What's the definition and the meaning of “soft dirt runway”? What's the definition and the meaning of "soft dirt runway"? You can read that expression in the following text:


  ..The aircraft's rolling resistance, μ, is determined by the type of
  runway surface and by the type, number, inflation pressure and
  arrangement of the tires. A thin, high-pressure tire operated over a
  soft dirt runway will have so much rolling resistance that the
  aircraft may be unable to move. A large, low pressure tire can
  operate over a softer runway surface but will have more aerodynamic
  drag if not retracted, or will take up more room if retracted. Values
  of μ for different runway surfaces are provided in the detailed
  takeoff analysis in Chapter 17. ...


Source: Daniel P. Raymer, Aircraft design: a conceptual approach. Chapter 5 Thrust-to-weight ratio and wing loading, paragraph 5.3 Wing Loading, sub-paragraph Takeoff Distance, page 88.
The are many types of runway. But the basic are paved, unpaved. Paved runway may be in form of rigid and flexible. Rigid is one which is made of concrete.Flexible runway are made of like bituminous. And the soft runway is one which is not paved. The runway may be on ice sand or water. But generally for a soft runway we can assume it as a grassy runway.    I did not find anything specific about the dirty runway. But in general we can think dirty means the runway conditions which are not so good for the engine when using of reverse thrust , applying brakes or maintaining direction while on take off roll.