本研究探討掃描線法(scanline method)使用於岩塊體積比(volume block proportion, VBP)量測之不確定性。使用掃描線法量測物體時，不同的掃描線長度，影響量測岩塊體積比的不確定性(uncertainty)。郭明傳(2005)使用四種不同外框形狀與橢圓或圓顆粒的表徵單元(representative volume element, RVE)隨機串接成不同長度的掃描線，經由簡單隨機抽樣的數值模擬得到不同掃描線長度對量測的不確定性。本研究由統計推導方式，利用樣本點法和中央極限定理，計算量測長度對不確定性的解析解，進一步解釋郭明傳(2005)數值模擬所得的結果。結果顯示解析解與郭明傳(2005)數值模擬兩者相符合。現地量測資料，可使用本研究解析解，計算掃描線法量測岩塊體積比之不確定性。

This research discusses “scanline method” which is used in volume block proportion (VBP) for uncertainty. The major factor which affects the uncertainty of VBP is different scanline lengths. Kuo(2005) uses four kinds of representative volume element (RVE) with different outer edge shape and ellipse or the circular blocks connects the different length of the scanline by simple random sample to simulate VBP uncertainty. This research use the statistical sample point, the central limit theorem, and the length of computation for the uncertainty analytic solution, to explain the Kuo(2005) result of simulation. This research showed the analytic solution match the numerical simulation of Kuo(2005). For the in-situ data, we suggest that use analytic solution of this research to calculate the scanline method for measuring VBP uncertainty.

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