Why do old chimneys curl?

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A slow consistent curl in a chimney is a common observation in an old chimney constructed with lime mortar.

This phenomenon appears to be the result of two actions.
Over time, the mortar joints on one side of the chimney are absorbing and retaining water which freezes and expands the mortar breaking the composition of the mortar and the bond of the mortar to the brick. On the opposite side of the chimney, the mortar may be actually washing out of the joints. The chimney is getting taller on one side and possibly shorter on the other side. Hence, the curl.

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And…when they do start to curl, just throw in a 2x8 plank to assist in holding it up…

Because they cap them with mortar instead of seamless metal caps!

There has been an addition to the explanation as to why they curl based upon a 60 minute discussion with a mortar teck at a plant who is a lime mortar buff. See above.

You also have carbonic acid doing its thing.