圓錐貫入試驗空間相關性之研究

Abstract

關聯性長度一直被視為是描述空間相關性的重要（也可能是唯一的）參數，但在最近的研究中，樣本路徑平滑度也被接受為重要的參數，尤其是大地工程含有找弱帶破壞機制的案例，更是突顯平滑度的重要性。故本研究以估計關聯性長度及平滑度參數為目標進行探討。 研究中採用的評估方法有method of moments、maximum likelihood method，搭配不同的自相關函數模型下去分析及比較，其中自相關函數模型又分為傳統及非傳統，兩者的差別在於傳統的自相關函數模型僅包含關聯性長度一個參數，非傳統的自相關函數模型( 即Whittle-Matérn 模型 )可以同時將關聯性長度及平滑度參數納入考量。 研究結果顯示，傳統自相關模型如果搭配maximum likelihood method，可能導致關聯性長度估計錯誤，這是因為參數間互相制衡的現象，若要同時捕捉關聯性長度及平滑度參數，可以採用maximum likelihood method搭配非傳統的模型。另外，估計樣本路徑平滑度時並不建議採用method of moments，因為method of moments 評估參數的機制對於平滑度並不敏感，即使搭配非傳統模型仍然無法捕獲到正確的平滑度。

The scale of fluctuation ( SOF ) has been regarded as an important ( and probably the only ) parameter to characterize the auto-correlation of a spatially variable soil property. However, the sample path smoothness is also accepted as an important parameter in recent studies. Especially the weakest path seeking mechanism in the geotechnical engineering has highlighted the importance of sample path smoothness. Therefore, the aim of this study is to estimate the SOF and smoothness more accurately. Method of moments and maximum likelihood method with different auto-correlation function ( ACF ) models are adopted in this study. The ACF model is divided into classical and non-classical. The classical ACF models have only a single parameter ( SOF ), while the non-classical ACF model ( i.e., Whittle-Matérn model ) take both of the SOF and smoothness into account. The results reveal that classical ACF models may produce misleading SOF estimates if the maximum likelihood method is adopted, because of the trade-off between two parameters. If we want to capture the SOF and smoothness simultaneously, we can use the Maximum likelihood method with non-classical model. In addition, the method of moments is not recommended for estimating the sample path smoothness because the mechanism of the method of moments is not sensitive to smoothness, even with non- classical model still cannot capture the smoothness accurately.