本研究利用簡化模式建立通用集中參數模型，模擬半無限空間上雙層均質土壤與方形埋置基礎互制系統承受水平與旋轉外力之動態行為，能夠適用於基礎質量比b_x=0~20範圍內之實際系統。此通用集中參數模型由水平組件與旋轉組件組成，而通用集中參數模型之等值參數由基因演算法與鑑識科學流程演算法進行最佳化分析所求得，並將提出的簡化模式應用於典型校舍，以驗證此簡化模式的適用性與正確性。
本研究以簡化模式模擬不同剪力波速比、土層厚度比及基礎質量比之實際系統，實際系統利用SASSI程式進行分析，簡化模式利用SAP2000程式建立通用集中參數模型進行分析，並且於頻率域及時間域檢視實際系統與簡化模式反應的擬合度。(1)頻率域最佳化分析結果顯示實際系統與簡化模式之放大係數與相位角反應一致。(2)時間域分析結果顯示，在強制載重及地震運動作用下，實際系統與簡化模式之反應仍保持高擬合度，這說明本研究建立之簡化模式可以有效的模擬半無限空間上雙層均質土壤與方形埋置基礎動態互制系統。(3)將簡化模式應用於典型校舍，分析結果顯示在地震運動作用下實際系統與簡化模式基礎的反應仍保持高擬合度，然而上部結構反應的誤差卻達18.05%~31.35%，因此，欲改善上部結構反應的誤差，在建立簡化模式時，不僅需要考慮土壤與基礎互制效應，可能也須將上部結構之影響納入簡化模式。

This study utilizes a simplified model to establish a generic lumped-parameter model to simulates the dynamic interaction system of embedded square foundation and two soil layers in half-space subjected to horizontal and rocking vibrations. The developed model is applicable to actual systems within the range of foundation mass ratio b_x from 0 to 20. The generic lumped-parameter model consists of both horizontal components and rotational components. The equivalent parameters of the generic lumped-parameter model are determined through optimization analysis using genetic and forensic-based investigation algorithms. The proposed simplified model is then applied to a typical school building to verify its applicability and accuracy.
This study uses the simplified model to simulate two different shear wave velocity ratios and two soil layer thickness ratios in actual systems. The actual systems are simulated using the SASSI program, while the simplified model is simulated using the SAP2000 program to establish the generic lumped-parameter model. The adequacy between the actual systems and the simplified model is examined in both the frequency domain and the time domain. (1) The results of frequency domain optimization analysis show that the amplification factors and phase angles of the actual systems are consistent with those of the simplified model. (2) The results of time domain analysis show that the response of the actual systems remains highly consistent with the simplified model under both forced loading and seismic motion, indicating the effectiveness of the proposed simplified model in simulating the dynamic interaction system of embedded square foundation and two soil layers in half-space subjected to horizontal and rocking vibrations. (3) When the simplified model is applied to the typical school building, the results show that the response of the actual system and the simplified model at the foundation level still exhibit high adequacy. However, the errors in the response of the upper structure range from 18.05% to 31.35%. Therefore, to improve the accuracy of the upper structure response, it may be necessary to consider the influence of the upper structure when establishing the simplified model, in addition to considering the soil-foundation interaction effects.

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