I seem to be unclear as to what you are asking for. It seems you are looking for the ability to characterize a time interval. Can you be more clear?

These fires are the result of self-heating to thermal runaway. The most significant variables are the size of the pile and the exposure temperature. They are coupled in this case, so there is no single temperature or pile sizes. Only a critical pile size for a specified exposure temperature and a critical temperature for a specified pile size.

There is a theoretical and quantitative means to estimate the time to thermal runaway if the FK parameters are known. There is some data on this in P C Bowes. So for a given pile size and temperature, one can estimate the time to thermal runaway, at least in the context of an order of magnitude (minutes, hours, days, weeks, months). This reference was published in your "neck of the woods" by BRE and the Crown. See the SFPE Handbook of Fire Protection Engineering for the theory of the FK methodology. The problem is that the estimated time to thermal runaway can only be assessed at the point when the FK parameters predict first thermal runaway and not if theses parameters significantly exceed this critical point. Thus, useful in some cases, but not for all values of the pile size and temperatures.

See:

Bowes, P. C., "Self-heating: Evaluating and Controlling the Hazards," Building Research Establishment, Her Majesty's Stationary Office, London, 1984.

Babrauskas, V., Ignition Handbook, pp. 845 to 847 ...

Douglas J. Carpenter, MScFPE, CFEI, PE, FSFPE
Vice President & Principal Engineer
Combustion Science & Engineering, Inc.
8940 Old Annapolis Road, Suite L
Columbia, MD 21045
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