Yes, and on most walls it is required rather than optional. Water trapped behind a retaining wall adds hydrostatic pressure the wall was not designed to carry, and that pressure is the most common cause of a wall leaning, bulging or coming apart. The drain goes in as the wall is built, not afterwards.
What the soil behind a wall here weighs when wet
The slowest mapped soil under Layton still moves water down at 0.4 inches an hour, on ground the survey puts in hydrologic group C. That is quick enough that a well-built stone column behind a wall will actually empty, which is the condition under which the standard detail works as designed. It is also quick enough to be complacent about, and the detail is cheap while the wall is being built and expensive afterwards.
The reasoning behind that
A retaining wall holds back soil. Saturated soil weighs far more than dry soil and pushes far harder, so a wall that drains freely is carrying a fraction of the load a wall that does not.
The drain sits at the base of the wall, behind it, bedded in clean stone that extends up behind the face. Fabric separates the stone from the retained soil so the voids stay open. The pipe falls to an outlet through or past the end of the wall.
Weep holes alone are not a drainage system. They let out water that has already reached the face, which means the pressure has already been applied.
Retrofitting is possible and it means excavating the retained side, which is most of the cost of building the wall again. That asymmetry is why this is a decision made once.
More on this: Commercial Drainage and Site Excavation in Layton, UT.
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