本研究之間接土壓力模式，係以一維波動方程模擬地盤側潰狀態下之樁基礎動力反應，依據現場土層鑽探資料與鄰近測站之地震紀錄，由Tokimatsu（2003）建議之地盤變位模式估算地盤永久變位量，再將地震加速度積分兩次而得之正規化地震位移視為地震力對地盤變位的影響，進而求得地盤受震過程之位移反應，並以此為前置解，最後藉由樁身土壤彈簧將地盤變位傳遞於樁身上。樁身剛度以簡易Bouc-Wen模式模擬其非線性行為，以瞭解液化地盤內基樁之變形行為與破壞機制。本研究以參數研究及日本地震時之基樁破壞案例驗證本模式之合理性。 研究結果顯示：（1）針對底層未液化土層，傳統方法僅適用於堅硬土層；本研究所採用Ishihara & Cubrinovski（2004）建議之方法可用於不同類型土層，並將底層未液化土壤以土壤彈簧模擬其非線性行為；（2）本研究採用簡易Bouc-Wen模式處理樁體非線性行為，其中α、z參數由基樁資料彎矩-曲率圖回算求得；（3）由參數研究發現，永久變位模式之五參數皆各有其影響力。其中地下水位深度的模擬效果較差；基樁長度與液化層厚度若太為相近，會使得樁底位移有所滑移；土壤彈簧折減因子β將使得基樁位移減小；（4）由參數研究與實際案例分析結果顯示，樁基礎之最大彎矩易發生於液化層上下方交界處而致使基樁發生破壞，其原因在於上下方交界處附近之土壤位移反應因弱化而造成基樁整體變形曲線中之轉折，應於液化層上下交界處加強樁基礎結構強度，確保其結構物之安全性；（5）本研究以樁基波動分析程序（EQWEAP）為架構，以地盤變位模式為前置解，進行地盤側潰後對樁基礎影響之行為分析。亦可以土壓力模式為前置解進行分析；（6）與直接土壓力模式比較之下，本研究之分析結果應較為略小；（7）本研究所建立之動力分析模式，可清楚反映樁基礎於受震期間對液化影響產生之變形行為與內力反應，亦能透過位移、彎矩、剪力之剖面圖，瞭解較能代表樁基礎實際受震行為之瞬間反應。 The indirect earth pressure model with one dimensional wave equation analyses is used to simulate the seismic responses of a single pile affected by soil lateral spreading. With the field investigation, the permanent ground displacement can be estimated according to the method proposed by Tokimatsu（2003）. The permanent ground displacement multiplied by the normalized seismic displacement function is regarded as the seismic responses of the ground displacement. Finally, the dynamic ground displacement profile is applied to the pile elements through the soil springs , and the pile non-linearity is simulated by the simplified Bouc-Wen Model. Thus the deformations and failure mechanism of the pile are able to be understood. This analysis is also validated by the parameter studies and the case studies of pile failure due to earthquake in Japan. The results of this study are concluded as follows:（1）For the underlying non-liquefied layer, the soil springs are used to simulated its non-linearity. （2）The pile non-linear behavior is characterized by the simplified Bouc-Wen Model where α and z are back calculated from the tri-linear moment-curvature relationship. （3）From the parameter studies: It can be found that the five parameters of the Permanent Model all influence the analyses. However , the simulation of the factor, zw is not as fine as others. Compared with the thickness of the liquefied layer, if the length of the pile is not long enough, the displacement of the pile tip will be not so closer to zero. The pile response is smaller when the stiffness reduction coefficient, β, is applied. （4）The largest pile displacement would occurs at the pile head. The values of the moments at the pile head or the interface between the liquefied layer and the underlying non-liquefied layer may exceed the ultimate moment. So the two section of a pile is in need of strengthening to ensure the safety of the superstructure. （5）The frame of this study is based on the Earthquake Wave Equation Analysis of Pile（for short: EQWEAP）. The pre-solution involved is the ground displacement profile, and it also can be the direct earth pressure profile. （6）Compared with the direct earth pressure model ,the responses of this study are smaller. （7）The indirect earth pressure model is relatively simple, and the instant responses at different times are able to be caught easily.
