Investigating the Accuracy of the Averaging Method in Estimating the Input Excitation to the Foundation by Considering the Effect of Incomplete Contact between the Walls and the Surrounding Soil

Calculating the input motion to the foundation as a result of kinematic interaction is one of the challenging issues in the topic of soil-structure interaction, which is accompanied by computational difficulties. In order to overcome these difficulties, approximate approaches have been presented in the past, which are based on the relations of design and evaluation regulations. The averaging method is one of the conventional approximate methods for calculating the horizontal and rotational displacement component of the foundation, which is used by structural design engineers. In the past, the acceptable approximation of this method in estimating the input motions imposed on foundations, having full contact with the surrounding environment, has been approved by researchers. However, the accuracy of this approach in the case of incomplete contact of the foundation with the surrounding soil has not been investigated so far. However, for many approaches in the construction sequences of structures, the lack of contact between the foundation walls and the surrounding environment is inevitable. In this research, the capability of the averaging method to estimate the input motion to the foundations, assuming the possibility of incomplete contact between the foundation and the surrounding environment in three-dimensional mode, has been investigated. According to the results, in the case that the contact of the walls with the soil is complete, the maximum estimation error in the horizontal component reaches 30% and in the rotation component, this value is about 20%. Nevertheless, the averaging method has been able to correctly predict the trend of the graphs in the same case and resulted in a relatively acceptable approximation. When the contact state is reduced from the full state to 75% of the wall surface, the averaging method still provides reasonable results for both components. In the rotational component, the maximum estimated error is 15%, which is a lower error than the full contact state, but the frequency at which the maximum rotation occures has not been detected correctly. For the horizontal component in this case, the error is 30%. Further, by reducing the contact surface and reaching a regular incomplete contact state of 50%, the values of the horizontal component are almost predicted correctly both in ordinate and trend. However the differences have become more significant in the estimation of the rotational component. In the contact state of 25%, the horizontal displacement component is well estimated by the averaging method, but in the rotational component, the values are close to zero, which show a significant difference with the actual results. The weakness of the averaging method intensifies in the case of zero wall contact and the rotational component about the y axis is completely vanished. The inability of the averaging method to detect the existence of a component, maybe more critical for imperfect irregular contact modes and may occur many times in an uncontrolled manner. Examples of such wrong approximations are presented in this research. Finally, it can be stated that using the averaging method in estimating the input motion to foundations with incomplete contact with the surrounding environment can be associated with large errors and can unconservatively overshadow the seismic design and evaluation procedures.