Vol.:(0123456789) 1 3 Modeling Earth Systems and Environment https://doi.org/10.1007/s40808-020-00737-6 ORIGINAL ARTICLE Seismic response analysis of soil profle: comparison of 1D versus 2D models and parametric study Navid Soltani 1,2  · Mohammad Hossein Bagheripour 2 Received: 25 February 2020 / Accepted: 7 March 2020 © Springer Nature Switzerland AG 2020 Abstract One of the most important parts of geotechnical earthquake engineering is evaluation of the ground motion due to incident earthquake. Seismic ground response evaluation can be categorized into time and frequency domain methods. In this study, an applied method is proposed to evaluate 2D ground response analysis in frequency domain. The results are presented in terms of peak acceleration and velocity diagrams as well as the diagrams of 2D/1D results using four real earthquakes, two in the far feld and two in the near feld as an incident waves. The accuracy of the proposed method is shown by comparison of results obtained using current method with those of 1D method in free feld condition. Then, to evaluate the efect of irregular topographies on seismic ground response, parametric study is carried out on empty valleys and diagrams of amplifcation factors have been presented. The obtained results confrm the necessity of 2D modeling and the use of precise and applied methods in the case of irregular topography. The superiority of the proposed 2D method than 1D method is elimination of limiting assumption of 1D method such as horizontal bedrock and parallel soil layer despite its simplicity and practicality. Keywords Ground response · 2D analysis · Frequency domain Introduction The phenomenon of seismic wave amplifcation or attenu- ation due to site efect constitutes a major factor to evalu- ate destruction during strong ground motion. In common seismic events, body waves travel from the source mostly across a bedrock and fnally end in soil layers. This is while most of the changes in the characteristics of ground motions occur in the soil layers (Kramer 1996). These changes are generally discussed with focusing and scattering phenom- enon of seismic waves. Due to the drastic variation of the nature of seismic waves passing through soil layers, it is very important to incorporate realistic and precise seismic excita- tion models into the analysis of structural seismic response. Hence, vulnerability of structures can be a function of an important factor known as the site seismic response. Ground response analyses can properly satisfy the needs for realistic and precise seismic excitation in analysis of structures or in soil–structure interaction. Based on dimension of calculation, numerical studies of seismic ground response are categorized into 1D, 2D, and 3D analyses. Analyses by these methods can be carried either in time or in frequency domain. 1D analysis is car- ried out in many cases but it has some serious limitations that completely discuss in the following. Generally, multi- dimensional analyses use various approaches such as fnite element method (FEM) (e.g., Di Fiore 2010; Soltani et al. 2019; Soltani and Bagheripour 2017), boundary element method (BEM) (e.g., Kham et al. 2013; Nguyen and Gatmiri 2007), spectral element method (SEM) (e.g., He et al. 2015), finite difference method (FDM) (e.g., Bouckovalas and Papadimitriou 2005), and hybrid methods such as coupled fnite and infnite element method (FE-IFE) (e.g., Duzgun and Budak 2010; Zhao and Valliappan 1993), coupled Finite and boundary element method (FEM-BEM) (e.g., Kamalian et al. 2006; Gatmiri et al. 2008). It should be noted that most of the multidimensional problems are performed using 2D analysis; however, with the development of memory pro- cessing, 3D modeling became possible but recommended for specifc cases (Hosseini and Pajouh 2012). Interested readers can fnd some 3D modeling in diferent references, * Navid Soltani n.soltani@ardakan.ac.ir 1 Department of Civil Engineering, Faculty of Engineering, Ardakan University, P.O. Box 184, Ardakan, Iran 2 Department of Civil Engineering, Faculty of Engineering, Shahid Bahonar University of Kerman, Kerman, Iran