Ib-
If you care to research it, all the engineering standards and specs are available online for your respective city:
City of Wichita - Engineering Standard Specifications
You should find all necessary info under section 300 and 400.
Three other thoughts are:
1. All 'borrow' materials are considered engineered soils, some are designed for structural integrity, some for water flow. Keep that in mind when you're backfilling.
2. If you do have a clay issue you may want to lay down a layer of 5 oz. filter fabric before you backfill with gravel. If you look at clay under a microscope it's essentially the finest silt imaginable, and the dense fabric helps keep infiltration into your drain or structural gravel to a minimum for a longer period of time.
3. I'd use a jumppingjack to compact into that small tight area. You'll be looking for 95 plus % compaction, and foot stomping or using a hand tamper just won't cut it.
So far you've had lots of opinions from all corners of the country (me included) but the link I gave you should help you on the path to how your local engineers have sorted out how to best deal with your local conditions.