A tread bump like that we usually want to offset so it makes grooves, cutting into the tire. Instead of expanding the treads, you want to shrink everything that is not-tread.

Hook the displacement map up to a Color_math node. Set Value_1 = white and connect to the map. Click on Value_2's color and sample the brightest spot on the tread map. Hook the Color_Math node to the displacement channel.

This will cause the bright spot to be neutral - no change - and everything darker will be a depression. Thus - the radius of the tire will not be altered.

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