How would an icicle "grow" upwards?
If there is enough water underground, in a sealed reservoir (like under the concrete in the picture), as that water freezes, it will expand, putting pressure on what ever water is left unfrozen. That water will be squeezed out through what ever cracks it can find - in this case, upwards. Because the water is already near-freezing (perhaps even slightly below, if it's super cooled), it will freeze very quickly when it hits the air (which will be much colder than the ground, late at night). But if there is still water being pushed up from below, that ice will have to move out of the way (it's weaker than concrete). The friction of the flow of cool upwards might warm it just enough to keep it liquid, and the "stalagmite" will end up with a hollow core that the water is being pumped through, and that structure can just keep building on itself, until it is toppled by wind or gravity.

The picture is a bit grainy, but it looks like that's what's happened there. It also looks like the side of the hollow "stalagmite" has fallen off up the top, and released a bit of the remaining water (or maybe it just melted in the sun).

Edit: Hah, I knew I'd seen this somewhere before - in my freezer! This page describes how Ice spikes form - I basically got it right. It seems that they're more likely to form with de-mineralised water, and the temperature has to be within certain narrow limits.