Cool problem! A little phase transition thermodynamics, though more information will be necessary for a complete answer, e.g. ambient air temperature, container surface temperature, and the temperature range change for each, if applicable. You may have to bust out the old pchem book for this one.
Water will freeze first at the boundary where it's losing energy. Let's look at the scenarios:
1) water freezes from the top first because that's where it's losing energy the fastest.
- the thicker the water layer gets, the greater chance you have of doing damage to the container, because the frozen layer is in place while the liquid water beneath is freezing and expanding. It will expand into the path of least resistance; it's likely that as the ice wall becomes thicker, the path of least resistance will be the material of your container, unless it's a very thick and strong material. What's it made out of? How thick is it?
2) water freezes against the container walls first (if the walls are really cold. Is this outside or in a lab?)
- if each wall surface is the same temperature, then the water will freeze uniformly and expand against the liquid towards the air barrier. In this case, you're safe.
3) water freezes against the container and air boundaries with a liquid core. This result will be similar to case 1.
For the floor of your container, 1m^3 of Vienna standard mean ocean water has a density of 1000kg/m^3, and this will exert a pressure on it of P = F/A = mg/A = (1000 kg)(9.80665 m s^-2)/(1 m^2) = 9806 N m^-2 = 1.422 psi, from the weight alone. Liquids will exert a pressure on the side walls, but if you've got case 2, ice will not once it's solid.
That's the best I can do with the given information; temperature measurements from the walls and air, as well as information about the container will let us answer your question more concisely.