Linear and nonlinear analysis investigation on soil dynamic behavior (Case study: Urmia city, Iran)

Iran is seismically a very active region. Earthquakes with high magnitudes occur every year in Iran, averagely. Therefore, dynamic response analysis is one of the most important issues in evaluating the soil behavior. In seismic response analysis method of earth layers, deformation issues during earthquakes are important. Two methods exist for dynamic analysis: equivalent linear method and nonlinear method. If seismic motion is weak, shear strain of alluvium will be less than 10-4 percent and earth layer behavior will be elastic. For strains greater than 10-4 percent, soil behavior will be nonlinear; then nonlinear and equivalent linear methods should be used. In large shear strain that soli behavior is completely nonlinear, the problem should be solved at time domain, step by step. Difference between nonlinear and equivalent linear method depends on soil nonlinear behavior.
Ground response can be analyzed with 1D, 2D and 3D modeling. These methods have different capabilities in terms of problem and wave geometry modeling, also to the solution of equation of motion. 1D ground response analysis is used for horizontal structures that boundaries between their layers are distinct, but inclined surfaces, nonlinear ground, heavy and rigid buried structures, walls and tunnels need 2D and sometimes 3D analysis. In other words, while one of the two soil profile dimensions (surface or sub-surface dimension) is much bigger than the other one, transmission synthesis is acceptable. Nonlinear behavior of soil can be modeled as equivalent linear or nonlinear medium by 1D, 2D or 3D methods. Equivalent linear method is popular between engineers, due to its relative simplicity and its simple and clear parameters. Using accelerometers, geotechnical boreholes and equivalent linear and nonlinear analysis, acceleration spectra can be compared.DEEPSOIL software can analyze the alluvium. It is based on direct and continuous solution of equation of transmitted waves and calculates responses of a system with homogenous and viscoelastic layers to shear waves. DEEPSOILis a one dimensional ground response analyzing software which is able to examine the defined layers by both of linear and nonlinear analysis methods.
Urmia city has experienced many large and moderate earthquakes in last years. According to Iranian standard 2800, the design base acceleration in this city is 0.25g. For studying the Urmia bedrock, two borehole data of the city with depth at 16 and 24 meters were used and some appropriate accelerograms were selected and scaled for matching with design spectra. These accelerograms were scaled with the same form spectrum, but they had different maximum acceleration (0.2g, 0.25g, 0.3g, 0.35g, 0.4g, 0.45g and 0.5g). Using DEEPSOIL software with capability of nonlinear and equivalent linear analysis, acceleration spectrawere compared.
The aim of this study is to compare the results of the alluvial analysis with linear and non linear dynamics in estimating the amplification coefficient and the amount of amplification of the waves in then earthquake event
Therefore, in order to evaluate the nonlinear behavior of soil, Equivalent linear  and non linear analysis  in time domain were performed on one-dimensional models of subsurface layer using borehole data in Urmia. The results of the two analyzes were compared with each other. By comparing spectral accelerations at the Earth's surface during different periods with corresponding values on seismic bed rock, the amplification coefficient is presented in different periods.
The results show that in the range of 0.1 to 1 second, the greatest amplification and the greatest difference were present between the two analyzes.
In conclusion, we conclude that both Equivalent linear and nonlinear linear methods can be successfully used to analyze the one-dimensional ground response. The method of applying and interpreting each of these methods requires information about the assumptions of the Ground floor, the manner in which each method operates, the recognition of its constraints, and none of them can be considered decisively and precisely. However, the accuracy of these methods decreases with changes in soil conditions, uncertainty in soil characteristics and the empirical data dispersion, with a large number of input parameters based on them.