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| PRELIMINARY RESEARCH ON COMPLETE TRACE LENGTH DISTRIBUTION BASED ON AREAL SAMPLES |
| ZHANG Guoqiang1，2，DENG Jianhui1，2，FEI Wenping1，2，ZHANG Ru1，2 |
| (1. State Key Laboratory of Hydraulics and Mountain River Engineering，Sichuan University，Chengdu，Sichuan 610065，China；2. College of Water Resources and Hydropower，Sichuan University，Chengdu，Sichuan 610065，China) |
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Abstract A sampling window method is adopted to estimate the origin moments of trace length for the Poisson disc joint model，and the origin moment equations of trace length are deduced from the complete trace intersected with the circular and rectangular sampling windows. When the rectangular sampling window covers the maximum trace length of the infinite sampling window，the three trace number equations are proposed to estimate the number of the traces. On this basis，the concentric sampling window method is proposed to estimate the appropriate sampling window size which not only covers the maximum trace length of the infinite sampling window，but also contains the appropriate number of complete trace length samples. Based on the mathematical characteristics of the Poisson point process，when the joint diameter distribution is continuous，the approximate form and constraints of polynomial of the trace length distribution are proposed in the infinite sampling window. If the appropriate rectangular sampling window size was verified by concentric sampling window method，an estimation method is proposed to estimate the complete trace length distribution. The maximum trace length of the infinite sampling window is inferred by using the small step searching algorithm. The origin moment equations of trace length are tested for accuracy by theoretical solutions of two cases. To check the validity of concentric sampling window method and complete trace length distribution inference method，an case is simulated by Monte Carlo method，and their results are compared with theoretical solutions.
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Received: 30 April 2010
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2011, Vol. 30 
