People confuse the two because they work on the same engineering principles. The stability of the structures both depend heavily on the thickness of the barrel and the depth of the fill above it. But their physical/geographical characteristics and purpose cannot be more different from each other.
An arch bridge typically is a small width structure which usually does not cut through hills/under a town like a tunnel would do. There is also significant difference in their lengths and depth of fill above structure. A tunnel is longer in width and usually carries more fill above it, although I have seen arches that carry some significant dead load on top. An arch is built to accomodate traffic/pedestrian load to span over rivers/roads/etc. A tunnel is usually built to accomodate a railway line/traffic/pedestrian through a hill or under a town, generally because the direction of path is being obstructed by an obstacle or because it is not feasible to have the path at ground level.
So to answer your question, I really don't think an arch can actually become a tunnel at any point. The characteristics of both structures are too varied for them to become anything similar.
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An arch works by transfering the load on the central portion of the arch outward and downward into the columns which support it.
An arch or lintel supported by corbels, or protrusions from a wall.
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The Jefferson National Expansion Memorial, The Gateway Arch, is located in St. Louis, Missouri.
Arch loop whirl tented arch ridge composite