Removing bridges and dams from DEM

I am also struggling with that. At present time, the best solution I have found is the following:

1. remove the bridges by doing so: (i) create a polygon for each bridge (or for all of them), (ii) rasterize those polygons, and (iii) use the raster(s) to eliminate bridges from the original DEM
2. interpolate the gaps with focal statistics.

However, I encounter many trobules when dealing with point nr.2. Close to the banks the interpolation is very poor, even though I am using an irregular kernel filter for the focal statystics analysis.

UPDATED ANSWER

I found a solution which works pretty well:

1. clip raster by extent with a polygon that contains the part you wish to modify
2. create breaklines/points which will have an elevation (you need to add the Z field when you create the layer)
3. assign elevations to breaklines/points: with the vertex editor right click on the feature, on the bottom right a panel with vertices/points coordinates will appear. There you can assign the elevation to the vertices/points.
4. create a mask for the part of DEM you wish to modify: (i) polyognize (create a polygon inside the points/breaklines if they do not correspond to the clip-polygon); (ii) generate a raster from the polygon (v.to.rast with 1 inside and NULL outside. Settings: GRASS Region extent = Use layer extent and Source of raster values = Val; Value=1); (iii) use r.null to replace NULL values with zeroes (settings: The value to replace the null value by = 0).
5. use TIN Interpolation to generate a raster from the points/breaklines: under Interpolation Attribute select Use Z as interpolation attribute (settings: GRASS Region extent = Use layer extent and choose a resolution that is smaller than the one of the original dtm);
6. clip the dtm on the mask created at 4.(iii) with raster calculator using the formula mask_0*DTM_interp;
7. combine the original DTM with the interpolated one with the following expression in raster calculator: "DTM_clipped_at_1" * ("mask_created_at_6"=0)+"DTM_interpolated_at_5"

By following these points you will interpolate a part of the raster and insert it in the old raster.