Fundamental period formula for horizontal layered soil profiles

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.