International Journal of Advances in Engineering & Technology, Dec., 2017. ©IJAET ISSN: 22311963 592 Vol. 10, Issue 5, pp. 592-603 A COMPARATIVE STUDY OF VARIOUS METHODS TO EVALUATE IMPEDANCE FUNCTION FOR SHALLOW FOUNDATIONS Chandra Mohan 1 and Samirsinh Parmar 2 1 Department of Civil Engineering, Indian Institute of Technology, Kanpur, India. cmohan@iitk.ac.in 2 Department of Civil Engineering, DD University, Nadiad, Gujarat, India. samirddu@gmail.com ABSTRACT The dynamic response of rigid shallow foundations can be evaluated by impedance functions which is defined as a ratio between force or moment (input) versus displacement or rotation (steady state), (output) at the centroid of the base of massless foundation. The foundation vibration problems are described in six degrees of problems hence the impedance functions derived for translational modes. Stiffness and Radiation affects the dynamic soil- structure interaction as Impedance function is a function of stiffness as well as radiation damping. The present paper is comparative study of various methods like Barkan, Dominguez, Dobry and Gazetas for evaluation of impedance functions for various modes of vibration of shallow foundation. The pros and cons of the methods for estimation of impedance function was discussed. The stiffness in vertical direction shows similar trend for all four methods. The use of equivalent radius approach to compute dynamic stiffness and radiation damping causes large errors which leads wrong estimation of impedance functions. KEYWORDS: Impedance function, Foundation Vibration, dynamic soil-structure interaction. I. INTRODUCTION A variable force or motion may be used as input and output variables in defining a system transfer function. For vibrating motion three particular choices are commonly used which is impedance functions, mobility functions and transmissibility functions. The dynamic impedance is a function of the soil-foundation system and nature and type of exciting loads and moments. For particular case of simple harmonic excitations the dynamic impedance function(s) can be defined as the ratio between force (or moment) R and the resulting steady state displacement (or rotations) U at the centroid of the base of massless foundation. Sz = (1) in which Rz(t)= Rz exp (iωt) and is the harmonic vertical force; and Uz(t)= Uz exp (iωt) harmonic vertical displacement of the soil-foundation interface. The entity Rz is the total dynamic reaction against the foundation and includes normal traction against the base mat and shear traction along any vertical sidewalls. The similar impedance functions for the possible degrees of freedom is Sy- lateral sliding, Sx longitudinal swaying, Srx- rocking impedance (moment-rotation ratio) along x axis, Sry- rocking impedance with respect to y axis. St is a torsional impedance for rotation about z axis (vertical). In case of embedded foundation we can incorporate two more “cross -coupling” horizontal rocking impedance Sx-ry and Sy-rx. This cross coupled impedance effect is very small in case of surface foundations but its effect increases as the depth of embedment increases.