Newmark位移法是目前用來分析地震造成邊坡滑動最常用的一種方法。Newmark位移Dn是對地震加速度歷時中，大於臨界加速度Ac的部份做兩次積分而得。唯在分析過程中，地震加速度歷時只在有強震站的位置才有記錄，在沒有強震站或距離較遠的地點則須使用經驗式推求Dn。Jibson (1993)及 Jibson et al. (1998) 以愛氏震度Ia當參數，建立估計Dn的經驗式。
由於該經驗式發表至今已有一段時間，近年一些具代表性的強震資料尚未納入分析，在台灣地區之適用性也尚未檢驗，所以本研究利用台灣集集、日本Kobe，土耳其Kocaeli、Duzce以及美國Loma prieta和Northridge地震的強震資料來找出 Dn -Ia 和Dn -Ac 間的相關性，並利用此相關性來探討現有的迴歸模式的改進可能。
分析結果顯示Dn 和Ia的相對關係中，若將Dn 及Ia同時取對數，可得到較好的線性相關，而Dn 和Ac的相對關係中，若只對Dn 取對數也可以得到較好的直線關係。在迴歸分析中發現隨著Ac變大，LogDn- Log Ia 分佈圖的斜率會隨著變大，因此我們加入了新的變數來修正斜率的改變，並建立新的模式。將此新模式應用到前述六組強震資料後，均可得到較佳的迴歸成果，顯示此新模式較舊有的模式佳。
最後將不同場址分類的強震資料分別代入新模式進行迴歸分析，得到岩盤站及土壤站的經驗式。此兩個經驗式的估計誤差及合適度皆較不分類經驗式佳。在應用上，計算一般邊坡的Newmark位移時應採用岩盤站經驗式，回填土及軟弱土壤的邊坡則宜使用土壤站的經驗式。

Modification of Newmark Displacement Empirical Formula by Using Recent Large Magnitude Earthquakes
Shang-Yu Hsieh
Abstract
The use of Newmark displacement is an effective approach to measure the stability of a natural slope under shaking of an earthquake. The Newmark’s method helps to calculate the co-seismic relative cumulative displacement of a sliding block by integration of the acceleration time history data of a strong-motion record above certain critical value. It may also be estimated by applying an empirical equation, like the Jibson’s formula.
This research employs strong-motion data of the 1999 Chi-Chi Earthquake, the 1999 Kocaeli Earthquake, the 1999 Duzce Earthquake, the 1994 Northridge Earthquake and the 1989 Loma prieta Earthquake to refine the relationship among critical acceleration (Ac) Arias Intensity (Ia), and Newmark displacement (Dn). The result revealed that Dn is just as expect to be proportional to Ia, when Ac is small. As Ac gets larger, the linearity becomes less. We also found that logDn is proportional to Ac, when Ia is large. As Ia goes small, the linearity becomes less. These features are common in the six set of data. Therefore, we add a third term in addition to the Jibson’s form to cover the abovementioned problem, and propose a new form for the relationship among Ia, Ac and Dn.
Two alternative forms were tested by using each of the data set from the six, and a final form was selected. Parameters for the selected form were regressed by using the total data set, and a final empirical formula is proposed.
Besides, this study also considered site conditions and developed an empirical formula for soil site and rock site, respectively. The estimation error is smaller and the goodness of fit is higher for either soil site formula or rock site one. Because landslide is usually occurred on hillside, rock site formula may be more valid in this case. Soil site formula may be used at slope of landfills.

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