The thermite reaction yields molten iron (yes, I am a youth brought up on the anarchists cookbook), as this melts through the bottom of the bucket it will come into contact with the ice below, The extreme temperature of the liquid iron coming into contact with the low temperature of the ice will cause it to melt and turn to steam almost instantly, this sudden increase in pressure will not be able to escape through the molten iron, falling onto it, so it must build in pressure until the ice breaks up, the forces involved will most likely be more than adequate to blow the ice to pieces.

The reation sems to be similar to that of water onto a chip-pan fire, the temperatures involved are so high that the water turns to steam instantly, causing a large escape of the hot gasses.

Might want to have a look at the steam cannon episode to explore this principle further.

From what I understand, ice turns from a solid to liquid at 0 degrees celsius, then from liquid to gas at 100, as a result of the molecules not being stable enough to contain the levels of energy being exerted on them, thus they must change their state of matter. On top of this, thermite burns at approximately 2500 degrees celsius, this huge temperature is clearly enough to sublime ice from a solid into a gas as water. I would then further suggest that water vapour (water's gaseous form) cannot cope with the levels of energy that would have been exerted on it causing one of two possibilities: a) the atomic bonds are broken, which would cause a reaction itself, while simultaneous the hydrogen molecules (freshly split from the water) would explode, or b) the temperature causes the ice to sublime straight to the fourth state of matter, a plasma, for a very immediate space of time causing the explosion. These are the only two explanations i can see for the reaction, unless the molten iron from the bucket has an effect on the experiment (which i find unlikely), though i haven't studied science since GCSE so i can't decide which idea i find more sensible...

If you heat a sealed glass tube of water the increase in pressure will eventually burst the tube and a loud bang will result due to the almost instantaneous creation and expansion of water vapour from the super heated water. The same effect can occur when volcanos errupt underwater. In the thermite/ice experiment the high temperatures generated by thermite vapourise some of the ice causing the explosion, the smoke and flames coming from the remains of the thermite.

It seems likely that the extremely high temperature caused by the reaction will cause the ice to sublime to a gas and expand rapidly and adding to the reaction and causing the explosion.  During an induction at an aluminium smelter I had to watch a video of the aftermath of water coming into contact with molten aluminium at a smelting plant which caused a large explosion which destroyed the building it happened in.

It was explained to me that there were two stages, the first when the aluminium comes into contact with the water causing the water to turn to steam causing an initial explosion.  Then the heat of the reaction causes the water to split into hydrogen and oxygen, this then reacts resulting in a second explosion.

I would be interesting to repeat the experiment with a container of water buried in the powder to see if a similar result occurs.

Agree totally that the high temp causes the ice to sublime into steam, massively increasing in volume, and causing the water to split into hydrogen and oxygen gas, with further volume increases and a resulting recombination explosion.  In the iron and steel industry this "very dangerous" effect is well known and precautions are taken to avoid direct contact between molten iron/steel and water.  When the bottom of a cupola or blast furnace is opened at the end of a shift and the molten contents pour out, large explosions can ensue and send chunks of ironwork many metres into the air.  An ex-colleague of mine witnessed a massive explosion when molten steel was poured into an empty "torpedo" (railway car for carrying molten metal around a steelworks) that had rainwater pooling in the bottom.