A note on the stress-dilatancy relation for simulated fault gouge

Theoretical constraints on the stress-dilation relation for a deforming Coulomb material requirev ifC=0 andv sin^-1( _m / _m ) always, wherev is the dilation angle, is the friction angle,C is cohesion, _m is the maximum shear stress, and _m is the mean effective stress. Recent laboratory measurements of friction and dilatancy of simulated fault gouge show that small amplitude shear-load cycling causes compaction and consolidation. Comparison of the data with theory indicates that such load cycling produces: (1) increased coefficient of friction (or friction angle), (2) increased cohesion, and (3) increased dilatancy rate (or dilation angle). Under certain conditions of load cycling without significant plastic shear strain accumulation ( ^p <0.005) we find thatv exceeds both and, in contrast to theory, sin^-1( _m / _m ). This result is interpreted in terms of enhanced cohesion and overconsolidation, which lead to residual stresses within the gouge. An analogy is drawn between these special loading conditions and those extant on natural faults. In particular, our results imply that jostling and minor stress variations associated with microearthquakes may produce strengthening of fault gouge and changes in the fault zone's stress-dilatancy relation. Hence, compaction associated with microseismicity may lead to subsequent dilation of fault gouge, even for faults with large displacement rates and large net offsets (e.g., San Andreas). In regions where such dilation persists over sufficient displacements (on the order of the critical slip distance for seismic faulting) it may tend to inhibit unstable slip.     

Minimum work, fault activity and the growth of critical wedges in fold and thrust belts

Many studies of critical wedges treat the interior of the wedge as continuous and do not address the manner in which it grows from the undeformed state to a typical imbricate wedge. In this paper we present a 2D kinematic–mechanical model which attempts to explain the development of a critical wedge in a fold and thrust belt in terms of both gravitational and frictional work. In the undeformed model a series of thrust faults are defined which have the potential to take up an external displacement. The active fault at a given time is that which minimizes gravitational and frictional work as a result of displacement. Displacement on the active fault causes a change in topography and deformation of other faults which may favour an alternative fault at the next time step. The model is a mixed Lagrangian–Eulerian scheme in which the upper surface, in addition to being deformed, is also subject to erosion, transport and sedimentation. The model predicts propagation of thrust fault activity towards the foreland through time as a result of increasing topographic (gravitational) loads and frictional work on deformed hinterland faults. As the zone of fault activity progresses through the developing critical wedge several faults are active over time-scales of ≈1 Myr. However, a simple chronology or sequence of fault activity cannot be assumed as out-of-sequence thrusting occurs during this overall foreland propagation. The detailed spatial and temporal activity of faults is complex and reflects the interaction between the development of topography, the contrast between basal (décollement) and internal coefficients of friction and the effects of erosion and sedimentation. In particular, rates of erosion and sedimentation are found to be important controls on fault activity both spatially and temporally. Erosion, by locally removing topography above a fault, reduces gravitational and frictional work enabling continued fault activity or reactivation. Sedimentation, conversely, acts to increase gravitational and frictional work on a fault, and therefore has the potential to blanket faults and render them inactive. Model results illustrate the complex feedbacks that can exist between tectonic and surficial mass transport processes.     

Hipparcos absolute magnitudes for metal-rich K giants and the calibration of DDO photometry

Parallaxes for 581 bright K giants have been determined using the Hipparcos satellite. We combine the trigonometric parallaxes with ground-based photometric data to determine the K giant absolute magnitudes. For all these giants, absolute magnitude estimates can also be made using the intermediate-band photometric David Dunlop Observatory (DDO) system. We compare the DDO absolute magnitudes with the very accurate Hipparcos absolute magnitudes, finding various systematic offsets in the DDO system. These systematic effects can be corrected, and we provide a new calibration of the DDO system allowing absolute magnitude to be determined with an accuracy of 0.35 mag in the range 2 >  M _v  > −1. The new calibration performs well when tested on K giants with DDO photometry in a selection of low-reddening open clusters with well-measured distance moduli.     

The radial disc structure around a magnetic neutron star: analytic and semi-analytic solutions

The radial structure of a thin accretion disc is calculated in the presence of a central dipole magnetic field aligned with the rotation axis. The problem is treated using a modified expression for the turbulent magnetic diffusion, which allows the angular momentum equation to be integrated analytically. The governing algebraic equations are solved iteratively between 1 and 10⁴ stellar radii. An analytic approximation is provided that is valid near the disruption radius at about 100 stellar radii. At that point, which is approximately 60 per cent of the Alfvén radius and typically about 30 per cent of the corotation radius, the disc becomes viscously unstable. This instability results from the fact that both radiation pressure and opacity caused by electron scattering become important. This in turn is a consequence of the magnetic field which leads to an enhanced temperature in the inner parts. This is because the magnetic field gives rise to a strongly enhanced vertically integrated viscosity, so that the viscous torque can balance the magnetic torque.     

Numerical simulations of rotating cooling flows in galaxy cluster environments

We have used 2D numerical simulations to study the evolution of galaxy cluster cooling flows undergoing a rotational perturbation. We show that such rotations in the intracluster medium may arise from cluster/subcluster mergers. Our galaxy cluster initial conditions involve spherically symmetric, steady-state cooling flows with varying mass-dropout strengths. The rotational perturbation serves to break the symmetry for each of the initial cooling flows, resulting in the formation of thin, gaseous disc-like structure extending radially out to ∼10 kpc. Disc-like structure formed for low mass-dropout strength simulations appears to contain cooling condensations whereas disc-like structure in higher mass-dropout strength simulations appears smooth. This is due to the influence of mass-dropout on the degree of cooling, which serves to reduce the strength of thermal instabilities by the removal of 'cold' gas from the flow. Morphological comparisons of the disc-like structure formed in our simulations are made to structure observed in the X-ray emitting gas of A4059. Comparisons of the gas dynamics within the disc-like structure are also made to the solid-body rotation profile observed from emission-line gas within the central galaxy of Hydra A. The influence of grid effects on the simulations is also discussed.     

Hipparcos and the age of the Galactic disc

We use the Hipparcos colour–magnitude diagram of field stars with Tycho colours to make a new minimum age estimate for the Galactic disc. The method is based on fits to the red envelope of subgiants in the Hipparcos colour–magnitude diagram with synthetic isochrones covering the range of disc metal abundance. The colours and luminosities of the isochrones as a function of abundance are checked using new techniques involving 'red-clump' stars in the giant branch region and on the main sequence using G and K dwarfs. We derive a minimum disc age of 8 Gyr, in good agreement with other methods.     

Coulomb constitutive laws for friction: Contrasts in frictional behavior for distributed and localized shear

We describe slip-rate dependent friction laws based on the Coulomb failure criteria. Frictional rate dependence is attributed to a rate dependence of cohesionc and friction angle . We show that differences in the stress states developed during sliding result in different Coulomb friction laws for distributed shear within a thick gouge layer versus localized shear within a narrow shear band or between bare rock surfaces. For shear within gouge, shear strength is given by =c cos + _n sin, whereas for shear between bare rock surfaces the shear strength is =c cos + _n tan, where and _n are shear and normal stress, respectively. In the context of rate-dependent Coulomb friction laws, these differences mean that for a given material and rate dependence of the Coulomb parameters, pervasive shear may exhibit velocity strengthening frictional behavior while localized shear exhibits velocity weakening behavior. We derive from experimental data the slip-rate dependence and evolution ofc and for distributed and localized shear. The data show a positive rate dependence for distributed shear and a negative rate dependence for localized shear, indicating that the rate dependence ofc and are not the same for distributed and localized shear, even after accounting for differences in stress state. Our analysis is consistent with the well-known association of instability with shear localization in simulated fault gouge and the observation that bare rock surfaces exhibit predominantly velocity weakening frictional behavior whereas simulated fault gouge exhibits velocity strengthening followed by a transition to velocity weakening with increasing displacement. Natural faults also exhibit displacement dependent frictional behavior and thus the results may prove useful in understanding the seismic evolution of faulting.     

Hydrochemical variations during flood pulses in the south‐west China peak cluster karst: impacts of CaCO3–H2O–CO2 interactions

High‐resolution measurements of rainfall, water level, pH, conductivity, temperature and carbonate chemistry parameters of groundwater at two adjacent locations within the peak cluster karst of the Guilin Karst Experimental Site in Guangxi Province, China, were made with different types of multiparameter sonde. The data were stored using data loggers recording with 2 min or 15 min resolution. Waters from a large, perennial spring represent the exit for the aquifer's conduit flow, and a nearby well measures water in the conduit‐adjacent, fractured media. During flood pulses, the pH of the conduit flow water rises as the conductivity falls. In contrast, and at the same time, the pH of groundwater in the fractures drops, as conductivity rises. As Ca²⁺ and HCO₃^? were the dominant (>90%) ions, we developed linear relationships (both r² > 0·91) between conductivity and those ions, respectively, and in turn calculated variations in the calcite saturation index (SI_C) and CO₂ partial pressure (P) of water during flood pulses. Results indicate that the P of fracture water during flood periods is higher than that at lower flows, and its SI_C is lower. Simultaneously, P of conduit water during the flood period is lower than that at lower flows, and its SI_C also is lower. From these results we conclude that at least two key processes are controlling hydrochemical variations during flood periods: (i) dilution by precipitation and (ii) water–rock–gas interactions. To explain hydrochemical variations in the fracture water, the water–rock–gas interactions may be more important. For example, during flood periods, soil gas with high CO₂ concentrations dissolves in water and enters the fracture system, the water, which in turn has become more highly undersaturated, dissolves more limestone, and the conductivity increases. Dilution of rainfall is more important in controlling hydrochemical variations of conduit water, because rainfall with higher pH (in this area apparently owing to interaction with limestone dust in the lower atmosphere) and low conductivity travels through the conduit system rapidly. These results illustrate that to understand the hydrochemical variations in karst systems, considering only water–rock interactions is not sufficient, and the variable effects of CO₂ on the system should be evaluated. Consideration of water–rock–gas interactions is thus a must in understanding variations in karst hydrochemistry. Copyright © 2004 John Wiley & Sons, Ltd.