Earthquakes can cause a lot of geotechnical damage, including the phenomenon of liquefaction (Ishihara 1996; Sonmez and Ulusay 2008; Zhuang et al. 2016). Liquefaction occurs when saturated soil loses strength due to the earthquake loading and increased pore water pressure (Papathanassiou et al. 2011; Javdanian and Hoseini 2016; Mehrzad et al. 2016; Javdanian and Seidali 2016). Traumatic experiences from this phenomenon has stimulated researchers to use various methods to estimate the potential for liquefaction (e.g., Kaveh et al. 2016; Rahman and Siddiqua 2017). Models based on strain energy (W) absorption in soils are amongst the newest methods for estimation of liquefaction potential (Baziar et al. 2011; Jafarian et al. 2012). In the strain energy method, liquefaction within the critical state framework occurs with the arrival of a seismic wave of energy exceeding a certain threshold that represents the liquefaction potential of the soil deposit in terms of energy. The stress-based method (Youd et al. 2001; Seed and Idriss 1971; Whitman 1971) and strain-based method (Dobry et al. 1982) are common techniques for the estimation of liquefaction potential (Baziar and Jafarian 2007). In these methods, the generation of pore water pressure and subsequently liquefaction incidence is correlated with the amount of seismic shear stresses and shear strains in the soil, respectively. In fact, the energy-based method relates the incidence of liquefaction to the levels of stress and strain induced by cyclic loading. Therefore, the strain energy method is physically more realistic than these other two techniques (Kokusho and Mimori 2015). The quantity of energy needed for the initiation of liquefaction is obtained from experimental results or field data. The area inside the hysteresis loop (the shear stress-shear strain curve) indicates the amount of dissipated strain energy at the unit volume of the soil mass (Figueroa et al. 1994; Jafarian et al. 2011). The total amount of this strain energy needed for the occurrence of liquefaction is equal to the amount of strain energy needed for initiation of this phenomenon. The existence of more accurate models for estimation of this amount of strain energy reduces uncertainty in the estimation of liquefaction potential.