What constraints does one wish to apply to the problem? One could hypothesize on a single natural phenomenon (earthquake, or typhoon, or flood), or a combination of phenomena (earthquake + tsunami (flood) + . . . .). The current event was an earthquake for which the magnitude exceeded the design basis assumed in the plant design, AND a tsunami, which exceeded the design basis assumed for the plant design.
Had the plant been able to maintain cooling of Units 1, 2 and 3, and the SFP at Unit 4, we wouldn't be discussing the resulting accident, although we might be discussing a leak if that containment has been damaged, as indicated at Unit 2.
Utilities are required to activate Emergency Operating Procedures (EOPs) to shut a plant down in an emergency. The TEPCO staff probably did that. They had lost off-site power due to the earthquake, but they had the EDGs as backup. The problem started when they lost the EDGs (unplanned, and unanticipated), and then the batteries (batteries are really for instrumentation and control - not cooling systems). So not only did they lose off-site power (anticipated), they lost their only backup (unanticipated).
So, they were dealing with a situation for which there is no game plan, e.g., how to get new generators and fuel supply in place, while the region has been devastated by earthquake and tsunami, while dealing with the fact that three reactors have lost cooling of the cores! Add to that stress the possibility that the primary systems, feedwater systems, and containment may have been damaged, but the extent of damage is unknown.
There is a lot to be said for off-site backup of vital information systems.
Of interest may be -
IDENTIFICATION AND ASSESSMENT OF BWR IN-VESSEL
SEVERE ACCIDENT MITIGATION STRATEGIES
Stephen A. Hodge
J. C. Cleveland
T. S. Kress