Abstract Probability relation between trace length and diameter of rock discontinuities applicable for semi-trace scanline sampling needs to be studied. And five kinds of possibilities are assumed as follows:endpoints of chords are distributed randomly on circumference;midpoints of chords are distributed randomly on a circular diameter;midpoints of chords are distributed randomly in sector;midpoints of chords are distributed randomly both on sectorial arc and diameter;midpoints of chords are distributed randomly on sectorial diameter(generalized model),five models of probability relations between untruncated-uncensored semi-trace length and diameter are acquired. Theory and practice demonstrate that the former four models are not applicable or not quite applicable for semi-trace scanline sampling;while generalized model is quite applicable. The five models supply a gap in previous knowledge of relation between the probability densities of untruncated-uncensored semi-trace length and diameter. When diameters follow uniform distribution pattern,a new diameter algorithm of generalized model is proposed. The new algorithm is applied to Wenchuan earthquake successfully and worth popularizing.
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Received: 20 January 2011
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