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Abstract Based on the views of random point process theory and stereological interpretation，the first criterion is proposed to check that the trace midpoint in sampling window is the scope of structural homogeneity zone，which is simulated by the Poisson disc joint model and trace information revealed by sampling window. To check the validity of the first criterion，two examples are simulated by Monte Carlo method and their results are checked by statistical tests. Based on the characteristics of two dimensional Poisson process，the second criterion for the relationship between measuring scale of grid and Poisson point number covered by square grid is derived，which shows fractal characteristics in a specific scale range. Joint distribution density and joint orientation are both considered in the derivation of the formula. The Lyman formula is tested for accuracy by theoretical equations. The detailed implementation steps of the two criteria mentioned above are suggested. To check the validity of the detailed implementation steps，two examples are simulated by Monte Carlo method and their results are checked by statistical tests. Geological survey data of the experimental adit #3 in Jinping hydropower station are used to verify the existence of relationship between measuring scale of grid and Poisson point number；and it is shown that the two criterion is very convenient for engineering applications.
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Received: 14 February 2011
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2011, Vol. 30 
