Civil 3D Stresses and Successes: The True Slope is Greater than the Grading Object Slope

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The True Slope is Greater than the Grading Object Slope. It is a Puzzlement.

I cannot solve the puzzle for you, but I can show you how to compute an adjustment. 

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Cross Slope on Steep Grades

The actual cross slopes on steeply sloped roadways are steeper than the designed cross slope.

This is also true for site grading. The situation exists for feature line grading, grading objects, and corridors.
Grading Optimization (GO) may or may not be immune.

This is a previously discussed topic in the Civil 3D forum.
Disclaimer: Most of this information is from a reply I made to a recent Civil 3D forum post.

The deviation between the perpendicular cross slope and the actual slope is often ignored.
It is negligible for road/baseline slopes under 5%.

I do not recall there being a consensus regarding when and where this issue should be addressed.

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An Adjustment to Maintain Maximum Slope

The calculations are reasonably simple if you, your boss, or your reviewer wish to adjust the design cross slope to control the true cross slope.

The following illustrations use a surface created by a grading object.
One-point slope labels show the actual slope; 2-point slope labels show the design cross slope.

A reasonably simple slope geometry review shows the following:

For a given Road Slope (RdSl), Cross slope (XSl), Maximum slope (Slope):

The maximum slope (Slope) = (RdSl² + XSl²)^1/2.

Given RdSl = 20% (0.20) and XSl = 4:1 (0.25): Slope = 32% (0.320 or 3.12:1) 

The adjusted Cross Slope (XSl) = (Slope² - RdSl²)^1/2.

Given RdSl = 20% (0.20) and Slope = 4:1 (0.25): XS = 15% (0.1499 or 6.67:1) 

Note: The equations fail for road slopes greater than the maximum desired slope.
Upon observation, it becomes apparent that the least slope solution is XSl = 0 (Horizontal), resulting in Slope = RdSL.

More information than you could possibly care about is illustrated below and in the attached PDF file.

If you'd like to research for yourself, I've attached a drawing file for you to take a look at. 

Any feedback will be appreciated.

Good Luck!

Sloped Grading Cross Slope.dwg