面積比法量測異質性介質體積比之不確定性

異質性介質為非單一同材料所組成，在大地材料中我們可將併構岩視為異質性介質，其力學性質與體積比(volumetric fraction,Vf)兩者呈現正相關或負相關的成長，因此，本文探討重點為量測體積比時的不確定性。透過立體量測學(stereology)的概念，以二維量測(2-D probes)來求取面積比，進而推估其三維形貌(3-D feature)下的體積比。本文針對三維形貌下以二維量測體積比之不確定性提出數值解與解析解。在解析解方面，利用球－立方體之表徵單元(representative volume element, RVE)作為數學模型，以應用統計學之方法，推導出在不同量測面積與體積比下，二維量測時所產生的不確定性，也提出如何處理多重粒徑的問題。在數值解方面，利用MATLAB撰寫三維空間中球顆粒隨機分佈的程式，以作為數值解分析所用模型，探討當隨機選取二維量測面下，各量測面上體積比的不確定性。兩者結果均顯示，當體積比越高時，以二維量測體積比的不確定性越低。最後，以磨石子地磚的案例，利用隨機抽樣方法對解析解、數值解比較。

關鍵字

表徵單元；面積比法；體積比；異質性介質

並列摘要

This research presented analytical solution and numerical simulation to quantify the uncertainty of volumetric fraction (Vf) estimates in a heterogeneous material using 2-D probes. The analytical solution was derived based upon the concept of representative volume element (RVE).The numerical simulation was used random model to determine the uncertainty of volumetric fraction. The results show that the uncertainties of the estimates depend upon the size of blocks, measurement area, and volumetric fraction. Finally, using case of terrazzo tiles application examples to compare the analytical solution and numerical simulation at the end.

並列關鍵字

representative volume element ； 2-D probes ； volumetric fraction ； heterogeneous material

參考文獻

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