The How-to-build guide on fencing compiled by BRANZ (based on using H3.2 treated radiata) recommends a minimum ground clearance of 50 mm.
With untreated wood the concern is that rain splash will put dirt onto the bottom of the paling, causing it to accumulate on the horizontal bottom edge. This then pushes the decay hazard above the H3.2 level. If there is fresh earth next to the palings then the dirt can be splashed higher than 50mm. If there is grass or paving then there might be no dirt splashed up at all.
Depending upon the application, therefore, it might be advisable to have a greater ground clearance than the 50mm recommended for H3.2 treated radiata.
Fencing is not a structural situation so compliance with the Building Code is generally not required if the completed structure is under 1.8mtrs high. It will also depend on what sort of a fence you are building, so check with your local council before you undertake any construction just to be sure.
See Macrocarpa on the species sectoin
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