Snow Mechanics: Avalanche Release and Crack Propagation

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Description

This lecture covers the mechanics behind snow slab avalanche release, including stress, strain, elasticity, and failure initiation. It delves into stability indices, weak layer strength, stability tests, crack propagation mechanisms, and the UCLA/Disney Snow model. The presentation also explores the Propagation Saw Test (PST) for evaluating slope stability, propagation speed, and release size. Various simulation models are discussed, from purely elastic slabs to elastic-brittle slabs accounting for tensile failure. The lecture concludes with a detailed examination of stress redistribution, equilibrium equations, and practical examples like safety distances between skiers and remote triggering.

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https://mediaspace.epfl.ch/media/0_0q4hkbgm

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Price elasticity of demand

A good's price elasticity of demand (, PED) is a measure of how sensitive the quantity demanded is to its price. When the price rises, quantity demanded falls for almost any good, but it falls more for some than for others. The price elasticity gives the percentage change in quantity demanded when there is a one percent increase in price, holding everything else constant. If the elasticity is −2, that means a one percent price rise leads to a two percent decline in quantity demanded.

Elasticity (economics)

In economics, elasticity measures the responsiveness of one economic variable to a change in another. If the price elasticity of the demand of something is -2, a 10% increase in price causes the quantity demanded to fall by 20%. Elasticity in economics provides an understanding of changes in the behavior of the buyers and sellers with price changes. There are two types of elasticity for demand and supply, one is inelastic demand and supply and other one is elastic demand and supply.

Cross elasticity of demand

In economics, the cross (or cross-price) elasticity of demand measures the effect of changes in the price of one good on the quantity demanded of another good. This reflects the fact that the quantity demanded of good is dependent on not only its own price (price elasticity of demand) but also the price of other "related" good. The cross elasticity of demand is calculated as the ratio between the percentage change of the quantity demanded for a good and the percentage change in the price of another good, ceteris paribus:The sign of the cross elasticity indicates the relationship between two goods.

Crack growth equation

A crack growth equation is used for calculating the size of a fatigue crack growing from cyclic loads. The growth of fatigue cracks can result in catastrophic failure, particularly in the case of aircraft. A crack growth equation can be used to ensure safety, both in the design phase and during operation, by predicting the size of cracks. In critical structure, loads can be recorded and used to predict the size of cracks to ensure maintenance or retirement occurs prior to any of the cracks failing.

Elasticity of a function

In mathematics, the elasticity or point elasticity of a positive differentiable function f of a positive variable (positive input, positive output) at point a is defined as or equivalently It is thus the ratio of the relative (percentage) change in the function's output with respect to the relative change in its input , for infinitesimal changes from a point . Equivalently, it is the ratio of the infinitesimal change of the logarithm of a function with respect to the infinitesimal change of the logarithm of the argument.