Smeared crack approach: back to the original track

This paper briefly reviews the formulations used over the last 40 years for the solution of problems involving tensile cracking, with both the discrete and the smeared crack approaches. The paper focuses on the smeared approach, identifying as its main drawbacks the observed mesh‐size and mesh‐bias spurious dependence when the method is applied ‘straightly’. A simple isotropic local damage constitutive model is considered, and the (exponential) softening modulus is regularized according to the material fracture energy and the element size. The continuum and discrete mechanical problems corresponding to both the weak discontinuity (smeared cracks) and the strong discontinuity (discrete cracks) approaches are analysed and the question of propagation of the strain localization band (crack) is identified as the main difficulty to be overcome in the numerical procedure. A tracking technique is used to ensure stability of the solution, attaining the necessary convergence properties of the corresponding discrete finite element formulation. Numerical examples show that the formulation derived is stable and remarkably robust. As a consequence, the results obtained do not suffer from spurious mesh‐size or mesh‐bias dependence, comparing very favourably with those obtained with other fracture and continuum mechanics approaches. Copyright © 2006 John Wiley & Sons, Ltd.     

Strength and stability of frictional sliding of gabbro gouge at elevated temperatures

To investigate the strength of frictional sliding and stability of mafic lower crust, we conducted experiments on oven-dried gabbro gouge of 1 mm thick sandwiched between country rock pieces (with gouge inclined 35° to the sample axis) at slip rates of 1.22 × 10^− 3 mm/s and 1.22 × 10^− 4 mm/s and elevated temperatures up to 615 °C. Special attention has been paid to whether transition from velocity weakening to velocity strengthening occurs due to the elevation of temperature.Two series of experiments were conducted with normal stresses of 200 MPa and 300 MPa, respectively. For both normal stresses, the friction strengths are comparable at least up to 510 °C, with no significant weakening effect of increasing temperature. Comparison of our results with Byerlee's rule on a strike slip fault with a specific temperature profile in the Zhangbei region of North China shows that the strength given by experiments are around that given by Byerlee's rule and a little greater in the high temperature range.At 200 MPa normal stress, the steady-state rate dependence a − b shows only positive values, probably still in the “run-in” process where velocity strengthening is a common feature. With a normal stress of 300 MPa, the values of steady-state rate dependence decreases systematically with increasing temperature, and stick-slip occurred at 615 °C. Considering the limited displacement, limited normal stress applied and the effect of normal stress for the temperatures above 420 °C, it is inferred here that velocity weakening may be the typical behaviour at higher normal stress for temperature above 420 °C and at least up to 615 °C, which covers most of the temperature range in the lower crust of geologically stable continental interior. For a dry mafic lower crust in cool continental interiors where frictional sliding prevails over plastic flow, unstable slip nucleation may occur to generate earthquakes.     

Mongolian gerbils and Daurian pikas responded differently to changes in precipitation in the Inner Mongolian grasslands

Mongolian gerbils (Meriones unguiculatus) and Daurian pikas (Ochotona dauurica) are two key small mammal species in the Inner Mongolian grasslands, China. Mongolian gerbils displayed density-dependent population growth, but the time lag of density dependence was short and within season. The spring–autumn population growth rate was inversely related to population density in Mongolian gerbils of the Erdos desert grasslands. The autumn–spring population growth rate of Mongolian gerbils was inversely related to winter precipitation. Precipitation had stronger effects on the population growth of gerbils during the non-breeding season. The monthly population growth rate of Daurian pikas was positively related to the monthly precipitation and was inversely related to population density in central Inner Mongolia. Daurian pikas select habitats with tall plants. Increased precipitation enhances plant production and increases the height of plants in arid and semi-arid regions. This enhancement of plant height might increase the population growth of Daurian pikas. Mongolian gerbils live in short grasslands. Increased winter precipitation might result in higher winter mortality of Mongolia gerbils, or taller plants might supress gerbil population growth in wet years. Therefore, responses of small mammal species to changes in precipitation depend on the life history of small mammals and changes in vegetation induced by climatic changes.     

How to obtain alert velocity thresholds for large rockslides

A reliable forecast of the failure stage of large rockslides is difficult, because of non-linear time dependency of displacements and seasonal effects. Aim of this paper is to suggest a practical method to prepare alert thresholds for large rockslides, assessing critical values of velocity for carrying out civil protection actions using monitoring data. Adopted data concern the 20 Mm³ Ruinon rockslide (Valfurva, Central Alps, Italy), still evolving and suitable to originate a fast moving rock avalanche. Multitemporal analysis of aerial photos, LIDAR-ALTM laser topography, field survey and geomechanical analyses allowed to infer the rockslide kinematics and better understand data provided by a monitoring network including distometers, extensometers, GPS benchmarks and inclinometers. The analysis of displacement and rainfall data over five years (1997–2001) allowed to recognise three different evolutionary patterns of displacements, showing a continuously increasing rate since 1997. Data representing large-scale behaviour of the rock mass were fitted by power-law curves, according to the “accelerating creep” model by Voight, in order to evaluate a suitable failure time. This was hampered by the large seasonal deviations, which can significantly delay the occurrence of failure. Data were fitted using the Voight’s equation, expressed in terms of displacement, through non-linear estimation techniques, in order to find values of the controlling parameters (A, α and t_f) suitable to represent the mechanical behaviour of the rock mass approaching the failure. This allowed to compute velocity–time theoretical curves and to define different velocity threshold values (pre-alert, alert and emergency) to be used for emergency management.     

Characterisation of the 1997 Vulcanian explosions of Soufrière Hills Volcano,Montserrat, by video analysis

The activity of Convention at Montserrat Soufrière Hills Volcano, Montserrat, during the period 1995–1999 included numerous violent explosions. Two major cycles of Vulcanian explosions occurred in 1997: a first of 13 explosions between 4 and 12 August and a second of 75 between 22 September and 21 October. The explosions were short-lived events lasting a few tens of seconds during which partial fountain collapse generated pyroclastic surges and pyroclastic flows, and buoyant plumes ascended 3–15 km into the atmosphere. Each explosion discharged on average 3×10⁵ m³ (dense-rock equivalent, DRE) of magma, draining the conduit to depths of 1–2 km. The paper focuses on the first few seconds of three explosions of the 75 that occurred in September/October 1997: 6 October 1997 at 17:50, 7 October 1997 at 16:02 and 9 October 1997 at 12:32. Physical parameters such as exit velocities, magmatic water contents and magma pressures at fragmentation are estimated by following and modelling the ascent of individual momentum-dominated finger jets visible on videos during the initial stages of each explosion. The model treats each finger jet as an incompressible flow sustained by a steady flux of gas and particles during the few seconds of ascent, and produces results that compare favourably with those using a multiphase compressible code run using similar eruptive parameters. Each explosion reveals a progressive increase in eruptive intensity with time, jet exit velocities increasing from 40 m s^–1 at the beginning of the explosion up to 140 m s^–1 after a few seconds. Modelling suggests that the first magma to exit was largely degassed, whereas that discharged after a few seconds contained up to 2 wt% water. Magma overpressures up to ~10 MPa are estimated to have existed in the conduit immediately prior to each explosion. Progressive increases in jet exit velocity with time over the first few seconds of each explosion provide direct evidence for strong pre-eruptive gradients in water content and magma pressure in the upper reaches (probably 100–500 m) of the conduit. Fountain collapse occurred during the first 10–20 s of each explosion because the discharging jets had bulk densities up to 100 times that of the atmosphere and were unable to entrain enough air to become buoyant. Such high eruptive densities were due to the presence of partially degassed magma in the conduit.Editorial responsibility: A. Woods     

Attenuation of body waves in Southeastern Sicily (Italy)

The attenuation of P- and S-waves in Southeastern Sicily was estimated by applying two different methods in time and frequency domains. We analyzed waveforms from about 290 local events (0.6≤M_L≤4.6) recorded at a three-component digital network.By applying the pulse broadening method to the first P-wave pulse, we found an average Q_p value of ca. 140. The application of the frequency decay method provided a Q_p value of ca. 120, in the low-frequency band (3-9 Hz). Conversely, in the high frequency range (16-27 Hz) the average Q_p is significantly larger (ca. 640). The frequency decay method was also applied to S-waves spectra. In the low frequency range (2-5 Hz) the estimated average Q_s is ca. 190. As for Q_p, also Q_s, in the high frequency range (16-27 Hz), is larger (ca. 700). These results evidenced a frequency dependence of both the quality factors Q_p and Q_s, as commonly observed in tectonically active zones characterized by high degree of heterogeneity.