1. Seed, H.B. and Idriss, I.M Analysis of soil liquefaction: Niigata earthquake", Journal of the Soil Mechanics and Foundations Division, 93(3), pp. 83{ 108 (1967) 2. Youd, T.L. Liquefaction-induced damage to bridges", Report U.S Transportation Research Record, 1411, pp. 35{41 (1993). 3. Elgamal, A.W., Zeghal, M., and Parra, E. Liquefaction of reclaimed island in Kobe, Japan", Journal of Geotechnical Engineering, 122(1), pp. 39{49 (1996). 4. National Research Council (US). Committee on Earthquake Engineering. Liquefaction of soils during earthquakes", 1, pp. 4{6 (1985). 5. Nguyen, T.V., Rayamajhi, D., Boulanger, R.W., Ashford, S.A., Lu, J., Elgamal, A., and Shao, L. Design of DSM grids for liquefaction remediation", J. Geotech. Geoenviron. Eng., 139(11) pp. 1923{1933 (2013). 6. Namikawa, T., Koseki, J., and Suzuki, Y. Finite element analysis of lattice-shaped ground improvement by cement mixing for liquefaction mitigation", Soils and Found, 47(3), pp. 559{576 (2007). 7. Derakhshani, A., Takahashi, N., Bahmanpour, A. Yamada, S., and Towhata, I. Experimental study on e_ects of underground columnar improvement on seismic behavior of quay wall subjected to liquefaction", Proc. of 2011Pan-Am CGS Geotechnical Conference, Toronto, Canada (2011). 8. O'Rourke, T.D. and Goh, S.H. Reduction of liquefaction hazards by deep soil mixing", NCEER/INCEDE Workshop, MCEER, Univ. at Bu_alo, State Univ. of New York, Bu_alo, NY (1997). 9. Elgamal, A., Lu, J., and Forcellini, D. Mitigation of liquefaction-induced lateral deformation in a sloping stratum: Three-dimensional numerical simulation", J. Geotech. Geoenvir. Eng., ASCE, 135(11), pp. 1672{ 1682 (2009). 10. Asgari, A., Oliaei, M., and Bagheri, M. Numerical simulation of improvement of a lique_able soil layer using stone column and pile-pinning techniques", Soil Dyn. Earthquake. Eng., 51, pp. 77{ 96 (2013). 11. Green, R.A., Olgun, C.G, and Wissmann, K.J. Shear stress redistribution as a mechanism to mitigate the risk of liquefaction", In Geotechnical Earthquake Engineering and Soil Dynamics IV, pp. 1{10 (2008). 12. Olgun, C.G. and Martin, J.R. Numerical modeling of the seismic response of Columnar reinforced ground", In Geotechnical Earthquake Engineering and Soil Dynamics IV, pp. 1{11 (2008). 13. Rayamajhi, D., Nguyen, T.V., Ashford, S.A., Boulanger, R.W., Lu, J., Elgamal, A., and Shao, L. Numerical study of shear stress distribution for discrete columns in lique_able soils", J. Geotech. Geoenviron. Eng, 140(3), 04013034{1 (2013). 14. Baez, J.I. A design model for the reduction of soil liquefaction by vibro-stone columns", PhD Thesis, Univ. of Southern California, Los Angeles, CA (1995). 15. Durguno_glu, H.T. Utilization of high modulus columns in foundation engineering under seismic loadings", US 8th National Conference on Earthquake Engineering, San Francisco, CA., USA (2006). 16. Gueguin, M., Buhan, P., and Hassen G. A homogenization approach for evaluating the longitudinal shear sti_ness of reinforced soils: column versus cross trench con_guration", Int. J. Numer. Anal. Meth. Geomech, 37, pp. 3150{3172 (2013). 17. Rayamajhi, D., Nguyen, T.V., Ashford, S.A., Boulanger, R.W., Lu, J., Elgamal, A., and Shao, L. Numerical study of shear stress distribution for discrete columns in lique_able soils", J. Geotech. Geoenviron. Eng., 140(3), 04013034{1 (2013). 18. Rayamajhi, D. Shear reinforcement e_ects of discrete columns in lique_able soils displacements", PhD Thesis, Oregon: Oregon State University (2014). 19. Iai, S. and Sugano, T. Soil{structure interaction studies through shaking-table tests", Proceedings of 2nd International Conference on Earthquake Geotechnical Engineering, Lisbon, pp. 927{940 (1999). 2208 H. Dehghan Khalili et al./Scientia Iranica, Transactions A: Civil Engineering 27 (2020) 2198{2208 20. Sadrekarimi, A. and Ghalandarzadeh, A. Evaluation of gravel drains and compacted sand piles in mitigating liquefaction", Proceedings of the ICE{Ground Improvement, 9(3) pp. 91{104 (2005). 21. Shibata, T., Oka, F., and Ozawa, Y. Characteristics of ground deformation due to liquefaction", Soils and Foundations, 36, pp. 65{79 (1996). 22. Yoshimi, Y. and Kuwabara, F. E_ects of subsurface liquefaction on the strength of surface soil", Soils and Foundations, 13(2), pp. 67{81 (1973). 23. Whitman, R.V. and Lambe, P.C. Earthquake like shaking of a structure founded on saturated sand", Proceedings of the International Conference on Geotechnical Centrifuge Modelling, Paris, pp. 529{538 (1998). 24. Adalier, K., Elgamal, A.W., and Martin, G.R. Foundation liquefaction countermeasures for earth embankments", Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 124(6), pp. 500{517 (1998). 25. Adalier, K., Elgamal, A.W., Meneses, J., and Baez, J.I. Stone columns as liquefaction countermeasure in non-plastic silty soils", Soil Dynamics and Earthquake Engineering, 23(7), pp. 571{584 (2003). 26. Koga, Y. and Matsuo, O. Shaking table tests of embankments resting on lique_able sandy ground", Soils and Foundations Journal, 30(4), pp. 162{174 (1990). 27. Brandenberg, S.J., Wilson, D.W., and Rashid, M.M. Weighted residual numerical di_erentiation algorithm applied to experimental bending moment data", J. of Geotech. and Geoenviron. Eng., 136(6), pp. 854{863 (2009). 28. Kamai, R. and Boulanger, R.W. Characterizing localization processes during liquefaction using inverse analyses of instrumentation arrays", Meso-Scale Shear Physics in Earthquake and Landslide Mechanics, I. Vardoulakis, pp. 219{238 (2010).
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