摘要 本研究主要採用三維動力有限元素分析模式，模擬土層受微地動反應，在時間域進行彈性分析，以探討Nakamura方法估算土層第一模態頻率之適用性。 在案例分析中，主要針對不規則土層及雙層土層進行研究。所謂不規則土層包含底部岩盤不規則，及土層中有塊狀體兩種情況，至於雙層土層則分為上軟下硬及上硬下軟兩種模式。 研究結果顯示：在合乎一維模式條件下，三維分析時只要模擬的參數選取適當，Nakamura方法所估算的頻率就會和一維模式的解析解非常接近。在不規則土層方面，當測站下方岩盤有突出塊時，一維解析解與Nakamura方法的結果並不相符，但隨著突出塊的長寬尺寸放大，兩者的差異便會減少，此結果或許可以說明過去許多學者利用一維模式驗証Nakamura方法，所得的結果不一致的原因。而當土層中有塊狀體的情況，塊狀體位於力量源與測站間，且切於測站下方0m處，其尺寸大小會影響所估算的頻率；由雙層土層的研究結果可觀察出，規範所提供的公式在兩種模式中，只適用於兩層土層的剪力波速相差不大的情況，而Nakamura方法在上軟下硬的模式中，皆可得到準確的結果，只是當土層軟硬相差急遽時，頻譜圖中的低頻處會有上揚擾動的現象，易造成使用者誤判，應該特別注意；若在上硬下軟的模式中，在相鄰土層的剪力波速相差不大的情況下，Nakamura方法才適用。 Abstract In this study, a three-dimensional finite element method is employed to simulate the response of site induced by microtremor in time domain. We investigate the suitability of Nakamura’s method in evaluating the fundamental frequency of soil stratum. Cases investigated are the irregular ground and a two-layer model. The irregular ground includes a hunch rock in bottom bedrock and rock mass. Two types of the two-layer model are discussed：one is that the upper layer is softer than the lower layer, while the situation is reversed for the second type. Based on the results obtained, it is found that if the soil stratum meets the requirement for the one-dimensional analysis, the Nakamura method can give almost the same fundamental frequency as the one-dimensional analytical solution. For a hunch rock in bottom bedrock, we would realize a blind spot that many researchers used one-dimensional analytical solution to prove Nakamura’s result. When rock mass locates between source and measured site, the size of rock mass would influence Nakamura’s method accuracy. For two-layer model, the empirical formulas given in the code behave well only in low impedance contrast； the Nakamura method ,however, gives good estimation for all the impedance contrast considered in this study but a caution has to be taken in the low frequency range where the spectral ratio plot shows peak which may lead to wrong judgment. In the second model, Nakamura’s method is only suitable in low-impedance contrast.
