Mathematical modelling of the flow of snow carried out at the School of Mathematics has been used to design structures that arrest or deflect avalanches.

The research has been used in guidance for engineers and many defence dams and barriers have been built that today protect communities and assets worth hundreds of millions of pounds.

“We undertook fundamental research to analyse the interaction between rapid granular flows and rigid stationary obstacles and the work revealed several new phenomena. It is satisfying knowing that the output from our calculations is being used to protect communities and reduce the risk of damage from avalanches.” - Dr Andrew Hogg

In the 1990s, Iceland was hit by several snow avalanches that caused devastation and fatalities. Several large-volume and rapidly moving flows struck inhabited regions that were thought to be safe from avalanches. At the time, there was relatively little guidance on how to design structures that could have protected these communities and very limited understanding of the fundamental dynamics underlying the interaction between the snow flow and the obstacles.

When the Icelandic Meteorological Office wanted to build structures to protect vulnerable communities from avalanches, it turned to researchers at the University of Bristol for help.

Understanding the flow of snow - and other granular materials

“Our understanding of the flow of granular materials such as sand or snow is still in its infancy because modelling their behaviour is incredibly complex,” said Dr Hogg from the School of Mathematics. “We undertook fundamental research to analyse the interaction between rapid granular flows and rigid stationary obstacles and the work revealed several new phenomena.”

Hogg and his PhD student Kristin Martha Hákonardóttir built models in their lab and designed experiments using granular glass material to mimic snow. They also used a huge snow chute in Switzerland to test some of their theories. These experiments were used to develop mathematical models that could predict accurately the transformation of the flowing state.

They found that granular flow could be airborne on impact and jump over the dams and mounds. They also found that the flow could be transformed abruptly by the deflector (via a ‘granular shock’) into a new flowing state and that the flow could be deflected by three-dimensional objects, losing a proportion of its energy.

In each study, measurements of flow speeds and flow depths at the obstacle provided empirical guidelines for the design of these defence structures.

Informing the design of avalanche defence dams and barriers

This research has now been embodied in a series of guidance documents for engineers on the design of such structures and many defence dams and barriers have been built across Europe since 2008. The guidance is now adopted as standard practice in many of the countries that experience avalanches. Investment in avalanche defence projects based on the design principles set out in the guidance runs into tens of millions of pounds. The Bristol research is also used internationally in the training of engineers who specialise in avalanche protection schemes.

“Since we completed our work, six projects totalling more than €31 million have been completed in Iceland using the research findings,” said Hogg.

“Overall, the Icelandic government is spending €5.1 million per year on avalanche defence and this level of spending will continue until at least 2020.”

Used across Europe

The work is also being used by several other countries affected by avalanches. For example, in Norway, the guidelines have been used in the dimensioning and design of a deflection dam protecting a power station, dams, a hotel, a transformer, hydroelectric power station, and exposed masts of high-voltage power lines through avalanche-prone terrain. The cost of such works is approximately €2-3 million, but the value of the infrastructure they protect is dramatically higher (at least €100 million).

Other projects include mounds and deflecting/catching dams in Chamonix, France, and a deflection and a catching dam in the Tirol, Austria, which provides protection for 34 dwellings.

“It is satisfying knowing that the output from our calculations is being used to protect communities and reduce the risk of damage from avalanches,” said Hogg. “The fact that our work has been used in guidelines and training for engineers who specialise in avalanche protection schemes means the impact will be on-going.”