Fundamental period formula for horizontal layered soil profiles
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摘要: 针对已有场地基本周期简化公式不适用含软夹层场地的问题，从振动的角度推导出能反映土层结构影响的场地基本周期估算公式。根据自振周期相等的原则，推导出单层土场地简化为单自由度体系的等效高度系数；以水平成层场地中任一土层厚度与这一系数之积作为体系高度，将场地简化为相应的单自由度体系，定义体系的自振周期为该土层的贡献基本周期，场地中所有土层贡献基本周期的平方和开平方即为场地的基本周期，并推导出相应的计算公式。检验结果表明，所推导公式不仅能够合理地反映土层结构对场地基本周期的影响，而且对实际工程场地基本周期的估算结果亦较已有公式的结果更接近地脉动测试结果。公式可用于估算水平成层场地的基本周期。Abstract: The current formula can not calculate the fundamental periods of the sites containing soft soil layers accurately. In order to solve the problem, a fundamental period formula for a horizontal layered site, on which the effect of soil layer construction is considered, is deduced based on the vibration theory. According to the rules of natural vibration periods being equal, a single layer site is simplified into a SDOF system by means of the lumped mass method, and the equivalent height coefficient between their heights is deduced. A horizontal multi-layer site can be simplified into a SDOF system based on any one soil layer, and the height of the SDOF system is equal to that of the soil layer multiplied by the equivalent height coefficient. The natural vibration period of the SDOF system is called contributing fundamental period of the soil layer here, and the fundamental period of the site should be equal to the square root of sum square (SRSS) of the contributing fundamental periods of all the soil layers in the site, and its formula is also deduced. The test results show that (a) the proposed formula can reflect the effect of soil layer construction on fundamental periods of sites very well, and (b) by comparing the calculated fundamental periods with the test ones of 5 engineering sites by use of the microtremor method, the proposed formula is of higher accuracy and reliability than the current formula. A conclusion is drawn that the deduced formula can be adopted to estimate the fundamental period of a layered horizontal site.
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