Effect of Soil on the Seismic Response of Structures Taking Into Consideration Soil-Structure Interaction

Introduction

Soil–structure interaction can significantly change the behavior of engineering works and structures. It has a direct or indirect interaction between the three elements (soil-foundation-superstructure). The soil shall be treated as an elastic multilayer. Surely all the geotechnical engineers are well aware that the soil is not an elastic material, but Terzaghi, himself, admitted that when the stresses are lower than the third of the limit values, then we may consider, with a reasonable degree of certainty, that the soil has an elastic behavior. Taking into account the effects of the surface. (Ahmadi & Eskandari, 2014), show that the axisymmetric problems related to the elastic half-space including the effects of the surface can be modelled in an equivalent way by an elastic medium reinforced at the surface. In the case of two perfectly elastic half-space mediums, the surface-interface effect on the elastic responses is more significant for the punctual load (Ahmadi, Samea, & Eskandari, 2016). A foundation founded in a semi-finite medium can be represented as circular disc at a distance from the soil free surface. The problems of interaction between this disc and its environment have usually been subject of interest to the engineers (Eskandari, Shodja, & Ahmadi, 2013). The superstructure will create a vertical stress, which is regarded as a concentrated point load acting at the center of the circular disc, which causes an additional vertical stress in a single point in the depth; this may be expressed by the formulas of Boussinesq (Shodja, Ahmadi, & Eskandari, 2014). It also causes the foundation to rotate and to give another degree of freedom, which may be expressed by Green and Nobel functions (Ahmadi & Eskandari, 2014). In the case of large span bridges, the foundations are embedded in the soil mass and considered stiff, to avoid major deformations under the effect of the applied dynamic loads, like the effect of vertical excitations of a rotating machine on a single pile (Srivastava, Choudhary, Biswas, & Manna, 2019). This response can be represented using analytical methods which allows us to determine the dynamic impedances of the foundation in the different degrees of freedom, in order to make a good rheological modelling in the underlying medium (Chen, Zhao, Jia, Han, & Guan, 2019). The dynamic behavior of axisymmetric foundations has been studied in the literature using the virtual work methods, which were applied on a hexarot constituting a parallel axisymmetric mechanism (Pedrammehr, Asadi, & Nahavandi, 2019).

The finite element method (FEM) considered as a method of solving the problem of interaction between the soil and the structure as a whole. This method was born in 1850 in the analysis of structures, in particular on the resistance of materials under conditions of small deformations. In 1940, the mathematical concept of the method was defined by Newmark, Hrenikoff, Henry and Courant. Nowadays, most researchers are interested in this numerical method of resolution, for to the many advantages given by it in modeling. It is used to solve the differential equations, which present the dynamic behavior of the soil, and their solutions are the unknown functions depending on several parameters, and verifying the boundary conditions, which are presented in the form of functions. It is a method of processing numerically complex problems in a faster and more precise manner.