本研究模擬土壤之簡化模式探討方形基礎與層狀土壤承受扭轉外力作用下之動態互制行為。土壤簡化分析模式係採用線性彈簧、黏滯阻尼盤及集中轉動慣量等三個離散元素組合成15類基本單元，再依特定之組合規則，遵循三個等值參數以及最多兩個自由度之原則組成33種簡化模型，並經由最佳化分析求得最佳簡化模型與實際基礎土壤互制系統之動態反應放大因數相互比較。研究結果顯示，簡化分析模式可有效模擬方形基礎與層狀土壤在扭轉外力作用下之動態互制行為，利用簡化模式計算基礎動態反應放大因數之誤差皆低於10%。
本研究亦針對基礎土壤互制系統之動態反應放大因數進行參數分析。研究結果顯示，埋置基礎具有抑制互制系統動態反應之作用，當基礎埋置深度比T=0.5-2.0時，埋置基礎與表面基礎系統尖峰反應之比例介於0.64-0.73；隨著基礎質量比由1增加至10，基礎尖峰反應將放大1.3-1.8倍，基礎與層狀均勻土壤互制系統之無因次共振頻率為2.9-3.7，土壤剪力波速呈線性變化之互制系統無因次共振頻率則為2.2-2.6；當土壤剪力波速比愈小時，基礎尖峰反應愈大，但隨著土層厚度比增加則該效應愈不顯著。

This study simulates soil layers using a simplified model to investigate the dynamic interaction between square foundations and layered media by a torque applied on the top of the foundation. Fifteen basic units are established by using linear springs, viscous dashpots, and lumped masses moment of inertia. Specific rules including three equivalent parameters and no more than two degrees-of-freedom are then applied to create thirty-three models. The best simplified model is then determined through an optimization process. This study compares the dynamic magnification factor of the simplified soil-foundation model and that of a real soil-foundation interaction system. The results showed that the simplified model may effectively simulate the dynamic interactions between square foundations and layered media subjected to torques. The dynamic magnification factor using the optimal simplified model results in a relative error lower than 10%.
This study also conducts a parametric analysis to investigate the dynamic magnification factor of soil-foundation interaction systems. The results showed that the foundation embedment reduces the dynamic system response. When the embedment ratio T is ranging from 0.5 to 2, the ratio of the peak response of the embedded foundation to that of the surface foundation would be reduced to a range of 0.64-0.73. When the foundation mass ratio increases from 1 to 10, the peak foundation response would be magnified by 1.3-1.8 times and the dimensionless resonant frequency for uniform soil is 2.9-3.7 and for nonuniform soil is 2.2-2.6. When the shear-wave velocity ratio of soil media decreases from 0.6 to 0.3, the peak foundation response becomes larger and this characteristic may be less significant as the soil depth ratio increases.

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