Aperiodicity in one-way Markov cycles and repeat times of large earthquakes in faults

A common use of Markov Chains is the simulation of the seismic cycle in a fault, i.e. as a renewal model for the repetition of its characteristic earthquakes. This representation is consistent with Reid's elastic rebound theory. Here it is proved that in {\it any} one-way Markov cycle, the aperiodicity of the corresponding distribution of cycle lengths is always lower than one. This fact concurs with observations of large earthquakes in faults all over the world

Experimental characterisation of textile compaction response: A benchmark exercise

This paper reports the results of an international benchmark exercise on the measurement of fibre bed compaction behaviour. The aim was to identify aspects of the test method critical to obtain reliable results and to arrive at a recommended test procedure for fibre bed compaction measurements. A glass fibre 2/2 twill weave and a biaxial (±45°) glass fibre non-crimp fabric (NCF) were tested in dry and wet conditions. All participants used the same testing procedure but were allowed to use the testing frame, the fixture and sample geometry of their choice. The results showed a large scatter in the maximum compaction stress between participants at the given target thickness, with coefficients of variation ranging from 38% to 58%. Statistical analysis of data indicated that wetting of the specimen significantly affected the scatter in results for the woven fabric, but not for the NCF. This is related to the fibre mobility in the architectures in both fabrics. As isolating the effect of other test parameters on the results was not possible, no statistically significant effect of other test parameters could be proven. The high sensitivity of the recorded compaction pressure near the minimum specimen thickness to changes in specimen thickness suggests that small uncertainties in thickness can result in large variations in the maximum value of the compaction stress. Hence, it is suspected that the thickness measurement technique used may have an effect on the scatter

Out-of-plane permeability measurement for reinforcement textiles: A benchmark exercise

The out-of-plane permeability of two glass fibre fabrics was measured by 26 institutions using silicone oil as a test fluid. Participants in this study were free to select the test procedure, specimen dimensions and data analysis method, provided that testing was carried out at three target fibre volume fractions, 46 %, 50 % and 54 %. While results showed a variability of two orders of magnitude between participants, most values were within a significantly narrower band. A majority of participants used 1D saturated test method. A few selected 1D unsaturated and 3D unsaturated flow method which gave very similar results. Focusing on analysis of data and results of 1D saturated flow measurements, results are not conclusive, but they are consistent with number of layers in a specimen, fibre volume fraction, injection pressure and sealing of specimen edges all having an effect on the measured permeability. Specifying limits for these parameters is expected to result in reduced scatter in measured permeability.ISSN:1359-835XISSN:1878-584

Experimental and Theoretical Study of Multiscale Damage-Failure Transition in Very High Cycle Fatigue

Multiscale mechanisms of failure of metals (Armco iron, titanium, aluminum) are studied for high cycle and very high cycle fatigue. By correlating with the results of structural studies, a theoretical approach is developed to describe fatigue crack kinetics in damaged material under high cycle and very high cycle fatigue loading conditions. Stages of crack nucleation and propagation are analyzed using the profilometry data from the fracture surface. The scale invariance of fracture surface roughness is established, which allows an explanation of the self-similar nature of fatigue crack kinetics under high cycle and very high cycle fatigue. Variation of elastic-plastic properties of Armco iron under very high cycle fatigue is studied using an acoustic resonance method. It is found that the material density decreases during fatigue damage accumulation, with the minimum of the material density in the bulk of the specimen

Benchmark exercise on image-based permeability determination of engineering textiles: Microscale predictions

Permeability measurements of engineering textiles exhibit large variability as no standardization method currently exists; numerical permeability prediction is thus an attractive alternative. It has all advantages of virtual material characterization, including the possibility to study the impact of material variability and small-scale parameters. This paper presents the results of an international virtual permeability benchmark, which is a first contribution to permeability predictions for fibrous reinforcements based on real images. In this first stage, the focus was on the microscale computation of fiber bundle permeability. In total 16 participants provided 50 results using different numerical methods, boundary conditions, permeability identification techniques. The scatter of the predicted axial permeability after the elimination of inconsistent results was found to be smaller (14%) than that of the transverse permeability (~24%). Dominant effects on the permeability were found to be the boundary conditions in tangential direction, number of sub-domains used in the renormalization approach, and the permeability identification technique

Black swans, power laws, and dragon-kings: Earthquakes, volcanic eruptions, landslides, wildfires, floods, and SOC models

Extreme events that change global society have been characterized as black swans. The frequency-size distributions of many natural phenomena are often well approximated by power-law (fractal) distributions. An important question is whether the probability of extreme events can be estimated by extrapolating the power-law distributions. Events that exceed these extrapolations have been characterized as dragon-kings. In this paper we consider extreme events for earthquakes, volcanic eruptions, wildfires, landslides and floods. We also consider the extreme event behavior of three models that exhibit self-organized criticality (SOC): the slider-block, forest-fire, and sand-pile models. Since extrapolations using power-laws are widely used in probabilistic hazard assessment, the occurrence of dragon-king events have important practical implications