"Post and trench" construction such as you described is called "jacal"
     in Spanish, and was typically used for temporary or short-lived
     buildings in Texas in the eighteeth century, and New Mexico in the
     seventeenth and eighteenth centuries, although the area of usage and
     the time period probably goes wider and farther back than that.  Roofs
     were usually thatched.  You might want to check and see if you had a
     local Spanish tradition of this kind of construction.
 
     Jake.