在大地工程討論中，地質不確定性有兩個來源：（1）地層模型不確定性（stratigraphic uncertainty）及（2）地工參數的不確定性。雖然大地工程設計上常考慮到大地材料性質的不確定性，但少有考慮地層不確定性之設計。一般而言，設置新增鑽孔會降低地層的不確定性，然而新增鑽孔位置對地層不確定性之量化關係卻鮮少被提及。 本文先假設之合成地層模型（已知地層模型），於其設置既有鑽孔及新增鑽孔，再利用馬可夫隨機場（Markov random field, MRF）模擬數百個潛在的地層模型，透過信息熵（information entropy）及總信息熵（total information entropy, TH）來量化地層模型的不確定性；經由一系列鑽孔位置及MRF的參數研究，得到不同新增鑽孔位置及MRF參數下，地層模型的不確定性（TH）。此外，本文根據合成地層模型與MRF模擬的地層模型進行比較，得到MRF模擬地層模型的準確度。研究結果顯示：（1）在本文案例中，TH為相對鑽孔位置的二次函數，最小值出現在新增鑽孔位置於兩既有鑽孔的中間；（2）MRF參數之空間影響半徑比越大代表地層的異向性越明顯，地層模型不確定性也較低，反之亦然；（3）空間影響半徑比傾角對TH較不顯著，但仍會影響地層模型及信息熵的分布；（4）根據上述3點，本文提出新增鑽孔位置、MRF參數及TH之迴歸模型，並透過隨機地層案例進行驗證；最後，以一案例說明提出的迴歸模型於工程案例之應用。 ;The uncertainty involved in the interpreted geological model may be categorized as: (1) the stratigraphic uncertainty and (2) the properties uncertainty. Although the influence of the properties uncertainty on the behavior or performance of the geotechnical system and the geotechnical design has been extensively reported in the literature, the studies that address the stratigraphic uncertainty are seldom. Generally, drilling an additional borehole will decrease the stratigraphic uncertainty. However, there has no systematic and comprehensive study to investigate the above relation. This paper utilized the stochastic Markov random field (MRF) to simulate hundreds of potential stratigraphic models (realizations) based on the designed borehole locations in a synthetic stratigraphic model (a benchmark model). The stratigraphic model uncertainty can be quantified by the information entropy that was calculated by the probability of soil type from the MRF simulations. The systematic parametric studies of borehole locations and MRF parameters were conducted. Additionally, the accuracy of MRF simulation was performed via the comparison of a synthetic stratigraphic mode and stratigraphic models generated by MRF. The results show that (1) the total information entropy is a quadratic function of the additional borehole location; the minimum value appears when the additional borehole at the middle of two inherent boreholes. (2) the stratigraphic uncertainty decreases with the increasing influence radius ratio and vice versa. (3) The dip of stratigraphic anisotropic ratio has no significant influence on the total information entropy. (4) Based on (1)-(3), the correlations among an additional borehole location, stratigraphic anisotropic ratio, and total information entropy were obtained by using multivariate regression analysis, which were verified with the case studies.
