Abstract: The conception of “randomness” is so fuzzy that there are three reasonable probability models between the trace length and the diameter of discontinuities under the presupposition that the discontinuities is thin disc and the chord is the trace. The three probability models are based on the three specific but different definitions of “randomicity”: the end points of trace lines distribute evenly on the cycle; the midpoints of trace lines distribute evenly on the diameter; and the midpoints of trace lines distribute evenly within the disc. The following analysis is performed and found that the three models are all correct exactly under their corresponding presuppositions and they fit different conditions. The field condition is between the model 2 and model 3, and so a reasonable study should give consideration to these two models at the same time. A good research should firstly study the distribution of the occurrences of those outcrops, and then give the model 2 and model 3 certain weights according to the relationship of the outcrops in order to get a more reliable probability model between the trace length and the diameter of discontinuities. The results make up the defect of present theories in which only the model 2 is considered.

Key words: discontinuities, randomicity, fuzziness, probability models, suited conditions, weights