I may be wrong, but if those trenches are on the same side of the river as Arkansas Post then they most likely were dug by Garland's Brigade intended as a blocking position to the Union advance that landed some two miles down river from the Fort, but were outflanked by primarily the gunboats on the river and also the Union Infantry and therefore abandoned. One of the myths of the Battle of Arkansas Post was that it was a surprise to the Confederates, as many would have one to believe. There is plenty evidence that Holmes was prepositioning what troops he had to counter any such attempt. Such as Walkers Division being moved from Austin, Arkansas to Pine Bluff less than two weeks before the Battle.