Extensions of Fibre Bundle Models

Antarctic Snow Failure Mechanics: Analysis, Simulations, and Applications

Snow failure is the process by which the stability of snow or snow-covered slopes is destroyed, resulting in the collapse or release of snow. Heavy snowfall, low temperatures, and volatile weather typically cause consequences in Antarctica, which can occur at different scales, from small, localized collapses to massive avalanches, and result in significant risk to human activities and infrastructures. Understanding snow damage is critical to assessing potential hazards associated with snow-covered terrain and implementing effective risk mitigation strategies. This review discusses the theoretical models and numerical simulation methods commonly used in Antarctic snow failure research. We focus on the various theoretical models proposed in the literature, including the fiber bundle model (FBM), discrete element model (DEM), cellular automata (CA) model, and continuous cavity-expansion penetration (CCEP) model. In addition, we overview some methods to acquire the three-dimensional solid models and the related advantages and disadvantages. Then, we discuss some critical numerical techniques used to simulate the snow failure process, such as the finite element method (FEM) and three-dimensional (3D) material point method (MPM), highlighting their features in capturing the complex behavior of snow failure. Eventually, different case studies and the experimental validation of these models and simulation methods in the context of Antarctic snow failure are presented, as well as the application of snow failure research to facility construction. This review provides a comprehensive analysis of snow properties, essential numerical simulation methods, and related applications to enhance our understanding of Antarctic snow failure, which offer valuable resources for designing and managing potential infrastructure in Antarctica.

Scaling laws of failure dynamics on complex networks

The topology of the network of load transmitting connections plays an essential role in the cascading failure dynamics of complex systems driven by the redistribution of load after local breakdown events. In particular, as the network structure is gradually tuned from regular to completely random a transition occurs from the localized to mean field behavior of failure spreading. Based on finite size scaling in the fiber bundle model of failure phenomena, here we demonstrate that outside the localized regime, the load bearing capacity and damage tolerance on the macro-scale, and the statistics of clusters of failed nodes on the micro-scale obey scaling laws with exponents which depend on the topology of the load transmission network and on the degree of disorder of the strength of nodes. Most notably, we show that the spatial structure of damage governs the emergence of the localized to mean field transition: as the network gets gradually randomized failed clusters formed on locally regular patches merge through long range links generating a percolation like transition which reduces the load concentration on the network. The results may help to design network structures with an improved robustness against cascading failure.

Temporal evolution of failure avalanches of the fiber bundle model on complex networks

We investigate how the interplay of the topology of the network of load transmitting connections and the amount of disorder of the strength of the connected elements determines the temporal evolution of failure cascades driven by the redistribution of load following local failure events. We use the fiber bundle model of materials' breakdown assigning fibers to the sites of a square lattice, which is then randomly rewired using the Watts-Strogatz technique. Gradually increasing the rewiring probability, we demonstrate that the bundle undergoes a transition from the localized to the mean field universality class of breakdown phenomena. Computer simulations revealed that both the size and the duration of failure cascades are power law distributed on all network topologies with a crossover between two regimes of different exponents. The temporal evolution of cascades is described by a parabolic profile with a right handed asymmetry, which implies that cascades start slowly, then accelerate, and eventually stop suddenly. The degree of asymmetry proved to be characteristic of the network topology gradually decreasing with increasing rewiring probability. Reducing the variance of fibers' strength, the exponents of the size and the duration distribution of cascades increase in the localized regime of the failure process, while the localized to mean field transition becomes more abrupt. The consistency of the results is supported by a scaling analysis relating the characteristic exponents of the statistics and dynamics of cascades.

True Strength of Ceramic Fiber Bundles: Experiments and Simulations

A study on the strength of ceramic fiber bundles based on experimental and computational procedures is presented. Tests were performed on single filaments and bundles composed of two fibers with different nominal fiber counts. A method based on fiber rupture signals was developed to estimate the amount of filament rupture during the test. Through this method, the fiber bundle true strength was determined and its variation with the initial fiber count observed. By using different load-sharing models and the single filament data as input parameter, simulations were also developed to verify this behavior. Through different approaches between experiments and simulations, it was noted that the fiber bundle true strength increased with the fiber count. Moreover, a variation of the fibers' final proportion in the bundles relative to the initial amount was verified in both approaches. Finally, discussions on the influence of different load-sharing models on the results are presented.

Record statistics of bursts signals the onset of acceleration towards failure

Forecasting the imminent catastrophic failure has a high importance for a large variety of systems from the collapse of engineering constructions, through the emergence of landslides and earthquakes, to volcanic eruptions. Failure forecast methods predict the lifetime of the system based on the time-to-failure power law of observables describing the final acceleration towards failure. We show that the statistics of records of the event series of breaking bursts, accompanying the failure process, provides a powerful tool to detect the onset of acceleration, as an early warning of the impending catastrophe. We focus on the fracture of heterogeneous materials using a fiber bundle model, which exhibits transitions between perfectly brittle, quasi-brittle, and ductile behaviors as the amount of disorder is increased. Analyzing the lifetime of record size bursts, we demonstrate that the acceleration starts at a characteristic record rank, below which record breaking slows down due to the dominance of disorder in fracturing, while above it stress redistribution gives rise to an enhanced triggering of bursts and acceleration of the dynamics. The emergence of this signal depends on the degree of disorder making both highly brittle fracture of low disorder materials, and ductile fracture of strongly disordered ones, unpredictable.

Relation between land cover and landslide susceptibility in Val d'Aran, Pyrenees (Spain): Historical aspects, present situation and forward prediction

The effects of land use and land cover (LULC) dynamics on landslide susceptibility are not fully understood. This study evaluates the influence of LULC on landslide susceptibility and assesses the historic and future LULC changes in a high mountain region. A detailed inventory map showing the distribution of landslides was prepared based on the 2013 episode in Val d'Aran, Pyrenees (Spain). This inventory showed that LULC clearly affected landslide susceptibility. Both the number of landslides and the landslide density triggered in grassland and meadow was highest (52% and 2.0 landslides/km²). In contrast, the landslide density in areas covered by forest and shrubs was much lower (15% and 0.4 landslides/km², and 23% and 1.7 landslides/km², respectively). Historical changes of LULC between 1946 and 2013 were determined by comparing aerial photographs. The results indicated that the forest and shrub areas increased by 68 and 65%, respectively; whereas grassland and scree areas decreased by 33 and 52%. Urban area also increased by 532%, especially between 1990 and 2001. Future LULC was predicted until 2097 using TerrSet software. The results showed that the forest area and urban area increased by 57 and 43%, severally; while shrubs, grassland and scree area decreased by 28, 46 and 78%, respectively. Heuristic and deterministic models were applied to create susceptibility maps, which classified the study area into four susceptibility degrees from very low to high. The maps were validated by the 2013 landslide dataset and showed satisfactory results using receiver operating characteristics curves and density graph method. Then, susceptibility maps until 2097 were calculated by the heuristic model and results revealed that landslide susceptibility will decrease by 48% for high-susceptible areas. In contrast, the areas of very-low susceptibility degree will increase 95%, while medium and low-susceptible areas will be more or less constant. This study only includes the effect of future LULC changes on the landslide susceptibility and does not analyze the future impacts of climate changes and the variation of rainfall conditions. Nevertheless, the results may be used as support for land management guidelines to reduce the risk of slope instabilities.

Experimental Investigation of Damage Formation in Planar Fibrous Networks During Stretching

This paper presents the results of unidirectional strain-controlled experiments on fibrous electrospun networks used to study damage formation during elongation. The experimental loading curve shows a symmetrical parabolic type dependence at large scale and saw tooth-like force−extension behaviour at small scale. The damage formation was quantified by determining the number and the magnitude of abrupt force drops. The experiments evidenced that damage evolution is a consequence of strain induced random events. The frequency distribution of the number of damages as well as the magnitude of rupture force were represented by histograms. The results of the present study provide a better insight into damage tolerance and complex nonlinear tensile properties of electrospun networks. In addition, it could suggest a possible probabilistic approach to the fiber bundle model which has mainly motivated this study.

Experimental Evidence of Accelerated Seismic Release without Critical Failure in Acoustic Emissions of Compressed Nanoporous Materials

The total energy of acoustic emission (AE) events in externally stressed materials diverges when approaching macroscopic failure. Numerical and conceptual models explain this accelerated seismic release (ASR) as the approach to a critical point that coincides with ultimate failure. Here, we report ASR during soft uniaxial compression of three silica-based (SiO_{2}) nanoporous materials. Instead of a singular critical point, the distribution of AE energies is stationary, and variations in the activity rate are sufficient to explain the presence of multiple periods of ASR leading to distinct brittle failure events. We propose that critical failure is suppressed in the AE statistics by mechanisms of transient hardening. Some of the critical exponents estimated from the experiments are compatible with mean field models, while others are still open to interpretation in terms of the solution of frictional and fracture avalanche models.