Dig the soft wood fibers out of the decaying log using a chisel. Remove all decaying wood and leave only solid, dry wood.
Drill 1/4-inch-deep, evenly spaced holes into the dry wood using a portable drill. Space the holes one inch apart, sloping them downward at a slight angle to create pockets.
Fill a plastic squeeze bottle with 4 ounces of epoxy consolidant. Squeeze the consolidant into the pockets in the logs, fully saturating the wood. Wear chemical-resistant gloves when working with the consolidant.
Saturate the solid wood surrounding the holes with consolidant using a disposable paintbrush. Let the consolidant dry for an hour.
Scoop out equal amounts of the components in a two-part epoxy wood filler onto a plywood mixing board using a putty knife.
Mix the two epoxy components with the putty knife. Continue wearing the chemical-resistant gloves when using epoxy.
Pack the epoxy filler into the gouged out portions of the logs using the putty knife. Completely fill the voids in the logs with the epoxy. You have approximately 30 minutes to use the epoxy filler before it starts to cure.
Shape the moist epoxy filler with the putty knife so that filler follows the contour of the log. Leave about 1/4-inch of excess filler to allow for sanding. Let the filler cure for 24 hours.
Rub 80-grit sandpaper over the cured epoxy filler using smooth strokes. Sand all excess filler to make the patch level with the log. Wear a dust mask and safety glasses when sanding.
Sand the filler with 120-grit sandpaper to provide a smooth area for sealing or staining. Wipe the sandpaper dust off the patch using tack cloths.
Coat the patched area with the same sealer or stain used on the surrounding logs. Follow the specific sealer or stain manufacturer's application directions.