n.
  - a long, narrow ditch. 
▸a ditch of this type dug by troops to provide shelter from enemy fire.
 - 
(also ocean trench)
 a long, narrow, deep depression in the ocean bed, typically running parallel to a plate boundary and marking a subduction zone.
 
v.
  - dig a trench or trenches in.
 - 
(trench on/upon)
 archaic border closely on; encroach upon.
 
 
  Etymology
  ME (in the senses ‘track cut through a wood’ and ‘sever by cutting’): from OFr. trenche (n.), trenchier (v.), based on L. truncare (see truncate).