Earth-surface mass flows such as debris flows, rock avalanches, and dam-break floods can grow greatly in size and destructive potential by entraining bed material they encounter. Increasing use of depth-integrated mass and momentum conservation equations to model these erosive flows motivates a review of the underlying theory. Our review indicates that many existing models apply depth-integrated conservation principles incorrectly, leading to spurious inferences about the role of mass and momentum exchanges at flow-bed boundaries. Model discrepancies can be rectified by analyzing conservation of mass and momentum in a two-layer system consisting of amoving upper layer and static lower layer. Our analysis shows that erosion or deposition rates at the interface between layers must, in general, satisfy three jump conditions. These conditions impose constraints on valid erosion formulas, and they help determine the correct forms of depth-integrated conservation equations. Two of the three jump conditions are closely analogous to Rankine-Hugoniot conditions that describe the behavior of shocks in compressible gasses, and the third jump condition describes shear traction discontinuities that necessarily exist across eroding boundaries. Grain-fluid mixtures commonly behave as compressible materials as they undergo entrainment, because changes in bulk density occur as the mixtures mobilize and merge with an overriding flow. If no bulk density change occurs, then only the shear traction jump condition applies. Even for this special case, however, accurate formulation of depth-integrated momentum equations requires a clear distinction between boundary shear tractions that exist in the presence or absence of bed erosion.

Entrainment of bed material by Earth‐surface mass flows: Review and reformulation of depth‐integrated theory

https://cyberleninka.org/article/n/141011.pdf

A review of source term estimation methods for atmospheric dispersion events using static or mobile sensors

Assessing the Reliability of Complex Models: Mathematical and Statistical Foundations of Verification, Validation, and Uncertainty Quantification

Plate motion and associated tectonics explain the location of magmatic systems along plate boundaries [1], however, they cannot give satisfactory explanations of the origin of intra‐ plate volcanism. Intraplate magmatism such as that which created the Hawaiian Islands (Figure 1, hereafter for the location of geographical places the reader is referred to Figure 1) far from plate boundaries is conventionally explained as a result of a large, deep-sourced, mantle-plume [2-4]. Less volumetric magmatic-systems also occur far from plate margins in typical intraplate settings with no evidence of a mantle-plume [5-7]. Intraplate volcanic sys‐ tems are characterized by small-volume volcanoes with dispersed magmatic plumbing sys‐ tems that erupt predominantly basaltic magmas [8-10] derived usually from the mantle with just sufficient residence time in the crust to allow minor fractional crystallization or wallrock assimilation to occur [e.g. 11]. However, there are some examples for monogenetic eruptions that have been fed by crustal contaminated or stalled magma from possible shal‐ lower depths [12-19]. The volumetric dimensions of such magmatic systems are often com‐ parable with other, potentially smaller, focused magmatic systems feeding polygenetic volcanoes [20-21]. These volcanic fields occur in every known tectonic setting [1, 10, 22-28] and also on other planetary bodies such as Mars [29-33]. Due to the abundance of monogen‐ etic volcanic fields in every tectonic environment, this form of volcanism represents a local‐ ized, unpredictable volcanic hazard to the increasing human populations of cities located close to these volcanic fields such as Auckland in New Zealand [34-35] or Mexico City in Mexico [36-37].

/pdf/monogenetic-basaltic-volcanoes-genetic-classification-growth-1f6tqqobvb.pdf

Monogenetic Basaltic Volcanoes: Genetic Classification, Growth, Geomorphology and Degradation

Flow-like landslides, such as debris flows and rock avalanches, travel at extremely rapid velocities and can impact large areas far from their source. When hazards like these are identified, runout analyses are often needed to delineate potential inundation areas, estimate risks, and design mitigation structures. A variety of tools and methods have been developed for these purposes, ranging from simple empirical–statistical correlations to advanced three-dimensional computer models. This paper provides an overview of the tools and methods that are currently available and discusses some of the main challenges that are currently being addressed by researchers, including the need for better guidance in the selection of model input parameter values, the challenge of translating model results into vulnerability estimates, the problem with too much initial spreading in the simulation of certain types of landslides, the challenge of accounting for sudden channel obstructions in the simulation of debris flows, an...

2014 Canadian Geotechnical Colloquium: Landslide runout analysis — current practice and challenges

[2] Determining the risk associated with hazards involves many factors; examining strategies for mitigation is, likewise, a complicated problem. It is increasingly common to turn to models and computer simulation to assist in the risk assessment and mitigation process. In studying hazardous natural flows with models and simulations, we seek answers to questions such as ‘‘Is a particular village likely to be affected by flows in a given time frame? Should we construct a road along this valley or along a different one?’’ The answer to such a question in full generality requires an accounting of the uncertainties in the frequency and magnitude of likely flow events. Then, given the occurrence of a flow of some specified size, we also require measurable confidence in the prediction of the flow physics by a computational model. However, for most models such predictions of flow physics are difficult to obtain in absolute terms due to the uncertainties associated with assumed values of model inputs, parameters, and, oftentimes, with the model itself (details of the parametric and model

Input Uncertainty Propagation Methods and Hazard Mapping of Geophysical Mass Flows

When characterizing geologic natural hazards, specifically granular flows including pyroclastic flows, debris avalanches and debris flows, perhaps the most important factor to consider is the area of inundation. One of the key parameters demarcating the leading edge of inundation is the run-out distance. To define the run-out distance, it is necessary to know when the flow stops. Numerical experiments are presented for determining a stopping criterion and exploring the suitability of the Savage-Hutter theory for computing inundation areas of granular flows. The stopping criterion is a function of dimensionless average velocity, pile aspect ratio and internal and bed friction angle and can be implemented on either a global (entire flow) or local (small areas of the flow) level. Slumping piles on a horizontal surface, and geophysical flows over complex topography were simulated. Mountainous areas, such as Colima volcano, Mexico; Casita, Nicaragua; Little Tahoma Peak, USA, and the San Bernardino Mountains, USA, were used as test regions. These areas have combinations of steep, open slopes and sinuous channels. Because of differences in topography and physical scaling, slumping piles in the laboratory and geophysical flows in natural terrain must be scaled differently to determine a reasonable dimensionless relationship for the stopping criterion.

Numerical issues in computing inundation areas over natural terrains using Savage-Hutter theory

Probabilistic digital hazard maps for avalanches and massive pyroclastic flows using TITAN2D

Incorporation of Variable Bed Friction into Titan2D Mass-Flow Model : Application to Little Tahoma Peak Avalanches (Washington)

In this paper we introduce a careful procedure for analyzing the impact of error and uncertainty in model inputs in volcanic mass flow hazard analysis. In particular we focus on uncertainty in elevation maps that are crucial to flow simulations. Our early results establish the soundness of the approach and the usefulness of the methodology for constructing probabilistic hazard maps.

/pdf/dem-uncertainty-and-hazard-analysis-using-a-geophysical-flow-xb72zzg8p1.pdf

DEM uncertainty and hazard analysis using a geophysical flow model

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