本論文提出一種簡化模式，模擬承受水平與旋轉振動之剛性岩盤上雙層土壤與方形埋置基礎動態互制系統，並於頻率域與時間域驗證簡化模式的準確度。
本論文基於實際土壤—基礎系統之阻抗函數，提出由5組水平單元及1組旋轉單元構成之集中參數模型，並透過鑑識科學流程演算法與基因演算法進行參數最佳化分析，建立適用於不同基礎質量比的簡化模式。本論文藉由量化實際土壤—基礎系統與簡化模式兩者動態反應的差異，驗證簡化模式的準確度。頻率域分析結果顯示，於不同土壤厚度比、土壤剪力波速比及基礎質量比下，整體而言，簡化模式的水平及旋轉放大係數均方根誤差皆小於 ；時間域分析結果顯示，於衰減簡諧外力與地震外力作用下，整體而言，簡化模式的尖峰誤差皆小於 。基於該研究成果，證明本論文所提出的簡化模式於頻率域與時間域皆有一定適用性及準確度。
此外，本論文於實際土壤—基礎系統及簡化模式中，引入上部建築結構並進行時間域分析。研究成果顯示，上部建築結構會降低簡化模式的準確度。因此，建立簡化模式可能需要考慮上部建築結構對整體系統的影響。

This thesis proposes a simplified model to simulate emulate the dynamic interaction system of square foundation embedded in two soil layers with rigid bedrock undergoing horizontal and rocking vibrations. The accuracy of the proposed simplified model is validated within both the frequency domain and the time domain.
This thesis proposes a lumped-parameter model constituted of five horizontal units and one rotational unit, based on the impedance function of an actual soil-foundation system. The lumped-parameter model undergoes optimization analysis using forensic-based investigation algorithm and genetic algorithm, which are utilized to approximate its dynamic response to that of the actual soil-foundation system. This enables the achievement of a simplified model, adaptable across diverse of foundation mass ratios. This thesis quantifies the difference between the dynamic responses of the actual soil-foundation system and the simplified model, thereby validating the accuracy of the simplified model. Frequency domain analysis results indicate that, in general, for different soil thickness ratios, soil shear wave speed ratios, and foundation mass ratios, the root mean square errors of both horizontal and rotational magnification factors in the simplified model are below 10%. Time domain analysis results indicate that, in general, undergoing decay harmonic force and seismic forces, the peak errors of the simplified model are below 3%. These finding validate the applicability and accuracy of the simplified model proposed in this thesis.
Additionally, an upper structure is incorporated into both the actual soil-foundation system and the simplified model and subjected to time-domain analysis. The results show that accuracy of the simplified model reduced due to the influence of the upper structure. Consequently, the construction of the simplified model may necessitate consideration of the impacts of the upper structure impose on the soil-foundation system.

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