The alpha/beta/gamma ionizing radiation that we're talking about here is not contagious. (Neutron radiation is contagious in some situations, but it's not relevant here.) During normal operation, the green secondary cooling water does not get radioactive. (Except from fugitive emissions such as leaks, spills, maintenance activities, etc.) The high levels of radioactivity that they're measuring now can only be due to fission products (contaminants) that originated in the core or in the spent fuel bays.
There are many ways in which the radioactive contaminants could have reached the sea. They might have been carried by steam that was vented to primary containment, condensed in the torus, and then released to sea (with as much filtration as they can do) per Fermi2's analysis. Or the contaminated torus water might have leaked out through a primary containment breach and bypassed the filters. Or the steam vented straight to atmosphere might have carried particulates and low-volatility liquids with it, and these would have fallen out in the neighboring area. But I suspect that the most likely possibility is simply that water leaked or overflowed out of the spent fuel bays.
But regardless of how the water is getting out, this is the essential reason why blindly dumping sand and concrete would accomplish little: contamination would still leak out into the groundwater. The stress of an unpredictable and poorly controlled event tends to push people to rash physical exertions. That stress mechanism was useful in the wild, but please keep in mind that this is a technological problem that can only be solved by clear level-headed thinking. In the end, the stress and depression may have a greater public health impact than the radiation. (At least no one here has suggested sending in an air strike to bomb the place. I've seen that in the comments section of some news websites.)
