No direct experience, but many ashes have pozzolanic properties (i.e. when mixed with lime and water, they set like cement). The Romans used volcanic ash extensively as a pozzolanic cement in their structures, many of which still survive, although their volcanic ash won't necessarily have the same composition as your peat ash. But biomass ash will be very similar. There's probably something in one of these articles that will tell all.
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In general, it seems it's not a bad thing to do and may have advantages if you don't add too much.
I visited a medieval house in Cheshire a few years go and found that some upstairs floors seemed to be made of concrete. I read that the material was a mix of ash and cattle dung.
I would suggest that any ash that has been hanging around will have regained the CO2 lost when originally heated so of little use. If bagged once cold and kept in a sealed then there is a fighting chance it might not go off.
Currently the area I want to concrete is under water, so there is little lost if there is a problem.
I have a large amount of sand left from a flooring project, so I thought that if the ash were added it would save a little on cement and a whole lot more on the cost of disposal.
I tried dropping the stuff onto the garden, but it takes years before anything grows on it. I just wish I had enough to redo the roadway to the house, I had it put down about three years ago and there must be something in the limestone chippings that the weeds adore. An earlier ash "dump" from the same period is still free of growth of any description.
Fresh wood ash is pretty caustic; I expect fresh peat ash would be similar. I imagine it would sterilise and destroy any weed seeds or seedlings in the area you spread it, and the area is now taking time to be recolonised. The limestone gravel on its own provides an ideal environment for weed seeds to germinate and grow - moist, good drainage, enough soil to get established and protection at the seedling stage when they're most vulnerable.
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