The parameters used to get dc-exponent values are: drilling rate, rotary speed, bit weight, bit diameter and mud weight; versus well depth.
As a drill bit bores a hole into the earth, it will gradually experience denser formations and therefore slower rates of penetration. (Though there are exceptions such as sands that normally drill faster, or faulted and uplifted formations). The general trend is normally a gradually slowing rate of penetration.
Sands often have above them, an impermeable layer of formation, normally shale, that may be hundreds of feet deep. When gas or fluids migrate up through the sand and reach this impermeable layer and has nowhere else to go, pressure begins to build up in the sand and pushes up against the impermeable layer of shale. Over time the pressure can becomes so great that it begins to fracture the shale, making it weaker and easier to penetrate by a drill bit. When a hole is drilled down towards this sand, it will gradually begin to experience faster rates of penetration as it drills through this shale gets closer to the high-pressure sand. It is this trend that the dc-exponent exposes. An examination of this fractured shale that is being drilled will reveal increasingly larger concave pieces and is where the term pressure shale comes from.