Hi Fred,
Depending on the type of wood, wood used in cord-wood projects will shrink, split and crack this isn't because of lime in cement though.
Most concrete and cement these days do not contain lime. When it contains lime its called Limecrete and generally it is used as a type of mortar for older buildings.
That being said, wood posts in the ground with cement can retain more moisture than those with rock for infill, and moisture is what rots the wood. Most recommend using toxic substances to preserve the wood you put into the ground, but I wouldn't do that with a building.
I had one post on the property I just bought 'rot' out - it was one of the very few in cement, but it was also under a fir tree completely shaded. So it's exposure to wet was great and the cement just held that moisture in. I just read where a natural builder recommends calking where the wood and cement meet when posts are vertical, and repeat yearly as needed. This prevents the rot you are speaking of.
Your cord-wood building
should not suffer as your
fence posts do, especially with a good roof overhang, air movement (keep brush back) and sun exposure.
All the best ~