My first thought... what is the raster cell size? If the trench is only a couple of meters wide and your cell size is similar, then the chance of estimating the trench width is pretty slim. So how wide are the trenches and how big are your cells, and are they relatively flat bottomed with steep sides? If the trenches are wide and deep with respect to the cell size, you might want to consider identifying areas with rapid changes in slope and/or curvature. If these features (linear in nature) can be identified, you could use Euclidean distance perhaps to estimate trench width from it.
Having said this... an image showing your study area would go a long way
