Evaluation of basis parameters for SSI analysis of shallow foundation via centrifuge test and analytical approach

Abstract

Since the response of a structure subjected to earthquake load is greatly influenced by the soil properties, it is very important to accurately determine the properties of the soil together with the structure during a seismic analysis. The formula for soil stiffness and damping derived from the elastic half space condition requires a constant input parameter, but actual properties of the soil show strain and depth dependency. Therefore, strain dependent soil stiffness and damping should be reduced and increased through rational methods, respectively, and depth dependent soil stiffness and damping should be averaged to the effective profile depth and used for the analysis. Up to now, the effective profile depth has not only been presented differently in each code, standard and researcher, but has not considered soil damping together, and has been derived from very limited conditions (i.e., the surface foundation and linear elastic soil conditions). Various values have been suggested for the effective height of the structure, which affects the rocking behavior of the structure, but all of them have been theoretically or empirically suggested. The two parameters mentioned above, the effective profile depth and the effective height of the structure, can be said to be the basis parameters that affect all the mass, stiffness and damping matrices of the soil-structure interaction Equation of motion. In this study, the dynamic centrifuge model test and the analytical approach based on the state-space Equation were conducted to find out the most reasonable values within the suggested range of the two basis parameters. First, three types of basis parameter scenarios were set, and analyses using a three-degree of freedom soil-structure model were performed considering all soil-structure interaction influencing factors, such as embedment effect and total soil damping ratio (i.e., radiation and material damping of soil), which was not considered in the previous study, and a procedure for comparing the analysis results with the centrifuge model test results was established. At this time, the comparison between the analysis results and the test results and whether they match each other was quantitatively evaluated using the mean squared error. In particular, in this study, the strain dependent soil properties, which were briefly considered in the conventional code and standard, were reflected in relatively detail using an equivalent linear one-dimensional site response analysis. As a result of this study, the reasonable values of the effective height of the structure and the effective profile depth were respectively determined according to (a) the height from the bottom part of the foundation to the center of the mass of the superstructure, and according to (b) the depth at a value equal to four times the effective radius of the foundation. The results of SDOF soil-structure interaction analyses presented in FEMA440 was less accurate than those of the 3-DOF linear dynamic analyses used in this study, and the results of modified SDOF analyses considering both total soil damping and embedment effects show similar trend to those of 3 DOF linear dynamic analyses, but the response results were relatively lower than the 3 DOF analysis results. This is due to a limitation of the SDOF soil-structure model in which each mode shape occurs simultaneously with same weight and the weight of each modal damping ratio is estimated not to be reasonably considered.