Eddie,

The primary objectives of a core trench are to: (1) Remove grass, tree roots and other debris that could compromise the structure and (2) Create a "keyway" that anchors the dam in place. In other words; The downhill pressure exerted on the structure from water will not tend to slide the structure down hill.

Given your planned structure height is only 4 ft., I would still doze out a 12 ft. wide core (matching dozer) about 2.5 ft. deep. Remember to slope the sides on the core no steeper than 1:1. A vertical cut will NOT allow for proper compaction when you begin to fill the core with proper earth material.

Ed