From the text on the placard:
During the winter rains, sligthly acidified water soaks deep into the porous sandstone and dissolves some of the calcite cement as it seeps through the rock.
During the dry summer season, water is drawn to the surface by evaporation. As water evaporates it re-deposits the calcite in the outer foot or so of the rock. Over time the outer surface of the rock becomes strengthened to form a resilient duricrust, while the interior is progressively weakened.
Once the duricrust is broken, such as when a large section breaks away, the weakened interior is exposed to the various forces of erosion and is easily eaten away.
As this process of cavernous weathering continues, the cavities of tafoni grow larger.
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