**Authors**

Department of Civil Engineering, Faculty of Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

**Abstract**

Topographical and mechanical properties of soil layers can lead to amplification or attenuation of seismic waves. Such a phenomena can be theoretically explained by means of ground response analysis. Definition of boundaries is of great concern in modeling ground response and application of boundaries with any constrain can lead to so called “trap box” effect in seismic waves in the model and hence to fictitious results. In present study, two-dimensional Finite Element Method (FEM) is applied in which boundaries known as “absorbing boundaries” are used to study the effect of wave scatter in valleys with different forms on the amplification or attenuation of SV waves. Comparison of the results is conducted for the current approach and those of the coupling Finite Element and the Infinite Element (sometimes called as FE-IFE) method. The results are also presented in non-dimensional diagrams of Au and Av for horizontal and vertical displacement amplitude respectively, through the valley span and its surrounding area. Comparison of the results also indicated that the proposed boundaries can improve the seismic analysis when coupled with the FEM. Also because of topographic irregularities, variations of displacement are seen inside the valley and around it.

**Keywords**

References:

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28. Brinkgreve, R., Plaxis: Finite Element Code for Soil and Rock Analyses: 2D-Version 8:[user's guide], Balkema (2002).

29. Lysmer, J. and Kuhlemeyer, R.L. "Finite dynamic model for infinite media", Journal of Engineering Mechanics Division, 95, pp. 859-878 (1969).

30. Weihua, L. and Chenggang, Z. "Scattering of plane SV waves by cylindrical canyons in saturated porous medium", Soil Dyn. Earthquake Eng., 25, pp. 981-995 (2005).

31. Bouchon, M. "Effect of topography on surface motion", Bull. Seismol. Soc. Am., 63, pp. 615-632 (1973).

32. Pagliaroli, A., Lanzo, G. and D'Elia, B. "Numerical evaluation of topographic effects at the Nicastro ridge in Southern Italy", J. Earthquake Eng., 15, pp. 404-432 (2011).

2. Idriss, I. "Finite element analysis for the seismic response of earth banks", Journal of Soil Mechanics & Foundations Div., 94, pp. 617-636 (1968).

3. Celebi, M. "Topographical and geological amplifications determined from strong-motion and aftershock records of the 3 March 1985 Chile earthquake", Bull. Seismol. Soc. Am., 77, pp. 1147-1167 (1987).

4. Celebi, M. "Topographical and geological amplification: case studies and engineering implications", Struct. Saf., 10, pp. 199-217 (1991).

5. Bouchon, M. and Barker, J.S. "Seismic response of a hill: the example of Tarzana, California", Bull. Seismol. Soc. Am., 86, pp. 66-72 (1996).

6. Celebi, M. "Northridge (California) earthquake: unique ground motions and resulting spectral and site effects", International Conference on Seismic Zonation, pp. 988-995 (1996).

7. Gazetas, G., Kallou, P. and Psarropoulos, P. "Topography and soil effects in the MS 5.9 Parnitha (Athens) earthquake: the case of Adames", Nat. Hazards., 27, pp. 133-169 (2002).

8. Bagheripour, M.H. and Marandi. S.M. "A Numerical model for unbounded soil domain in earthquake SSI analysis using periodic infinite elements", Int. J. Civ. Eng., 3, pp. 96-111 (2005).

9. Gatmiri, B., Arson, C. and Nguyen, K. "Seismic site effects by an optimized 2D BE/FE method I. Theory, numerical optimization and application to topographical irregularities", Soil Dyn. Earthquake Eng., 28, pp. 632-645 (2008).

10. Bagheripour, M.H., Rahgozar, R. and Malekinejad, M. "Efficient analysis of SSI problems using infinite elements and wavelet theory", Geomech. Eng., 2(4), pp. 229-252 (2010).

11. Nimtaj, A. and Bagheripour, M.H. "Non-linear seismic response analysis of the layered soil deposit using hybrid frequency-time domain (HFTD) approach", European Journal of Environmental and Civil Engineering, 17, pp. 1039-1056 (2013).

12. Kara, H.F. and Trifunac, M.D. "Two-dimensional earthquake vibrations in sedimentary basins-SH waves", Soil Dyn. Earthquake Eng., 63, pp. 69-82 (2014).

13. Ghaemian, M. and Sohrabi-Gilani, M. "Seismic responses of arch dams due to non-uniform ground motions", Scientia Iranica, 19, pp. 1431-1436 (2012).

14. Khanbabazadeh, H. and Iyisan, R. "A numerical study on the 2D behavior of the single and layered clayey basins", Bull Earthquake Eng., 12, pp. 1515-1536 (2014).

15. Lermo, J. and Chavez-Garcia, F.J. "Site effect evaluation using spectral ratios with only one station", Bull. Seismol. Soc. Am., 83, pp. 1574-1594 (1993).

16. LeBrun, B., Hatzfeld, D., Bard, P. and Bouchon, M. "Experimental study of the ground motion on a large scale topographic hill at Kitherion (Greece)", J. Seismolog., 3, pp. 1-15 (1999).

17. Fu, L.Y. "Rough surface scattering: comparison of various approximation theories for 2D SH waves", Bull. Seismol. Soc. Am., 95, pp. 646-663 (2005).

18. Bouckovalas, G.D. and Papadimitriou, A.G. "Numerical evaluation of slope topography effects on seismic ground motion", Soil Dyn. Earthquake Eng., 25, pp. 547-558 (2005).

19. Kamalian, M., Jafari, M.K., Sohrabi-Bidar, A., Razmkhah, A. and Gatmiri, B. "Time-domain twodimensional site response analysis of non-homogeneous topographic structures by a hybrid BE/FE method", Soil Dyn. Earthquake Eng., 26, pp. 753-765 (2006).

20. Asgari, A. and Bagheripour, M.H. "Earthquake response analysis of soil layers using HFTD approach", The GeoShanghai 2010 International Conference, Shanghai, China (2010).

21. Di Fiore, V. "Seismic site amplification induced by topographic irregularity: Results of a numerical analysis on 2D synthetic models", Eng. Geol., 114, pp. 109-115 (2010).

22. Bazrafshan Moghaddam, A. and Bagheripour, M.H. "Ground response analysis using non-recursive matrix implementation of hybrid frequency-time domain (HFTD) approach", Scientia Iranica, 18, pp. 1188- 1197 (2011).

23. Tripe, R., Kontoe, S. and Wong, T. "Slope topography effects on ground motion in the presence of deep soil layers", Soil Dyn. Earthquake Eng., 50, pp. 72-84 (2013).

24. Zhao, C. and Valliappan, S. "Incident P and SV wave scattering effects under different canyon topographic and geological conditions", Int. J. Numer. Anal. Methods Geomech., 17, pp. 73-94 (1993).

25. Yoshida, N., Seismic Ground Response Analysis, Springer (2015).

26. Desai, C.S. and Kundu, T. "Introductory finite element method", CRC Press (2001).

27. Zhao, C., Zhang, C. and Zhang, G. "Analysis of 3-D foundation wave problems by mapped dynamic infinite elements", Science In China Series A-Mathematics Physics Astronomy, 32, pp. 479-491 (1989).

28. Brinkgreve, R., Plaxis: Finite Element Code for Soil and Rock Analyses: 2D-Version 8:[user's guide], Balkema (2002).

29. Lysmer, J. and Kuhlemeyer, R.L. "Finite dynamic model for infinite media", Journal of Engineering Mechanics Division, 95, pp. 859-878 (1969).

30. Weihua, L. and Chenggang, Z. "Scattering of plane SV waves by cylindrical canyons in saturated porous medium", Soil Dyn. Earthquake Eng., 25, pp. 981-995 (2005).

31. Bouchon, M. "Effect of topography on surface motion", Bull. Seismol. Soc. Am., 63, pp. 615-632 (1973).

32. Pagliaroli, A., Lanzo, G. and D'Elia, B. "Numerical evaluation of topographic effects at the Nicastro ridge in Southern Italy", J. Earthquake Eng., 15, pp. 404-432 (2011).

Transactions on Civil Engineering (A)

January and February 2017Pages 110-120