Bayesian stochastic modelling for avalanche predetermination: from a general system framework to return period computations

Stochastic models are recent but unavoidable tools for snow avalanche hazard mapping that can be described in a general system framework. For the computation of design return periods, magnitude and frequency have to be evaluated. The magnitude model consists of a set of physical equations for avalanche propagation associated with a statistical formalism adapted to the input–output data structure. The friction law includes at least one latent friction coefficient. The Bayesian paradigm and the associated simulation techniques assist considerably in performing the inference and taking estimation errors into account for prediction. Starting from the general case, simplifying hypotheses allows computing the predictive distribution of high return periods on a case-study. Only release and runout altitudes are considered so that the model can use the French database. An inversible propagation model makes it possible to work with the latent friction coefficient as if it is observed. Prior knowledge is borrowed from an avalanche path with similar topographical characteristics. Justifications for the working hypotheses and further developments are discussed. In particular, the whole approach is positioned with respect to both deterministic and stochastic hydrology.     

Modelling the spatio-temporal repartition of right-truncated data: an application to avalanche runout altitudes in Hautes-Savoie

In this paper, we propose a novel approach for generating avalanche hazard maps based on the spatial dependence of avalanche runout altitudes. The right-truncated data are described with a Bayesian hierarchical model in which the spatio-temporal process is assumed to be the sum of independent spatial and temporal terms. Topography is roughly taken into account according to valley altitude and path exposition, and the spatial dependence is modelled with a Matérn covariance function. An application is performed to the Haute-Savoie region, French Alps. A spatial dependence in runout altitudes is identified, and an effective range of about 10 km is inferred. The temporal trend extracted highlights the increase of avalanche runout altitudes from 1955, attributed to both anthropogenic factors and climate warming. In a cross validation scheme, spatial predictions are provided on undocumented paths using kriging equations. All in all, although our model is unable to take into account small topographic features, it is a first-ever approach that produces very encouraging results. It could be enhanced in future work by incorporating a numerical physically-based code into the modelling.     

A New Method for the Estimation of Avalanche Distance Exceeded Probabilities

A crucial point in any methodology for avalanche hazard assessment is the evaluation of avalanche distance exceeded probability, i.e., the annual probability that any assigned location along a given path is reached or exceeded by an avalanche. Typically this problem is faced by estimating the snow volume in the starting zone that is likely to accumulate an average every T years by statistical analysis of snowfall record, and then using this volume as input to an appropriately calibrated avalanche dynamics model to determine the runout distancesfor this design event. This methodology identifies the areas that canbe affected by an avalanche for the considered value of the return period (i.e. the average interval of time for a certain event to repeat itself), ¯T. However, it does not allow us to evaluate the actual avalanche encounter probability for any given point in the runout zone. In the present work this probability is computed by numerical integration of the expression P(x) = ∫₀ ^∞ P^*(V)f(V) dV, where f is the probabilitydensity function (PDF) of the avalanche release volume V, and P^* is the probability of the point x being reached or passed by an avalanche if the release volume is V; this latter probability is calculated by avalanche dynamics simulations. The procedure is implemented using a one-dimensional hydraulic-continuum avalanche dynamic model, calibrated on data from different Italian Alpine ranges, and is applied to a real world hazard mapping problem.     

Influence of runout‐path material on emplacement of the Round Top rock avalanche,New Zealand

Factors influencing the distance a disintegrating rock mass travels as it spreads across the landscape after detaching from a slope include the volume and mechanical properties of the material, local topography and the materials encountered in the runout path. Here we investigate the influence of runout‐path material on the mobility and final morphology of the Round Top rock avalanche deposit, New Zealand. This rock avalanche of mylonitic schist ran out over a planar surface of saturated fluvial gravel. Longitudinal ridges aligned radial to source grade into smaller aligned hummocks and digitate lobes in the distal reach. Soils and river gravels in the runout path are found bulldozed at elongate ridge termini where they formed local obstacles halting avalanche motion at these locations, thus aiding development of prominent elongate ridges on the deposit. Further travel over the disrupted substrate led to avalanche–substrate mixing at the base of the debris mass. Field observations combined with subsurface geophysical investigations and laboratory analogue models illustrate the processes of substrate deformation features at the Round Top rock avalanche. Copyright © 2009 John Wiley & Sons, Ltd.     

Paleomagnetic estimate of the emplacement temperature of the long-runout Nevado de Colima volcanic debris avalanche deposit, Mexico

Stoopes and Sheridan have mapped a volcanic debris avalanche of Nevado de Colima which has an exceptionally long runout (120 km) and low fall-height to length ratio (H/L = 0.04). We present paleomagnetic results from this volcanic debris avalanche deposit which provide evidence that this avalanche was emplaced at elevated temperatures. The majority of samples, collected from lithic clasts in the volcanic debris avalanche deposit, exhibit two-component remanent magnetizations with a low-temperature component (25–350°C) which is well grouped about the geomagnetic field direction at Colima and a high-temperature component (350–580°C) which is randomly oriented. Although the temperature of the deposit most likely varied with distance from the volcanic source and the thickness of the deposit, our results suggest an emplacement temperature of approximately 350°C at intermediate distances (18–26 km) from the source. In order for the rock clasts (20–40 cm diameter) to be heated to these temperatures, the avalanche was most likely the results of a magmatic, Bezymianny-type eruption. The mixing of hot, juvenile gases with the clasts provides an explanation for the high degree of fluidization of this material, as evidenced by the long runout of this avalanche deposit.     

Granular flow experiments on the interaction with stationary runout path materials and comparison to rock avalanche events

The central focus of this work is to study the processes acting well below the surface of a moving rock or debris avalanche during travel over stationary substrate material. Small‐scale physical models at a linear scale of 1:10⁴ used coal as avalanche analogue material and different granular material simulating sedimentary substrates varying in frictional resistance, thickness and relative basal boundary roughness, as well as inerodible, non‐deformable runout path conditions. Substrate materials with the least frictional resistance showed the greatest response to granular flow overriding, becoming entirely mobilized beneath and ahead of the moving mass and producing the longest runout observed with a unique deposit profile shape. With a smooth substrate basal contact, failure occurred along this plane and avalanche and substrate became coupled during runout. With a rough base, however, temporary force chains of grain contacts in the substrate prevailed longer, imparted their resistance to motion/shear into the granular flow, and the flow rear section consequently halted earlier than when moving over substrates with a weak base. Reducing substrate thickness diminished the effect of basal contact roughness on granular flow runout and deposit length. Inerodible, non‐deformable substrate conditions caused changes in granular flow behaviour from essentially en masse sliding on low‐friction surfaces to increasing granular agitation over rougher paths. Copyright © 2012 John Wiley & Sons, Ltd.     

Topographic reflection of the Socompa debris avalanche,Chile

One of the most remarkable features of the exceptionally well preserved 26 km³ Socompa debris avalanche deposit is the evidence for topographically driven secondary flow. The avalanche formed by sector collapse of Socompa stratovolcano and spread 40 km across a pre-existing basin, forming a sheet of ∼50 m average thickness. As the avalanche impinged on the western and northern margins of the basin, it was reflected back, forming a secondary flow that continued to travel 15 km down a gentle slope at an oblique angle to the primary flow, the front of the return wave being preserved frozen on the surface of the deposit as a prominent escarpment. Satellite images, aerial photos, digital elevation models and field observations were used to reconstruct the sequence of events during avalanche emplacement, and in particular during secondary flow. The avalanche sheet was divided into distinct terrane groups, each believed to have experienced a particular strain history during emplacement. Evidence for avalanche reflection includes clearly recognizable secondary slide masses, sub-parallel sets of curvilinear shear zones, headwall scarps separating the (primary) levée from the secondary terranes, extensional jigsaw breakup of surface lithologies during return flow, and cross cutting, or deflection, of primary flow fabrics by secondary terranes. Reflection off the basin margin took place in an essentially continuous manner, most major return motions being simultaneous with, or shortly following, primary flow. The secondary flow occurred as a wave that swept obliquely across the primary avalanche direction, remobilizing the primary material, which was first compressed, then stretched, as it passed over and rearward of the wave front. As return flow occurred, surface lithologies were rifted in a brittle manner, and the slabs were sheared pervasively as they glided and rotated back into the basin; some sank into the more fluidal interior of the avalanche, which drained out into a prominent distal lobe. Extension by factors of up to 1.8 took place during return flow. Secondary flow took place on slopes of only a few degrees, and the distal lobe flowed 8 km on a slope of ∼1°. Overall the avalanche is inferred to have slid into place as a fast-moving sheet of fragmental rock debris, with a leading edge and crust with near-normal friction and an almost frictionless, fluidal interior and base. The avalanche emplacement history deduced from field evidence is consistent with the results of a previously published numerical model of the Socompa avalanche.     

Timing and seismic origin of the historic Luanshibao rock avalanche in the Maoyaba basin,SE Tibetan Plateau: New evidence from 10Be exposure-ages

Rock avalanche is one of the most notable geological disasters in the mountain areas, such as the southeastern Tibetan Plateau. A typical one therein is the Luanshibao (LSB) rock avalanche that occurred in the Maoyaba basin. This rock avalanche has attracted a great deal of attentions, as it has a potential threat to the construction of Sichuan-Tibet Railway. It has been widely accepted that the LSB rock avalanche was caused by a seismic event. However, it is still an open question as to the timing of the earthquake-triggered rock avalanche. Here, we report twenty new ¹⁰Be exposure-ages obtained from the deposition zone. These tightly clustered exposure-ages, combined with geomorphic evidence, indicate that the LSB rock avalanche occurred during the mid-Holocene, possibly at 5.2 ± 0.2 ka. A comparison between the timing of rock avalanche and seismic events suggests a close correlation of the LSB rock avalanche with recurrent earthquakes around ∼5 ka BP. Such a correlation is well supported by the view from previous studies.     

Earthquake loss estimation for Greater Cairo and the national economic implications

The Egyptian economy and culture are centralized in the Greater Cairo region. Thus, it is essential that the built environment is able to withstand the possible earthquake events that may occur, and to continue to operate and function. Failure to do so would result in significant economic losses. This study presents the latter stages of a multi-tiered probabilistic earthquake loss estimation model for Greater Cairo and builds upon previous studies of the seismic hazard. In order to assess possible damage to the built environment, and the resulting economic losses, the vulnerability of the built environment is first evaluated. Through the use of satellite images, Egypts building census, previous studies and field surveys, a building-stock inventory is compiled. This building inventory is classified according to structural type and height, and is geocoded by district. Using existing fragility curves, the vulnerability of the building stock is assessed. In addition, the vulnerability of both the electricity and natural gas networks are assessed, through the use of fragility curves, cut sets and an evaluation of the supply networks. Based on the assessment of direct losses, the losses associated with building damage far exceed those associated with the considered network infrastructure. A macro-economic model is developed that takes into account damage to the built environment and provides estimates of indirect economic losses, as well as enabling the identification of the optimal recovery process. Using this model, it is shown that the indirect losses can exceed direct losses for extreme scenarios where the economy is brought to a near standstill. The framework developed and presented herein can be extended to include more networks, and is also applicable to other regions.     

Varying Dam Height to Shorten the Run-Out of Dense Avalanche Flows: Developing a Scaling Law from Laboratory Experiments

Dry and dense snow avalanches are considered as dry granular flows. Theirinteraction with dams is the main objective of this paper. We studied howvarying the dam height could shorten a granular avalanche run-out thanksto a set of simple laboratory experiments carried out on different scales.Shortening the run-out was expected to depend on two effects: (i) storageof the granular material upstream of the dam, and (ii) local energy dissipations.A scaling law is highlighted. As suggested by dimensional arguments, thecontribution of the local energy dissipation was shown to be more dominantthan the storage effects.     

青海玉树7.1级地震房屋建筑震害调查和分析

2010年4月14日青海玉树7.1级地震灾害严重,给当地居民造成了巨大的损失。房屋破坏是造成人员伤亡和巨大财产损失的主要因素,通过现场调查给出房屋建筑震害情况,分析了房屋建筑的震害特征,提出了地震灾区恢复重建建议。     

Application of Gumbel I and Monte Carlo methods to assess seismic hazard in and around Pakistan

A proper assessment of seismic hazard is of considerable importance in order to achieve suitable building construction criteria. This paper presents probabilistic seismic hazard assessment in and around Pakistan (23° N–39° N; 59° E–80° E) in terms of peak ground acceleration (PGA). Ground motion is calculated in terms of PGA for a return period of 475 years using a seismogenic-free zone method of Gumbel’s first asymptotic distribution of extreme values and Monte Carlo simulation. Appropriate attenuation relations of universal and local types have been used in this study. The results show that for many parts of Pakistan, the expected seismic hazard is relatively comparable with the level specified in the existing PGA maps.     

基于MATLAB神经网络方法的多层砖房震害预测

提出利用MATLAB人工神经网络工具箱建立基于贝叶斯正则算法的BP神经网络模型,以地震区多层砖房震害调查数据为因子的震害预测方法.神经网络模型输入震害因子包括建筑的层数、施工质量、房屋整体性等,输出值为建筑物在地震作用下的破坏程度.结果表明,本方法可以对多层砖房的震害样本进行预测并达到较理想的效果.     

Pyroclastic flows from the 1991 eruption of Unzen volcano,Japan

Pyroclastic flows from Unzen were generated by gravitational collapse of the growing lava dome. As soon as the parental lobe failed at the edge of the dome, spontaneous shattering of lava occurred and induced a gravity flow of blocks and finer debris. The flows had a overhanging, tongue-like head and cone- or rollershaped vortices expanding outward and upward. Most of the flows traveled from 1 to 3 km, but some flows reached more than 4 km, burning houses and killing people in the evacuated zone of Kita-kamikoba on the eastern foot of the volcano. The velocities of the flows ranged from 15 to 25 m/s on the gentle middle flank. Observations of the flows and their deposits suggest that they consisted of a dense basal avalanche and an overlying turbulent ash cloud. The basal avalanche swept down a topographic low and formed to tongue-like lobe having well-defined levees; it is presumed to have moved as a non-Newtonian fluid. The measured velocities and runout distances of the flows can be matched to a Bingham model for the basal avalanche by the addition of turbulent resistance. The rheologic model parameters for the 29 May flow are as follows: the density is 1300 kg/m³, the yield strength is 850 Pa, the viscosity is 90 Pa s, and the thickness of the avalanche is 2 m. The ash cloud is interpreted as a turbulent mixing layer above the basal avalanche. The buoyant portions of the cloud produced ash-fall deposits, whereas the dense portions moved as a surge separated from the parental avalanche. The ash-cloud surges formed a wide devastated zone covered by very thin debris. The initial velocities of the 3 June surges, when they detached from avalanches, are determined by the runout distance and the angle of the energy-line slope. A comparison between the estimated velocities of the 3 June avalanches and the surges indicates that the surges that extended steep slopes along the avalanche path, detached directly from the turbulent heads of the avalanches. The over-running surge that reached Kita-Kamikoba had an estimated velocity higher than that of the avalanche; this farther-travelled surge is presumed to have been generated by collapse of a rising ash-cloud plume.     

Impact of a rock avalanche on a moraine‐dammed proglacial lake: Laguna Safuna Alta,Cordillera Blanca,Peru

Moraines that dam proglacial lakes pose an increasing hazard to communities in the Andes and other mountain ranges. The moraines are prone to failure through collapse, overtopping by lake waters or the effect of displacement waves resulting from ice and rock avalanches. Resulting floods have led to the loss of thousands of lives in the Cordillera Blanca mountains of Peru alone in the last 100 years. On 22 April 2002 a rock avalanche occurred immediately to the south‐west of Laguna Safuna Alta, in the Cordillera Blanca. The geomorphic evidence for the nature, magnitude and consequences of this event was investigated in August 2002. Field mapping indicated that the avalanche deposited 8–20 × 10⁶ m³ of rock into the lake and onto the surface of the frontal region of Glaciar Pucajirca, which flows into the lake. Repeated bathymetric surveying indicated that ～5 × 10⁶ m³ of this material was deposited directly into the lake. The immediate effect of this event was to create a displacement wave that gained in height as it travelled along the lake basin, overtopping the impounding moraine at the lake's northern end. To achieve overtopping, the maximum wave height must have been greater than 100 m. This, and subsequent seiche waves, caused extensive erosion of both the proximal and distal faces of the impounding terminal moraine. Further deep gullying of the distal face of this moraine resulted from the supply of pressurized water to the face via a relief overflow tunnel constructed in 1978. Two‐dimensional, steady‐state analysis of the stability of the post‐avalanche moraine rampart indicates that its proximal face remains susceptible to major large‐scale rotational failure. Copyright © 2005 John Wiley & Sons, Ltd.     

DISCUSSION ON ISSUES ASSOCIATED WITH SETBACK DISTANCE FROM ACTIVE FAULT

Living with disaster is an objective reality that human must face especially in China. A large number of earthquake case studies, such as the 2008 Wenchuan earthquake, 2010 Yushu earthquake, 2014 Ludian earthquake, have demonstrated that earthquake heavy damage and casualties stem from ground-faulting or rupturing along seismogenic active fault, near-fault high ground accelerations and building catastrophic structural failure. Accordingly, avoidance of active faults may be an important measure to effectively reduce earthquake hazard, which may encounter in the future, but how to avoid an active fault and how much a setback distance from the active fault is required to ensure that the ground faulting and rupturing has no any direct impact on buildings. This has been the focus of debate both for domestic and foreign scholars. This paper, first of all, introduces the definition of active fault. Then, quantitative analyses are done of the high localization of earthquake surface ruptures and relationship between the localized feature of the coseismic surface ruptures and building damages associated with the measured widths of the historical earthquake surface rupture zones, and an average sstatistic width is obtained to be 30m both for the earthquake surface rupture zones and heavy damage zones along the seismogenic fault. Besides, the widths of the surface rupture zones and spatial distribution of the building damages of the 1999 Chi-Chi earthquake and 2008 Wenchuan earthquake have also been analyzed to reveal a hanging-wall effect:Width of surface rupture zone or building damage zone on the hanging-wall is 2 or 3 times wider than that on its foot-wall for a dip-slip fault. Based on these latest knowledge learnt above, issues on avoidance object, minimum setback distance, location requirement of active fault for avoidance, and anti-faulting design for buildings in the surface rupture zone are further discussed. Finally, we call for national and local legislatures to accelerate the legislation for active fault survey and avoidance to normalize fault hazard zoning for general land-use planning and building construction. This preventive measure is significantly important to improve our capability of earthquake disaster reduction.     

Unraveling driving factors for large rock–ice avalanche mobility

Large rock–ice avalanches have attracted attention from scientists for decades and some of these events have caused high numbers of fatalities. A relation between rock slope instabilities in cold high mountain areas and climate change is currently becoming more evident and questions about possible consequences and hazard scenarios in densely populated high mountain regions leading beyond historical precedence are rising. To improve hazard assessment of potential rock–ice avalanches, their mobility is a critical factor. This contribution is an attempt to unravel driving factors for the mobility of large rock–ice avalanches by synthesizing results from physical laboratory experiments and empirical data from 64 rock–ice avalanches with volumes >1x10⁶ m³ from glacierized high mountain regions around the world. The influence of avalanche volume, water and ice content, low‐friction surfaces, and topography on the apparent coefficient of friction (as a measure of mobility) is assessed. In laboratory experiments granular ice in the moving mass was found to reduce bulk friction up to 20% while water led to a reduction around 50% for completely saturated material compared with dry flows. Evidence for the effects of water as a key driving factor to enhance mobility was also found in the empirical data, while the influence of the ice content could not be confirmed to be of much relevance in nature. Besides liquefaction, it was confirmed that mobility increases with volumes and that frictional surface characteristics such as flow paths over glaciers are also dominant variables determining mass movement mobility. Effects of the topography along the flow path as well as channeling are assumed to be other critical factors. The results provide an empirical basis to roughly account for different path and flow characteristics of large rock–ice avalanches and to find appropriate ranges for friction parameters for scenario modeling and hazard assessments. Copyright © 2011 John Wiley & Sons, Ltd.     

Cretaceous length of day perturbation by mantle avalanche

These last 10 years, numerical models of mantle convection have emphasized the role of the 670 km endothermic phase change in generating avalanches that trigger catastrophic mass transfers between upper and lower mantle. On the other hand, scientists have emphasized the concomitance of large-scale worldwide geophysical and tectonic events, which could find their deep thermal roots in the huge mass transfers induced by the avalanches. In particular, the paleontological records show two periods of length of day (l.o.d.) shortening between 420 and 360, and 200 and 80 Myr BP. This last event is synchronous with a strong true polar wander and a global warming of the upper mantle. In order to study the potential effects of the avalanche on the main component of the Earth’s rotation, the Liouville equation has been solved and the l.o.d. evolution has been calculated from the perturbations of the inertia tensor. The results show that the inertia tensor of the Earth’s is mainly sensitive to the global transfers through the 670 km discontinuity. The l.o.d. perturbations will be synchronous with the global thermal effects of the avalanche. These theoretical results allow proposing a self-consistent physical mechanism to explain periods of the Earth’s rotation acceleration. Within this context, the l.o.d. shortening during the Cenozoic and Cretaceous brings one more clue to the possible participation of a mantle avalanche in generating the concomitant large scale events which have occurred during this very particular period of the Earth’s history.     

Surface exposure dating of the Veliki vrh rock avalanche in Slovenia associated with the 1348 earthquake

Over 30 samples from bedrock and boulders from the Veliki vrh rock avalanche have been collected for surface exposure dating. The limestone rocks have been radiochemically treated to isolate and determine long-lived ³⁶Cl by accelerator mass spectrometry. It could be shown that the Veliki vrh rock avalanche from the Košuta Mountain (Slovenia) event can be very likely linked to one of the major historical earthquakes in Europe happening on the 25^th of January 1348. Taken into account independently determined denudation rates, inherited ³⁶Cl originating from pre-exposure at shallow depths (20–55 m) could be calculated. The high amount of inherited ³⁶Cl, i.e. 17–46% of the total ³⁶Cl, makes this site not suitable for a precise determination of the ³⁶Cl production rate as it was originally anticipated. Veliki vrh is a “classic” rock avalanche of high velocity. The slope failed in the upper part with a translational slide predominantly along the bedding planes, whereas dynamic fragmentation is the cause for further crushing of the material and the long runout.