region extending from the creeping section of the San Andreas fault to the south up to the latitude of Cape Mendocino to the north. Boundary conditions are specified by the relative motion between the Pacific plate and the Sierra Nevada‐Great Valley microplate [Argus and Gordon, 2000]. Rheologic‐frictional parameters are specified as independent variables, and prediction errors are calculated with respect to geologic estimates of slip rates and maximum compressive stress directions. The model that best explains the region‐wide observations is one in which the coefficient of friction on all of the major faults is less than 0.15, with the coefficient of friction for the San Andreas fault being approximately 0.09, consistent with previous inferences of San Andreas fault friction. Prediction error increases with lower fault friction on the San Andreas, indicating a lower bound of μSAF > 0.08. Discrepancies with respect to previous slip rate estimates include a higher than expected slip rate along the peninsula segment of the San Andreas fault and a slightly lower than expected slip rate along the San Gregorio fault.

Mechanical modeling of compressional basins: Origin and interaction of faults, erosion, and subsidence in the Ventura basin, California

Using geophysical observations and some basic geological ideas on the present structure of the Ventura basin, we model its possible mechanical evolution during the last 4 million years. We use a two‐dimensional finite element model with frictional and elastoviscoplastic rheologies that allow strain localization. This allows us to study the mechanical origin of the San Cayetano thrust fault (SCF) and its interaction with the Oak Ridge fault (ORF). The results of our modeling indicate that the geometry and activity of a shear zone which mimics the San Cayetano fault are conditioned both by the preexistence of the Oak Ridge fault and by the shape of the brittle‐ductile transition. Furthermore, the presence of a décollement level is shown to favor the development of the San Cayetano fault shear zone as a low‐angle structure. The value of the effective friction on the Oak Ridge fault is evaluated from this model. Possible values of the viscosity of the sediments are also estimated; it is shown that low sediment viscosity may completely hinder the activity of such a fault at the surface, while slip at depth continues. The stratigraphic profile of the basin is also shown to depend on the relative strengths of the ORF and SCF, which also provide an explanation for the shortening and rapid subsidence of the basin.

Frictional rheology: hardening by rotation of active normal faults

A simple model for work-hardening associated with rotation of active normal faults around horizontal axes mimics features of extended regions. We use Mohr-Coulomb envelopes to derive a frictional rheology for the upper crust. Sliding on block-bounding faults is assumed to constrain the stress state in the upper crust regardless of the deformation within the blocks. The model predicts that the stress-strain relations at a constant depth will be saw-toothed in shape with stages of gradual work-hardening following events of abrupt softening. The rupture of faults at the weakest zone in the loaded crust corresponds to the softening stage that is followed by work-hardening due to local block rotation. Work-hardening can drive lateral distribution of tectonic extension to form large extended regions with many domains of tilted blocks (Basin and Range type). In a thinning crust, however, material points undergo shallowing and the work-hardening is moderated by the effect of shallowing that decrease the frictional resistance. We use experimentally derived parameters of strength and friction to quantify the model predictions and to analyze the distribution of extension in Basin and Range and the frequency of tilt values in this region.

Computer simulations of California tectonics confirm very low strength of major faults

Recent improvements in the technique of modeling fault networks with thin-plate finite elements yield full convergence of the solutions, without any compromise in the representation of the frictional rheology of the upper crust or the transition to dislocation creep in the lower crust. We apply these techniques to model the California region, incorporating all faults with estimated slip rate over 1 mm/yr, as well as variations in elevation, heat flow, and crustal thickness. Velocity boundary conditions on the model sides are based on the NUVEL-1 plate model and an approximation of deformation in the Great Basin. The frictional and dislocation-creep rheologic constants of the crust are calibrated to reproduce the observed variations in the maximum depth of seismicity, which occurs at model temperatures of 350-410 °C. This leaves two free parameters: the (time-averaged) coefficient of friction on faults, and the apparent activation energy for creep in the lower crust. These parameters are systematically varied in three sets of 10, 81, and 64 experiments, respectively. The predictions of each model are tested against three published data sets: a set of 79 geologic limits on average slip rate on faults, a set of 221 principal stress directions, and a set of 841 secular rates of geodetic baselines (both trilateration and VLBI [very long baseline interferometry]). The patterns of model scores indicate that the time-averaged friction coefficient of major faults is only 0.17-0.25, or only 20%-30% of the value (0.85) that is assumed for the friction in the intervening blocks. (The laser trilateration data taken alone would indicate a preference for a high-stress model, but this model is one with very little fault slip and seismicity, which can be rejected on other grounds.) In the final three-parameter set of 64 models, we test whether the anomalous weakness of faults is uniform or proportional to net slip. With slip-dependent weakening, there is a general reduction in prediction errors, which supports the hypothesis. The geologic data and geodetic data agree in implying that fault weakness (that is, friction of 0.17) is general, with an additional 30% slip-dependent weakening of the San Andreas (to friction of 0.12, or 14% of normal). The stress data, however, are fit best if all weakness is slip dependent (effectively, only the San Andreas is weak). Thus, the hypothesis that all weakening is slip dependent should not be rejected. The best models predict all available data with RMS (root mean square) mismatch of as little as 3 mm/yr (6% of the relative plate velocity), so their predictions may be useful for seismic hazard estimation, at least along faults where no data are available. This study extends the finding of very low friction from subduction zones, where it was previously documented, to a dominantly strike-slip system in which underthrusting of wet sediment is not widespread. Return of previously subducted water from the mantle and its chemical or physical binding in fine-grained gouge are possible explanations for the very low friction.

A New Method for Predicting Friction Pressures and Rheology of Proppant-Laden Fracturing Fluids

Summary The prediction of friction pressures for proppant-laden fracturing fluids requires estimations of both the base-gel friction factor and the effect of proppant on fluid rheology. This paper introduces two new expressions, each theoretically based with constants determined from data, that address these two issues for hydroxypropyl guar (HPG)-based fracturing fluids in laminar and turbulent flow. The paper first introduces a new expression for the turbulent friction factor of HPG base gels. This implicit expression for the friction factor is more theoretically correct and requires one less empirical constant than explicit forms currently used. The effect of proppant on the effective viscosity of non-Newtonian fluids is then discussed and a new expression, which includes shear rate, temperature, gel concentration, and proppant volume fraction as parameters, is derived. Developed from laboratory data and existing slurry rheology theories, this expression is shown to provide excellent predictions of laboratory and field data for both tubing and annulus injection.