Is chalk porous - it's like blotting paper! But it's not difficult to smear a thin layer of plastic clay over it to make it watertight - very labour intensive though, and it would leave an archaeological trace. When the underlying bedrock chalk is saturated - in late winter, say - then a ditch cut into it will appear to hold water. Soon as the water percolates deeper it will dry out - appearing miraculous. We haven't got the means or expertise to investigate this though. The lost arts of agricultural irrigation!